id	sid	tid	token	lemma	pos
ap-5050	1	1	acta	acta	PROPN
ap-5050	1	2	polytechnica	polytechnica	PROPN
ap-5050	1	3	doi:10.14311	doi:10.14311	PROPN
ap-5050	1	4	/	/	SYM
ap-5050	1	5	ap.2019.59.0067	ap.2019.59.0067	PROPN
ap-5050	1	6	acta	acta	PROPN
ap-5050	1	7	polytechnica	polytechnica	PROPN
ap-5050	1	8	59(1):67–76	59(1):67–76	NUM
ap-5050	1	9	,	,	PUNCT
ap-5050	1	10	2019	2019	NUM
ap-5050	1	11	©	©	PROPN
ap-5050	1	12	czech	czech	PROPN
ap-5050	1	13	technical	technical	PROPN
ap-5050	1	14	university	university	PROPN
ap-5050	1	15	in	in	ADP
ap-5050	1	16	prague	prague	PROPN
ap-5050	1	17	,	,	PUNCT
ap-5050	1	18	2019	2019	NUM
ap-5050	1	19	available	available	ADJ
ap-5050	1	20	online	online	ADV
ap-5050	1	21	at	at	ADP
ap-5050	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-5050	1	23	particle	particle	NOUN
ap-5050	1	24	motion	motion	NOUN
ap-5050	1	25	over	over	ADP
ap-5050	1	26	the	the	DET
ap-5050	1	27	edge	edge	NOUN
ap-5050	1	28	of	of	ADP
ap-5050	1	29	an	an	DET
ap-5050	1	30	inclined	inclined	ADJ
ap-5050	1	31	plane	plane	NOUN
ap-5050	1	32	that	that	PRON
ap-5050	1	33	performs	perform	VERB
ap-5050	1	34	axial	axial	ADJ
ap-5050	1	35	movement	movement	NOUN
ap-5050	1	36	in	in	ADP
ap-5050	1	37	a	a	DET
ap-5050	1	38	vertical	vertical	ADJ
ap-5050	1	39	limiting	limit	VERB
ap-5050	1	40	cylinder	cylinder	NOUN
ap-5050	1	41	serhii	serhii	PROPN
ap-5050	1	42	f.	f.	PROPN
ap-5050	1	43	pylypakaa	pylypakaa	PROPN
ap-5050	1	44	,	,	PUNCT
ap-5050	1	45	mykola	mykola	PROPN
ap-5050	1	46	b.	b.	PROPN
ap-5050	1	47	klendiib	klendiib	PROPN
ap-5050	1	48	,	,	PUNCT
ap-5050	1	49	viktor	viktor	NOUN
ap-5050	1	50	m.	m.	NOUN
ap-5050	1	51	nesvidomina	nesvidomina	PROPN
ap-5050	1	52	,	,	PUNCT
ap-5050	1	53	viktor	viktor	NOUN
ap-5050	1	54	i.	i.	NOUN
ap-5050	1	55	trokhaniaka,∗	trokhaniaka,∗	PART
ap-5050	1	56	a	a	DET
ap-5050	1	57	national	national	ADJ
ap-5050	1	58	university	university	NOUN
ap-5050	1	59	of	of	ADP
ap-5050	1	60	life	life	NOUN
ap-5050	1	61	and	and	CCONJ
ap-5050	1	62	environmental	environmental	ADJ
ap-5050	1	63	sciences	science	NOUN
ap-5050	1	64	of	of	ADP
ap-5050	1	65	ukraine	ukraine	NOUN
ap-5050	1	66	,	,	PUNCT
ap-5050	1	67	heroiv	heroiv	VERB
ap-5050	1	68	oborony	oborony	NOUN
ap-5050	1	69	str	str	PROPN
ap-5050	1	70	.	.	PUNCT
ap-5050	1	71	,	,	PUNCT
ap-5050	1	72	15	15	NUM
ap-5050	1	73	,	,	PUNCT
ap-5050	1	74	kyiv	kyiv	ADJ
ap-5050	1	75	,	,	PUNCT
ap-5050	1	76	ukraine	ukraine	NOUN
ap-5050	1	77	.	.	PUNCT
ap-5050	2	1	b	b	PROPN
ap-5050	2	2	separated	separate	VERB
ap-5050	2	3	subdivision	subdivision	NOUN
ap-5050	2	4	of	of	ADP
ap-5050	2	5	national	national	ADJ
ap-5050	2	6	university	university	PROPN
ap-5050	2	7	of	of	ADP
ap-5050	2	8	life	life	NOUN
ap-5050	2	9	and	and	CCONJ
ap-5050	2	10	environmental	environmental	ADJ
ap-5050	2	11	sciences	science	NOUN
ap-5050	2	12	of	of	ADP
ap-5050	2	13	ukraine	ukraine	PROPN
ap-5050	2	14	berezhany	berezhany	PROPN
ap-5050	2	15	agrotechnical	agrotechnical	PROPN
ap-5050	2	16	institute	institute	PROPN
ap-5050	2	17	,	,	PUNCT
ap-5050	2	18	akademichna	akademichna	VERB
ap-5050	2	19	str	str	PRON
ap-5050	2	20	.	.	PUNCT
ap-5050	2	21	,	,	PUNCT
ap-5050	2	22	20	20	NUM
ap-5050	2	23	,	,	PUNCT
ap-5050	2	24	berezhany	berezhany	ADJ
ap-5050	2	25	,	,	PUNCT
ap-5050	2	26	ukraine	ukraine	NOUN
ap-5050	2	27	.	.	PUNCT
ap-5050	3	1	∗	∗	NOUN
ap-5050	3	2	corresponding	correspond	VERB
ap-5050	3	3	author	author	NOUN
ap-5050	3	4	:	:	PUNCT
ap-5050	3	5	trohaniak.v@gmail.com	trohaniak.v@gmail.com	X
ap-5050	3	6	abstract	abstract	ADJ
ap-5050	3	7	.	.	PUNCT
ap-5050	4	1	differential	differential	ADJ
ap-5050	4	2	equations	equation	NOUN
ap-5050	4	3	of	of	ADP
ap-5050	4	4	a	a	DET
ap-5050	4	5	relative	relative	ADJ
ap-5050	4	6	material	material	NOUN
ap-5050	4	7	particle	particle	NOUN
ap-5050	4	8	motion	motion	NOUN
ap-5050	4	9	over	over	ADP
ap-5050	4	10	the	the	DET
ap-5050	4	11	edge	edge	NOUN
ap-5050	4	12	of	of	ADP
ap-5050	4	13	an	an	DET
ap-5050	4	14	inclined	inclined	ADJ
ap-5050	4	15	flat	flat	ADJ
ap-5050	4	16	ellipse	ellipse	NOUN
ap-5050	4	17	that	that	PRON
ap-5050	4	18	rotates	rotate	VERB
ap-5050	4	19	around	around	ADP
ap-5050	4	20	the	the	DET
ap-5050	4	21	axis	axis	NOUN
ap-5050	4	22	of	of	ADP
ap-5050	4	23	a	a	DET
ap-5050	4	24	vertical	vertical	ADJ
ap-5050	4	25	limiting	limit	VERB
ap-5050	4	26	cylinder	cylinder	NOUN
ap-5050	4	27	have	have	AUX
ap-5050	4	28	been	be	AUX
ap-5050	4	29	deduced	deduce	VERB
ap-5050	4	30	.	.	PUNCT
ap-5050	5	1	the	the	DET
ap-5050	5	2	position	position	NOUN
ap-5050	5	3	of	of	ADP
ap-5050	5	4	a	a	DET
ap-5050	5	5	plane	plane	NOUN
ap-5050	5	6	relative	relative	ADJ
ap-5050	5	7	to	to	ADP
ap-5050	5	8	the	the	DET
ap-5050	5	9	axis	axis	NOUN
ap-5050	5	10	of	of	ADP
ap-5050	5	11	the	the	DET
ap-5050	5	12	rotation	rotation	NOUN
ap-5050	5	13	is	be	AUX
ap-5050	5	14	set	set	VERB
ap-5050	5	15	by	by	ADP
ap-5050	5	16	the	the	DET
ap-5050	5	17	angle	angle	NOUN
ap-5050	5	18	ranging	range	VERB
ap-5050	5	19	from	from	ADP
ap-5050	5	20	zero	zero	NUM
ap-5050	5	21	to	to	ADP
ap-5050	5	22	ninety	ninety	NUM
ap-5050	5	23	degrees	degree	NOUN
ap-5050	5	24	in	in	ADP
ap-5050	5	25	its	its	PRON
ap-5050	5	26	value	value	NOUN
ap-5050	5	27	.	.	PUNCT
ap-5050	6	1	if	if	SCONJ
ap-5050	6	2	the	the	DET
ap-5050	6	3	angle	angle	NOUN
ap-5050	6	4	is	be	AUX
ap-5050	6	5	equal	equal	ADJ
ap-5050	6	6	to	to	ADP
ap-5050	6	7	zero	zero	NUM
ap-5050	6	8	,	,	PUNCT
ap-5050	6	9	the	the	DET
ap-5050	6	10	plane	plane	NOUN
ap-5050	6	11	is	be	AUX
ap-5050	6	12	perpendicular	perpendicular	ADJ
ap-5050	6	13	to	to	ADP
ap-5050	6	14	the	the	DET
ap-5050	6	15	axis	axis	NOUN
ap-5050	6	16	of	of	ADP
ap-5050	6	17	rotation	rotation	NOUN
ap-5050	6	18	and	and	CCONJ
ap-5050	6	19	if	if	SCONJ
ap-5050	6	20	the	the	DET
ap-5050	6	21	angle	angle	NOUN
ap-5050	6	22	is	be	AUX
ap-5050	6	23	equal	equal	ADJ
ap-5050	6	24	to	to	ADP
ap-5050	6	25	ninety	ninety	NUM
ap-5050	6	26	degrees	degree	NOUN
ap-5050	6	27	,	,	PUNCT
ap-5050	6	28	it	it	PRON
ap-5050	6	29	passes	pass	VERB
ap-5050	6	30	through	through	ADP
ap-5050	6	31	the	the	DET
ap-5050	6	32	axis	axis	NOUN
ap-5050	6	33	of	of	ADP
ap-5050	6	34	rotation	rotation	NOUN
ap-5050	6	35	.	.	PUNCT
ap-5050	7	1	the	the	DET
ap-5050	7	2	equations	equation	NOUN
ap-5050	7	3	have	have	AUX
ap-5050	7	4	been	be	AUX
ap-5050	7	5	solved	solve	VERB
ap-5050	7	6	using	use	VERB
ap-5050	7	7	numerical	numerical	ADJ
ap-5050	7	8	methods	method	NOUN
ap-5050	7	9	.	.	PUNCT
ap-5050	8	1	analytical	analytical	ADJ
ap-5050	8	2	solution	solution	NOUN
ap-5050	8	3	has	have	AUX
ap-5050	8	4	been	be	AUX
ap-5050	8	5	found	find	VERB
ap-5050	8	6	for	for	ADP
ap-5050	8	7	certain	certain	ADJ
ap-5050	8	8	angles	angle	NOUN
ap-5050	8	9	.	.	PUNCT
ap-5050	9	1	the	the	DET
ap-5050	9	2	aim	aim	NOUN
ap-5050	9	3	of	of	ADP
ap-5050	9	4	the	the	DET
ap-5050	9	5	research	research	NOUN
ap-5050	9	6	is	be	AUX
ap-5050	9	7	to	to	PART
ap-5050	9	8	investigate	investigate	VERB
ap-5050	9	9	the	the	DET
ap-5050	9	10	transportability	transportability	NOUN
ap-5050	9	11	of	of	ADP
ap-5050	9	12	a	a	DET
ap-5050	9	13	technological	technological	ADJ
ap-5050	9	14	material	material	NOUN
ap-5050	9	15	in	in	ADP
ap-5050	9	16	a	a	DET
ap-5050	9	17	vertical	vertical	ADJ
ap-5050	9	18	direction	direction	NOUN
ap-5050	9	19	by	by	ADP
ap-5050	9	20	a	a	DET
ap-5050	9	21	cascade	cascade	NOUN
ap-5050	9	22	operating	operating	NOUN
ap-5050	9	23	element	element	NOUN
ap-5050	9	24	that	that	PRON
ap-5050	9	25	rotates	rotate	VERB
ap-5050	9	26	in	in	ADP
ap-5050	9	27	a	a	DET
ap-5050	9	28	cylindrical	cylindrical	ADJ
ap-5050	9	29	cover	cover	NOUN
ap-5050	9	30	.	.	PUNCT
ap-5050	10	1	the	the	DET
ap-5050	10	2	working	work	VERB
ap-5050	10	3	part	part	NOUN
ap-5050	10	4	of	of	ADP
ap-5050	10	5	the	the	DET
ap-5050	10	6	operating	operating	NOUN
ap-5050	10	7	element	element	NOUN
ap-5050	10	8	is	be	AUX
ap-5050	10	9	an	an	DET
ap-5050	10	10	inclined	inclined	ADJ
ap-5050	10	11	rigid	rigid	ADJ
ap-5050	10	12	plane	plane	NOUN
ap-5050	10	13	,	,	PUNCT
ap-5050	10	14	which	which	PRON
ap-5050	10	15	is	be	AUX
ap-5050	10	16	limited	limit	VERB
ap-5050	10	17	by	by	ADP
ap-5050	10	18	an	an	DET
ap-5050	10	19	ellipse	ellipse	NOUN
ap-5050	10	20	—	—	PUNCT
ap-5050	10	21	the	the	DET
ap-5050	10	22	line	line	NOUN
ap-5050	10	23	of	of	ADP
ap-5050	10	24	its	its	PRON
ap-5050	10	25	contact	contact	NOUN
ap-5050	10	26	with	with	ADP
ap-5050	10	27	a	a	DET
ap-5050	10	28	cover	cover	NOUN
ap-5050	10	29	.	.	PUNCT
ap-5050	11	1	the	the	DET
ap-5050	11	2	objective	objective	NOUN
ap-5050	11	3	of	of	ADP
ap-5050	11	4	the	the	DET
ap-5050	11	5	research	research	NOUN
ap-5050	11	6	is	be	AUX
ap-5050	11	7	to	to	PART
ap-5050	11	8	analytically	analytically	ADV
ap-5050	11	9	describe	describe	VERB
ap-5050	11	10	the	the	DET
ap-5050	11	11	movement	movement	NOUN
ap-5050	11	12	of	of	ADP
ap-5050	11	13	a	a	DET
ap-5050	11	14	single	single	ADJ
ap-5050	11	15	particle	particle	NOUN
ap-5050	11	16	of	of	ADP
ap-5050	11	17	the	the	DET
ap-5050	11	18	technological	technological	ADJ
ap-5050	11	19	material	material	NOUN
ap-5050	11	20	on	on	ADP
ap-5050	11	21	two	two	NUM
ap-5050	11	22	surfaces	surface	NOUN
ap-5050	11	23	,	,	PUNCT
ap-5050	11	24	namely	namely	ADV
ap-5050	11	25	,	,	PUNCT
ap-5050	11	26	an	an	DET
ap-5050	11	27	inclined	inclined	ADJ
ap-5050	11	28	plane	plane	NOUN
ap-5050	11	29	and	and	CCONJ
ap-5050	11	30	a	a	DET
ap-5050	11	31	vertical	vertical	ADJ
ap-5050	11	32	cover	cover	NOUN
ap-5050	11	33	.	.	PUNCT
ap-5050	12	1	the	the	DET
ap-5050	12	2	research	research	NOUN
ap-5050	12	3	methodology	methodology	NOUN
ap-5050	12	4	is	be	AUX
ap-5050	12	5	based	base	VERB
ap-5050	12	6	on	on	ADP
ap-5050	12	7	the	the	DET
ap-5050	12	8	methods	method	NOUN
ap-5050	12	9	of	of	ADP
ap-5050	12	10	differential	differential	ADJ
ap-5050	12	11	geometry	geometry	NOUN
ap-5050	12	12	and	and	CCONJ
ap-5050	12	13	the	the	DET
ap-5050	12	14	theory	theory	NOUN
ap-5050	12	15	of	of	ADP
ap-5050	12	16	surfaces	surface	NOUN
ap-5050	12	17	,	,	PUNCT
ap-5050	12	18	theoretical	theoretical	ADJ
ap-5050	12	19	mechanics	mechanic	NOUN
ap-5050	12	20	and	and	CCONJ
ap-5050	12	21	numerical	numerical	ADJ
ap-5050	12	22	methods	method	NOUN
ap-5050	12	23	of	of	ADP
ap-5050	12	24	solving	solve	VERB
ap-5050	12	25	differential	differential	ADJ
ap-5050	12	26	equations	equation	NOUN
ap-5050	12	27	.	.	PUNCT
ap-5050	13	1	the	the	DET
ap-5050	13	2	paper	paper	NOUN
ap-5050	13	3	presents	present	VERB
ap-5050	13	4	a	a	DET
ap-5050	13	5	first	first	ADJ
ap-5050	13	6	developed	develop	VERB
ap-5050	13	7	analytical	analytical	ADJ
ap-5050	13	8	description	description	NOUN
ap-5050	13	9	of	of	ADP
ap-5050	13	10	the	the	DET
ap-5050	13	11	relative	relative	ADJ
ap-5050	13	12	particle	particle	NOUN
ap-5050	13	13	motion	motion	NOUN
ap-5050	13	14	in	in	ADP
ap-5050	13	15	an	an	DET
ap-5050	13	16	ellipse	ellipse	NOUN
ap-5050	13	17	—	—	PUNCT
ap-5050	13	18	a	a	DET
ap-5050	13	19	contact	contact	NOUN
ap-5050	13	20	line	line	NOUN
ap-5050	13	21	of	of	ADP
ap-5050	13	22	an	an	DET
ap-5050	13	23	inclined	inclined	ADJ
ap-5050	13	24	plane	plane	NOUN
ap-5050	13	25	and	and	CCONJ
ap-5050	13	26	a	a	DET
ap-5050	13	27	limiting	limit	VERB
ap-5050	13	28	vertical	vertical	ADJ
ap-5050	13	29	cylinder	cylinder	NOUN
ap-5050	13	30	,	,	PUNCT
ap-5050	13	31	in	in	ADP
ap-5050	13	32	which	which	PRON
ap-5050	13	33	the	the	DET
ap-5050	13	34	inclined	inclined	ADJ
ap-5050	13	35	plane	plane	NOUN
ap-5050	13	36	rotates	rotate	NOUN
ap-5050	13	37	.	.	PUNCT
ap-5050	14	1	the	the	DET
ap-5050	14	2	kinematic	kinematic	ADJ
ap-5050	14	3	characteristics	characteristic	NOUN
ap-5050	14	4	of	of	ADP
ap-5050	14	5	such	such	ADJ
ap-5050	14	6	motion	motion	NOUN
ap-5050	14	7	have	have	AUX
ap-5050	14	8	been	be	AUX
ap-5050	14	9	determined	determine	VERB
ap-5050	14	10	.	.	PUNCT
ap-5050	15	1	keywords	keyword	NOUN
ap-5050	15	2	:	:	PUNCT
ap-5050	15	3	inclined	inclined	ADJ
ap-5050	15	4	cylinder	cylinder	NOUN
ap-5050	15	5	;	;	PUNCT
ap-5050	15	6	oscillating	oscillate	VERB
ap-5050	15	7	motion	motion	NOUN
ap-5050	15	8	;	;	PUNCT
ap-5050	15	9	vertical	vertical	ADJ
ap-5050	15	10	plane	plane	NOUN
ap-5050	15	11	;	;	PUNCT
ap-5050	15	12	particle	particle	NOUN
ap-5050	15	13	;	;	PUNCT
ap-5050	15	14	differential	differential	ADJ
ap-5050	15	15	equations	equation	NOUN
ap-5050	15	16	;	;	PUNCT
ap-5050	15	17	kinematic	kinematic	ADJ
ap-5050	15	18	parameters	parameter	NOUN
ap-5050	15	19	.	.	PUNCT
ap-5050	16	1	1	1	X
ap-5050	16	2	.	.	X
ap-5050	16	3	introduction	introduction	NOUN
ap-5050	16	4	a	a	DET
ap-5050	16	5	particle	particle	NOUN
ap-5050	16	6	motion	motion	NOUN
ap-5050	16	7	over	over	ADP
ap-5050	16	8	a	a	DET
ap-5050	16	9	horizontal	horizontal	ADJ
ap-5050	16	10	plane	plane	NOUN
ap-5050	16	11	in	in	ADP
ap-5050	16	12	the	the	DET
ap-5050	16	13	form	form	NOUN
ap-5050	16	14	of	of	ADP
ap-5050	16	15	a	a	DET
ap-5050	16	16	rigid	rigid	ADJ
ap-5050	16	17	disk	disk	NOUN
ap-5050	16	18	,	,	PUNCT
ap-5050	16	19	which	which	PRON
ap-5050	16	20	rotates	rotate	VERB
ap-5050	16	21	around	around	ADP
ap-5050	16	22	a	a	DET
ap-5050	16	23	vertical	vertical	ADJ
ap-5050	16	24	axis	axis	NOUN
ap-5050	16	25	,	,	PUNCT
ap-5050	16	26	is	be	AUX
ap-5050	16	27	the	the	DET
ap-5050	16	28	most	most	ADV
ap-5050	16	29	investigated	investigate	VERB
ap-5050	16	30	one	one	NUM
ap-5050	16	31	.	.	PUNCT
ap-5050	17	1	such	such	ADJ
ap-5050	17	2	disks	disk	NOUN
ap-5050	17	3	with	with	ADP
ap-5050	17	4	blades	blade	NOUN
ap-5050	17	5	attached	attach	VERB
ap-5050	17	6	to	to	ADP
ap-5050	17	7	them	they	PRON
ap-5050	17	8	are	be	AUX
ap-5050	17	9	used	use	VERB
ap-5050	17	10	in	in	ADP
ap-5050	17	11	scattering	scatter	VERB
ap-5050	17	12	centrifugal	centrifugal	ADJ
ap-5050	17	13	apparatuses	apparatus	NOUN
ap-5050	17	14	.	.	PUNCT
ap-5050	18	1	operating	operate	VERB
ap-5050	18	2	elements	element	NOUN
ap-5050	18	3	with	with	ADP
ap-5050	18	4	a	a	DET
ap-5050	18	5	horizontal	horizontal	ADJ
ap-5050	18	6	axis	axis	NOUN
ap-5050	18	7	of	of	ADP
ap-5050	18	8	rotation	rotation	NOUN
ap-5050	18	9	in	in	ADP
ap-5050	18	10	the	the	DET
ap-5050	18	11	form	form	NOUN
ap-5050	18	12	of	of	ADP
ap-5050	18	13	a	a	DET
ap-5050	18	14	shaft	shaft	NOUN
ap-5050	18	15	with	with	ADP
ap-5050	18	16	flat	flat	ADJ
ap-5050	18	17	blades	blade	NOUN
ap-5050	18	18	attached	attach	VERB
ap-5050	18	19	to	to	ADP
ap-5050	18	20	it	it	PRON
ap-5050	18	21	are	be	AUX
ap-5050	18	22	used	use	VERB
ap-5050	18	23	for	for	ADP
ap-5050	18	24	scattering	scatter	VERB
ap-5050	18	25	organic	organic	ADJ
ap-5050	18	26	fertilizers	fertilizer	NOUN
ap-5050	18	27	.	.	PUNCT
ap-5050	19	1	in	in	ADP
ap-5050	19	2	addition	addition	NOUN
ap-5050	19	3	,	,	PUNCT
ap-5050	19	4	they	they	PRON
ap-5050	19	5	can	can	AUX
ap-5050	19	6	be	be	AUX
ap-5050	19	7	used	use	VERB
ap-5050	19	8	for	for	ADP
ap-5050	19	9	mixing	mix	VERB
ap-5050	19	10	particles	particle	NOUN
ap-5050	19	11	and	and	CCONJ
ap-5050	19	12	their	their	PRON
ap-5050	19	13	scattering	scattering	NOUN
ap-5050	19	14	in	in	ADP
ap-5050	19	15	a	a	DET
ap-5050	19	16	centrifugal	centrifugal	ADJ
ap-5050	19	17	direction	direction	NOUN
ap-5050	19	18	.	.	PUNCT
ap-5050	20	1	the	the	DET
ap-5050	20	2	investigation	investigation	NOUN
ap-5050	20	3	of	of	ADP
ap-5050	20	4	the	the	DET
ap-5050	20	5	patterns	pattern	NOUN
ap-5050	20	6	of	of	ADP
ap-5050	20	7	a	a	DET
ap-5050	20	8	material	material	NOUN
ap-5050	20	9	particle	particle	NOUN
ap-5050	20	10	motion	motion	NOUN
ap-5050	20	11	over	over	ADP
ap-5050	20	12	the	the	DET
ap-5050	20	13	edge	edge	NOUN
ap-5050	20	14	of	of	ADP
ap-5050	20	15	an	an	DET
ap-5050	20	16	inclined	inclined	ADJ
ap-5050	20	17	flat	flat	ADJ
ap-5050	20	18	ellipse	ellipse	NOUN
ap-5050	20	19	that	that	PRON
ap-5050	20	20	rotates	rotate	VERB
ap-5050	20	21	around	around	ADP
ap-5050	20	22	the	the	DET
ap-5050	20	23	axis	axis	NOUN
ap-5050	20	24	of	of	ADP
ap-5050	20	25	a	a	DET
ap-5050	20	26	vertical	vertical	ADJ
ap-5050	20	27	limiting	limit	VERB
ap-5050	20	28	cylinder	cylinder	NOUN
ap-5050	20	29	is	be	AUX
ap-5050	20	30	interesting	interesting	ADJ
ap-5050	20	31	in	in	ADP
ap-5050	20	32	terms	term	NOUN
ap-5050	20	33	of	of	ADP
ap-5050	20	34	theory	theory	NOUN
ap-5050	20	35	and	and	CCONJ
ap-5050	20	36	practical	practical	ADJ
ap-5050	20	37	use	use	NOUN
ap-5050	20	38	.	.	PUNCT
ap-5050	21	1	major	major	ADJ
ap-5050	21	2	works	work	NOUN
ap-5050	21	3	[	[	X
ap-5050	21	4	1	1	NUM
ap-5050	21	5	,	,	PUNCT
ap-5050	21	6	2	2	NUM
ap-5050	21	7	]	]	PUNCT
ap-5050	21	8	consider	consider	VERB
ap-5050	21	9	the	the	DET
ap-5050	21	10	compound	compound	NOUN
ap-5050	21	11	particle	particle	NOUN
ap-5050	21	12	motion	motion	NOUN
ap-5050	21	13	on	on	ADP
ap-5050	21	14	rough	rough	ADJ
ap-5050	21	15	surfaces	surface	NOUN
ap-5050	21	16	of	of	ADP
ap-5050	21	17	agricultural	agricultural	ADJ
ap-5050	21	18	machinery	machinery	NOUN
ap-5050	21	19	operating	operating	NOUN
ap-5050	21	20	elements	element	NOUN
ap-5050	21	21	.	.	PUNCT
ap-5050	22	1	the	the	DET
ap-5050	22	2	particle	particle	NOUN
ap-5050	22	3	motion	motion	NOUN
ap-5050	22	4	on	on	ADP
ap-5050	22	5	a	a	DET
ap-5050	22	6	horizontal	horizontal	ADJ
ap-5050	22	7	disk	disk	NOUN
ap-5050	22	8	that	that	PRON
ap-5050	22	9	rotates	rotate	VERB
ap-5050	22	10	around	around	ADP
ap-5050	22	11	a	a	DET
ap-5050	22	12	vertical	vertical	ADJ
ap-5050	22	13	axis	axis	NOUN
ap-5050	22	14	,	,	PUNCT
ap-5050	22	15	which	which	PRON
ap-5050	22	16	is	be	AUX
ap-5050	22	17	either	either	CCONJ
ap-5050	22	18	equipped	equip	VERB
ap-5050	22	19	with	with	ADP
ap-5050	22	20	blades	blade	NOUN
ap-5050	22	21	of	of	ADP
ap-5050	22	22	the	the	DET
ap-5050	22	23	simplest	simple	ADJ
ap-5050	22	24	designs	design	NOUN
ap-5050	22	25	or	or	CCONJ
ap-5050	22	26	is	be	AUX
ap-5050	22	27	without	without	ADP
ap-5050	22	28	them	they	PRON
ap-5050	22	29	,	,	PUNCT
ap-5050	22	30	is	be	AUX
ap-5050	22	31	analysed	analyse	VERB
ap-5050	22	32	in	in	ADP
ap-5050	22	33	these	these	DET
ap-5050	22	34	papers	paper	NOUN
ap-5050	22	35	.	.	PUNCT
ap-5050	23	1	research	research	NOUN
ap-5050	24	1	[	[	X
ap-5050	24	2	3	3	X
ap-5050	24	3	]	]	PUNCT
ap-5050	24	4	considers	consider	VERB
ap-5050	24	5	the	the	DET
ap-5050	24	6	particle	particle	NOUN
ap-5050	24	7	motion	motion	NOUN
ap-5050	24	8	on	on	ADP
ap-5050	24	9	a	a	DET
ap-5050	24	10	flat	flat	ADJ
ap-5050	24	11	disk	disk	NOUN
ap-5050	24	12	,	,	PUNCT
ap-5050	24	13	which	which	PRON
ap-5050	24	14	rotates	rotate	VERB
ap-5050	24	15	around	around	ADP
ap-5050	24	16	the	the	DET
ap-5050	24	17	axis	axis	NOUN
ap-5050	24	18	that	that	PRON
ap-5050	24	19	is	be	AUX
ap-5050	24	20	inclined	incline	VERB
ap-5050	24	21	to	to	ADP
ap-5050	24	22	the	the	DET
ap-5050	24	23	horizon	horizon	NOUN
ap-5050	24	24	.	.	PUNCT
ap-5050	25	1	the	the	DET
ap-5050	25	2	patterns	pattern	NOUN
ap-5050	25	3	of	of	ADP
ap-5050	25	4	the	the	DET
ap-5050	25	5	particle	particle	NOUN
ap-5050	25	6	motion	motion	NOUN
ap-5050	25	7	on	on	ADP
ap-5050	25	8	a	a	DET
ap-5050	25	9	disk	disk	NOUN
ap-5050	25	10	without	without	ADP
ap-5050	25	11	blades	blade	NOUN
ap-5050	25	12	as	as	ADV
ap-5050	25	13	well	well	ADV
ap-5050	25	14	as	as	ADP
ap-5050	25	15	on	on	ADP
ap-5050	25	16	the	the	DET
ap-5050	25	17	one	one	NOUN
ap-5050	25	18	,	,	PUNCT
ap-5050	25	19	which	which	PRON
ap-5050	25	20	is	be	AUX
ap-5050	25	21	equipped	equip	VERB
ap-5050	25	22	with	with	ADP
ap-5050	25	23	rectilinear	rectilinear	ADJ
ap-5050	25	24	blades	blade	NOUN
ap-5050	25	25	located	locate	VERB
ap-5050	25	26	in	in	ADP
ap-5050	25	27	a	a	DET
ap-5050	25	28	radial	radial	ADJ
ap-5050	25	29	direction	direction	NOUN
ap-5050	25	30	from	from	ADP
ap-5050	25	31	the	the	DET
ap-5050	25	32	axis	axis	NOUN
ap-5050	25	33	of	of	ADP
ap-5050	25	34	the	the	DET
ap-5050	25	35	rotation	rotation	NOUN
ap-5050	25	36	,	,	PUNCT
ap-5050	25	37	are	be	AUX
ap-5050	25	38	presented	present	VERB
ap-5050	25	39	in	in	ADP
ap-5050	25	40	this	this	DET
ap-5050	25	41	research	research	NOUN
ap-5050	25	42	work	work	NOUN
ap-5050	25	43	.	.	PUNCT
ap-5050	26	1	paper	paper	NOUN
ap-5050	27	1	[	[	X
ap-5050	27	2	4	4	X
ap-5050	27	3	]	]	PUNCT
ap-5050	27	4	presents	present	VERB
ap-5050	27	5	the	the	DET
ap-5050	27	6	research	research	NOUN
ap-5050	27	7	,	,	PUNCT
ap-5050	27	8	which	which	PRON
ap-5050	27	9	is	be	AUX
ap-5050	27	10	similar	similar	ADJ
ap-5050	27	11	to	to	ADP
ap-5050	27	12	ours	ours	PRON
ap-5050	27	13	.	.	PUNCT
ap-5050	28	1	it	it	PRON
ap-5050	28	2	considers	consider	VERB
ap-5050	28	3	relative	relative	ADJ
ap-5050	28	4	particle	particle	NOUN
ap-5050	28	5	motion	motion	NOUN
ap-5050	28	6	at	at	ADP
ap-5050	28	7	a	a	DET
ap-5050	28	8	wide	wide	ADJ
ap-5050	28	9	range	range	NOUN
ap-5050	28	10	of	of	ADP
ap-5050	28	11	inclination	inclination	NOUN
ap-5050	28	12	angles	angle	NOUN
ap-5050	28	13	of	of	ADP
ap-5050	28	14	a	a	DET
ap-5050	28	15	plane	plane	NOUN
ap-5050	28	16	to	to	ADP
ap-5050	28	17	the	the	DET
ap-5050	28	18	axis	axis	NOUN
ap-5050	28	19	of	of	ADP
ap-5050	28	20	rotation	rotation	NOUN
ap-5050	28	21	,	,	PUNCT
ap-5050	28	22	beginning	begin	VERB
ap-5050	28	23	from	from	ADP
ap-5050	28	24	a	a	DET
ap-5050	28	25	horizontal	horizontal	ADJ
ap-5050	28	26	position	position	NOUN
ap-5050	28	27	and	and	CCONJ
ap-5050	28	28	finishing	finish	VERB
ap-5050	28	29	by	by	ADP
ap-5050	28	30	a	a	DET
ap-5050	28	31	vertical	vertical	ADJ
ap-5050	28	32	one	one	NUM
ap-5050	28	33	.	.	PUNCT
ap-5050	29	1	the	the	DET
ap-5050	29	2	development	development	NOUN
ap-5050	29	3	of	of	ADP
ap-5050	29	4	a	a	DET
ap-5050	29	5	bladed	bladed	ADJ
ap-5050	29	6	operating	operating	NOUN
ap-5050	29	7	element	element	NOUN
ap-5050	29	8	of	of	ADP
ap-5050	29	9	a	a	DET
ap-5050	29	10	conveyer	conveyer	NOUN
ap-5050	29	11	-	-	PUNCT
ap-5050	29	12	mixer	mixer	NOUN
ap-5050	29	13	is	be	AUX
ap-5050	29	14	considered	consider	VERB
ap-5050	29	15	in	in	ADP
ap-5050	29	16	paper	paper	NOUN
ap-5050	30	1	[	[	X
ap-5050	30	2	5–10	5–10	ADJ
ap-5050	30	3	]	]	PUNCT
ap-5050	30	4	.	.	PUNCT
ap-5050	31	1	2	2	X
ap-5050	31	2	.	.	X
ap-5050	31	3	material	material	NOUN
ap-5050	31	4	and	and	CCONJ
ap-5050	31	5	methods	method	NOUN
ap-5050	31	6	in	in	ADP
ap-5050	31	7	order	order	NOUN
ap-5050	31	8	to	to	PART
ap-5050	31	9	investigate	investigate	VERB
ap-5050	31	10	the	the	DET
ap-5050	31	11	patterns	pattern	NOUN
ap-5050	31	12	of	of	ADP
ap-5050	31	13	the	the	DET
ap-5050	31	14	material	material	NOUN
ap-5050	31	15	particle	particle	NOUN
ap-5050	31	16	motion	motion	NOUN
ap-5050	31	17	over	over	ADP
ap-5050	31	18	the	the	DET
ap-5050	31	19	edge	edge	NOUN
ap-5050	31	20	of	of	ADP
ap-5050	31	21	an	an	DET
ap-5050	31	22	inclined	inclined	ADJ
ap-5050	31	23	flat	flat	ADJ
ap-5050	31	24	ellipse	ellipse	NOUN
ap-5050	31	25	,	,	PUNCT
ap-5050	31	26	which	which	PRON
ap-5050	31	27	rotates	rotate	VERB
ap-5050	31	28	around	around	ADP
ap-5050	31	29	the	the	DET
ap-5050	31	30	axis	axis	NOUN
ap-5050	31	31	of	of	ADP
ap-5050	31	32	a	a	DET
ap-5050	31	33	vertical	vertical	ADJ
ap-5050	31	34	limiting	limiting	NOUN
ap-5050	31	35	cylinder	cylinder	NOUN
ap-5050	31	36	,	,	PUNCT
ap-5050	31	37	let	let	VERB
ap-5050	31	38	us	we	PRON
ap-5050	31	39	cut	cut	VERB
ap-5050	31	40	a	a	DET
ap-5050	31	41	segment	segment	NOUN
ap-5050	31	42	off	off	ADP
ap-5050	31	43	an	an	DET
ap-5050	31	44	inclined	inclined	ADJ
ap-5050	31	45	plane	plane	NOUN
ap-5050	31	46	with	with	ADP
ap-5050	31	47	the	the	DET
ap-5050	31	48	help	help	NOUN
ap-5050	31	49	of	of	ADP
ap-5050	31	50	a	a	DET
ap-5050	31	51	vertical	vertical	ADJ
ap-5050	31	52	cylinder	cylinder	NOUN
ap-5050	31	53	,	,	PUNCT
ap-5050	31	54	which	which	PRON
ap-5050	31	55	is	be	AUX
ap-5050	31	56	limited	limit	VERB
ap-5050	31	57	by	by	ADP
ap-5050	31	58	an	an	DET
ap-5050	31	59	ellipse	ellipse	NOUN
ap-5050	31	60	(	(	PUNCT
ap-5050	31	61	figure	figure	NOUN
ap-5050	31	62	1	1	NUM
ap-5050	31	63	)	)	PUNCT
ap-5050	31	64	.	.	PUNCT
ap-5050	32	1	let	let	VERB
ap-5050	32	2	us	we	PRON
ap-5050	32	3	rotate	rotate	VERB
ap-5050	32	4	this	this	DET
ap-5050	32	5	segment	segment	NOUN
ap-5050	32	6	around	around	ADP
ap-5050	32	7	a	a	DET
ap-5050	32	8	cylinder	cylinder	NOUN
ap-5050	32	9	axis	axis	NOUN
ap-5050	32	10	at	at	ADP
ap-5050	32	11	a	a	DET
ap-5050	32	12	constant	constant	ADJ
ap-5050	32	13	angular	angular	ADJ
ap-5050	32	14	velocity	velocity	NOUN
ap-5050	32	15	ω	ω	NOUN
ap-5050	32	16	.	.	PUNCT
ap-5050	33	1	if	if	SCONJ
ap-5050	33	2	a	a	DET
ap-5050	33	3	material	material	NOUN
ap-5050	33	4	particle	particle	NOUN
ap-5050	33	5	gets	get	VERB
ap-5050	33	6	onto	onto	ADP
ap-5050	33	7	a	a	DET
ap-5050	33	8	moving	move	VERB
ap-5050	33	9	segment	segment	NOUN
ap-5050	33	10	,	,	PUNCT
ap-5050	33	11	it	it	PRON
ap-5050	33	12	will	will	AUX
ap-5050	33	13	slide	slide	VERB
ap-5050	33	14	on	on	ADP
ap-5050	33	15	it	it	PRON
ap-5050	33	16	,	,	PUNCT
ap-5050	33	17	that	that	PRON
ap-5050	33	18	is	be	AUX
ap-5050	33	19	to	to	PART
ap-5050	33	20	say	say	VERB
ap-5050	33	21	,	,	PUNCT
ap-5050	33	22	it	it	PRON
ap-5050	33	23	will	will	AUX
ap-5050	33	24	perform	perform	VERB
ap-5050	33	25	a	a	DET
ap-5050	33	26	relative	relative	ADJ
ap-5050	33	27	motion	motion	NOUN
ap-5050	33	28	.	.	PUNCT
ap-5050	34	1	under	under	ADP
ap-5050	34	2	the	the	DET
ap-5050	34	3	action	action	NOUN
ap-5050	34	4	of	of	ADP
ap-5050	34	5	centrifugal	centrifugal	ADJ
ap-5050	34	6	force	force	NOUN
ap-5050	34	7	,	,	PUNCT
ap-5050	34	8	a	a	DET
ap-5050	34	9	particle	particle	NOUN
ap-5050	34	10	will	will	AUX
ap-5050	34	11	be	be	AUX
ap-5050	34	12	thrown	throw	VERB
ap-5050	34	13	away	away	ADV
ap-5050	34	14	to	to	ADP
ap-5050	34	15	the	the	DET
ap-5050	34	16	inner	inner	ADJ
ap-5050	34	17	surface	surface	NOUN
ap-5050	34	18	67	67	NUM
ap-5050	34	19	http://dx.doi.org/10.14311/ap.2019.59.0067	http://dx.doi.org/10.14311/ap.2019.59.0067	ADP
ap-5050	34	20	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-5050	34	21	s.	s.	PROPN
ap-5050	34	22	f.	f.	PROPN
ap-5050	34	23	pylypaka	pylypaka	PROPN
ap-5050	34	24	,	,	PUNCT
ap-5050	34	25	m.	m.	PROPN
ap-5050	34	26	b.	b.	PROPN
ap-5050	34	27	klendii	klendii	PROPN
ap-5050	34	28	,	,	PUNCT
ap-5050	34	29	v.	v.	PROPN
ap-5050	34	30	m.	m.	PROPN
ap-5050	34	31	nesvidomin	nesvidomin	PROPN
ap-5050	34	32	,	,	PUNCT
ap-5050	34	33	v.	v.	PROPN
ap-5050	34	34	i.	i.	PROPN
ap-5050	34	35	trokhaniak	trokhaniak	PROPN
ap-5050	34	36	acta	acta	PROPN
ap-5050	34	37	polytechnica	polytechnica	PROPN
ap-5050	34	38	figure	figure	NOUN
ap-5050	34	39	1	1	NUM
ap-5050	34	40	.	.	PUNCT
ap-5050	34	41	an	an	DET
ap-5050	34	42	inclined	inclined	ADJ
ap-5050	34	43	plane	plane	NOUN
ap-5050	34	44	,	,	PUNCT
ap-5050	34	45	which	which	PRON
ap-5050	34	46	is	be	AUX
ap-5050	34	47	limited	limit	VERB
ap-5050	34	48	by	by	ADP
ap-5050	34	49	a	a	DET
ap-5050	34	50	vertical	vertical	ADJ
ap-5050	34	51	cylinder	cylinder	NOUN
ap-5050	34	52	:	:	PUNCT
ap-5050	34	53	(	(	PUNCT
ap-5050	34	54	a	a	X
ap-5050	34	55	)	)	PUNCT
ap-5050	34	56	axonometric	axonometric	NOUN
ap-5050	34	57	projection	projection	NOUN
ap-5050	34	58	;	;	PUNCT
ap-5050	34	59	(	(	PUNCT
ap-5050	34	60	b	b	X
ap-5050	34	61	)	)	PUNCT
ap-5050	34	62	diagram	diagram	NOUN
ap-5050	34	63	of	of	ADP
ap-5050	34	64	forces	force	NOUN
ap-5050	34	65	acting	act	VERB
ap-5050	34	66	on	on	ADP
ap-5050	34	67	a	a	DET
ap-5050	34	68	particle	particle	NOUN
ap-5050	34	69	of	of	ADP
ap-5050	34	70	a	a	DET
ap-5050	34	71	limiting	limit	VERB
ap-5050	34	72	cylinder	cylinder	NOUN
ap-5050	34	73	and	and	CCONJ
ap-5050	34	74	,	,	PUNCT
ap-5050	34	75	from	from	ADP
ap-5050	34	76	this	this	DET
ap-5050	34	77	point	point	NOUN
ap-5050	34	78	on	on	ADP
ap-5050	34	79	,	,	PUNCT
ap-5050	34	80	it	it	PRON
ap-5050	34	81	will	will	AUX
ap-5050	34	82	move	move	VERB
ap-5050	34	83	along	along	ADP
ap-5050	34	84	a	a	DET
ap-5050	34	85	common	common	ADJ
ap-5050	34	86	intersection	intersection	NOUN
ap-5050	34	87	line	line	NOUN
ap-5050	34	88	of	of	ADP
ap-5050	34	89	a	a	DET
ap-5050	34	90	cylinder	cylinder	NOUN
ap-5050	34	91	and	and	CCONJ
ap-5050	34	92	a	a	DET
ap-5050	34	93	plane	plane	NOUN
ap-5050	34	94	,	,	PUNCT
ap-5050	34	95	that	that	PRON
ap-5050	34	96	is	be	AUX
ap-5050	34	97	to	to	PART
ap-5050	34	98	say	say	VERB
ap-5050	34	99	,	,	PUNCT
ap-5050	34	100	along	along	ADP
ap-5050	34	101	an	an	DET
ap-5050	34	102	ellipse	ellipse	NOUN
ap-5050	34	103	.	.	PUNCT
ap-5050	35	1	a	a	DET
ap-5050	35	2	particle	particle	NOUN
ap-5050	35	3	,	,	PUNCT
ap-5050	35	4	which	which	PRON
ap-5050	35	5	is	be	AUX
ap-5050	35	6	shown	show	VERB
ap-5050	35	7	in	in	ADP
ap-5050	35	8	figure	figure	NOUN
ap-5050	35	9	1b	1b	NUM
ap-5050	35	10	in	in	ADP
ap-5050	35	11	the	the	DET
ap-5050	35	12	down	down	ADJ
ap-5050	35	13	position	position	NOUN
ap-5050	35	14	on	on	ADP
ap-5050	35	15	a	a	DET
ap-5050	35	16	flat	flat	ADJ
ap-5050	35	17	segment	segment	NOUN
ap-5050	35	18	that	that	PRON
ap-5050	35	19	is	be	AUX
ap-5050	35	20	projected	project	VERB
ap-5050	35	21	into	into	ADP
ap-5050	35	22	a	a	DET
ap-5050	35	23	straight	straight	ADJ
ap-5050	35	24	line	line	NOUN
ap-5050	35	25	,	,	PUNCT
ap-5050	35	26	is	be	AUX
ap-5050	35	27	influenced	influence	VERB
ap-5050	35	28	by	by	ADP
ap-5050	35	29	the	the	DET
ap-5050	35	30	following	follow	VERB
ap-5050	35	31	forces	force	NOUN
ap-5050	35	32	:	:	PUNCT
ap-5050	35	33	weight	weight	NOUN
ap-5050	35	34	force	force	NOUN
ap-5050	35	35	of	of	ADP
ap-5050	35	36	a	a	DET
ap-5050	35	37	particle	particle	NOUN
ap-5050	35	38	mg	mg	PROPN
ap-5050	35	39	,	,	PUNCT
ap-5050	35	40	where	where	SCONJ
ap-5050	35	41	m	m	NOUN
ap-5050	35	42	–	–	PUNCT
ap-5050	35	43	mass	mass	NOUN
ap-5050	35	44	of	of	ADP
ap-5050	35	45	a	a	DET
ap-5050	35	46	particle	particle	NOUN
ap-5050	35	47	,	,	PUNCT
ap-5050	35	48	g	g	NOUN
ap-5050	35	49	=	=	PROPN
ap-5050	35	50	9.81m	9.81m	PROPN
ap-5050	35	51	/	/	SYM
ap-5050	35	52	s2	s2	PROPN
ap-5050	35	53	,	,	PUNCT
ap-5050	35	54	reaction	reaction	NOUN
ap-5050	35	55	n	n	PROPN
ap-5050	35	56	of	of	ADP
ap-5050	35	57	a	a	DET
ap-5050	35	58	surface	surface	NOUN
ap-5050	35	59	,	,	PUNCT
ap-5050	35	60	reaction	reaction	NOUN
ap-5050	35	61	nr	nr	PROPN
ap-5050	35	62	of	of	ADP
ap-5050	35	63	a	a	DET
ap-5050	35	64	cylinder	cylinder	NOUN
ap-5050	35	65	surface	surface	NOUN
ap-5050	35	66	with	with	ADP
ap-5050	35	67	a	a	DET
ap-5050	35	68	radius	radius	NOUN
ap-5050	35	69	r.	r.	NOUN
ap-5050	35	70	the	the	DET
ap-5050	35	71	last	last	ADJ
ap-5050	35	72	mentioned	mention	VERB
ap-5050	35	73	forces	force	NOUN
ap-5050	35	74	cause	cause	VERB
ap-5050	35	75	relative	relative	ADJ
ap-5050	35	76	friction	friction	NOUN
ap-5050	35	77	forces	force	NOUN
ap-5050	35	78	.	.	PUNCT
ap-5050	36	1	first	first	ADV
ap-5050	36	2	of	of	ADP
ap-5050	36	3	all	all	PRON
ap-5050	36	4	,	,	PUNCT
ap-5050	36	5	let	let	VERB
ap-5050	36	6	us	we	PRON
ap-5050	36	7	consider	consider	VERB
ap-5050	36	8	a	a	DET
ap-5050	36	9	situation	situation	NOUN
ap-5050	36	10	,	,	PUNCT
ap-5050	36	11	when	when	SCONJ
ap-5050	36	12	a	a	DET
ap-5050	36	13	plane	plane	NOUN
ap-5050	36	14	inclination	inclination	NOUN
ap-5050	36	15	angle	angle	NOUN
ap-5050	36	16	is	be	AUX
ap-5050	36	17	the	the	DET
ap-5050	36	18	following	following	NOUN
ap-5050	36	19	:	:	PUNCT
ap-5050	36	20	β	β	X
ap-5050	36	21	=	=	PUNCT
ap-5050	36	22	0	0	X
ap-5050	36	23	.	.	PUNCT
ap-5050	37	1	here	here	ADV
ap-5050	37	2	,	,	PUNCT
ap-5050	37	3	an	an	DET
ap-5050	37	4	ellipse	ellipse	NOUN
ap-5050	37	5	will	will	AUX
ap-5050	37	6	transform	transform	VERB
ap-5050	37	7	into	into	ADP
ap-5050	37	8	a	a	DET
ap-5050	37	9	circle	circle	NOUN
ap-5050	37	10	and	and	CCONJ
ap-5050	37	11	the	the	DET
ap-5050	37	12	problem	problem	NOUN
ap-5050	37	13	will	will	AUX
ap-5050	37	14	become	become	VERB
ap-5050	37	15	planare	planare	NOUN
ap-5050	37	16	,	,	PUNCT
ap-5050	37	17	which	which	PRON
ap-5050	37	18	makes	make	VERB
ap-5050	37	19	the	the	DET
ap-5050	37	20	problem	problem	NOUN
ap-5050	37	21	solving	solve	VERB
ap-5050	37	22	much	much	ADV
ap-5050	37	23	easier	easy	ADJ
ap-5050	37	24	.	.	PUNCT
ap-5050	38	1	let	let	VERB
ap-5050	38	2	us	we	PRON
ap-5050	38	3	deduce	deduce	VERB
ap-5050	38	4	a	a	DET
ap-5050	38	5	differential	differential	ADJ
ap-5050	38	6	equation	equation	NOUN
ap-5050	38	7	of	of	ADP
ap-5050	38	8	an	an	DET
ap-5050	38	9	absolute	absolute	ADJ
ap-5050	38	10	particle	particle	NOUN
ap-5050	38	11	motion	motion	NOUN
ap-5050	38	12	in	in	ADP
ap-5050	38	13	a	a	DET
ap-5050	38	14	projection	projection	NOUN
ap-5050	38	15	onto	onto	ADP
ap-5050	38	16	a	a	DET
ap-5050	38	17	moving	move	VERB
ap-5050	38	18	axis	axis	NOUN
ap-5050	38	19	s	s	PART
ap-5050	38	20	–	–	PUNCT
ap-5050	38	21	motion	motion	NOUN
ap-5050	38	22	direction	direction	NOUN
ap-5050	38	23	(	(	PUNCT
ap-5050	38	24	figure	figure	NOUN
ap-5050	38	25	2	2	NUM
ap-5050	38	26	)	)	PUNCT
ap-5050	38	27	.	.	PUNCT
ap-5050	39	1	let	let	VERB
ap-5050	39	2	us	we	PRON
ap-5050	39	3	write	write	VERB
ap-5050	39	4	the	the	DET
ap-5050	39	5	equation	equation	NOUN
ap-5050	39	6	in	in	ADP
ap-5050	39	7	the	the	DET
ap-5050	39	8	following	follow	VERB
ap-5050	39	9	form	form	NOUN
ap-5050	39	10	:	:	PUNCT
ap-5050	39	11	mw	mw	X
ap-5050	39	12	=	=	PUNCT
ap-5050	39	13	∑	∑	PROPN
ap-5050	39	14	f	f	PROPN
ap-5050	39	15	,	,	PUNCT
ap-5050	39	16	where	where	SCONJ
ap-5050	39	17	w	w	X
ap-5050	39	18	–	–	PUNCT
ap-5050	39	19	absolute	absolute	ADJ
ap-5050	39	20	acceleration	acceleration	NOUN
ap-5050	39	21	of	of	ADP
ap-5050	39	22	a	a	DET
ap-5050	39	23	particle	particle	NOUN
ap-5050	39	24	,	,	PUNCT
ap-5050	39	25	∑	∑	PROPN
ap-5050	39	26	f	f	PROPN
ap-5050	39	27	–	–	PUNCT
ap-5050	39	28	total	total	ADJ
ap-5050	39	29	force	force	NOUN
ap-5050	39	30	exerted	exert	VERB
ap-5050	39	31	upon	upon	SCONJ
ap-5050	39	32	a	a	DET
ap-5050	39	33	particle	particle	NOUN
ap-5050	39	34	.	.	PUNCT
ap-5050	40	1	a	a	DET
ap-5050	40	2	circular	circular	ADJ
ap-5050	40	3	segment	segment	NOUN
ap-5050	40	4	of	of	ADP
ap-5050	40	5	a	a	DET
ap-5050	40	6	plane	plane	NOUN
ap-5050	40	7	rotates	rotate	VERB
ap-5050	40	8	with	with	ADP
ap-5050	40	9	the	the	DET
ap-5050	40	10	angular	angular	ADJ
ap-5050	40	11	velocity	velocity	NOUN
ap-5050	40	12	ω	ω	NOUN
ap-5050	40	13	.	.	PUNCT
ap-5050	41	1	during	during	ADP
ap-5050	41	2	the	the	DET
ap-5050	41	3	time	time	NOUN
ap-5050	41	4	t	t	NOUN
ap-5050	41	5	it	it	PRON
ap-5050	41	6	rotates	rotate	VERB
ap-5050	41	7	through	through	ADP
ap-5050	41	8	the	the	DET
ap-5050	41	9	angle	angle	NOUN
ap-5050	41	10	of	of	ADP
ap-5050	41	11	ωt	ωt	PROPN
ap-5050	41	12	.	.	PUNCT
ap-5050	42	1	a	a	DET
ap-5050	42	2	particle	particle	NOUN
ap-5050	42	3	will	will	AUX
ap-5050	42	4	rotate	rotate	VERB
ap-5050	42	5	in	in	ADP
ap-5050	42	6	the	the	DET
ap-5050	42	7	same	same	ADJ
ap-5050	42	8	direction	direction	NOUN
ap-5050	42	9	,	,	PUNCT
ap-5050	42	10	but	but	CCONJ
ap-5050	42	11	its	its	PRON
ap-5050	42	12	rotation	rotation	NOUN
ap-5050	42	13	will	will	AUX
ap-5050	42	14	be	be	AUX
ap-5050	42	15	slower	slow	ADJ
ap-5050	42	16	,	,	PUNCT
ap-5050	42	17	since	since	SCONJ
ap-5050	42	18	its	its	PRON
ap-5050	42	19	motion	motion	NOUN
ap-5050	42	20	will	will	AUX
ap-5050	42	21	be	be	AUX
ap-5050	42	22	restricted	restrict	VERB
ap-5050	42	23	by	by	ADP
ap-5050	42	24	the	the	DET
ap-5050	42	25	friction	friction	NOUN
ap-5050	42	26	force	force	NOUN
ap-5050	42	27	caused	cause	VERB
ap-5050	42	28	by	by	ADP
ap-5050	42	29	sliding	slide	VERB
ap-5050	42	30	over	over	ADP
ap-5050	42	31	a	a	DET
ap-5050	42	32	cylinder	cylinder	NOUN
ap-5050	42	33	plane	plane	NOUN
ap-5050	42	34	.	.	PUNCT
ap-5050	43	1	an	an	DET
ap-5050	43	2	absolute	absolute	ADJ
ap-5050	43	3	angle	angle	NOUN
ap-5050	43	4	of	of	ADP
ap-5050	43	5	rotation	rotation	NOUN
ap-5050	43	6	will	will	AUX
ap-5050	43	7	be	be	AUX
ap-5050	43	8	equal	equal	ADJ
ap-5050	43	9	to	to	ADP
ap-5050	43	10	ωt−	ωt−	X
ap-5050	43	11	α	α	NOUN
ap-5050	43	12	,	,	PUNCT
ap-5050	43	13	where	where	SCONJ
ap-5050	43	14	α	α	X
ap-5050	43	15	–	–	PUNCT
ap-5050	43	16	the	the	DET
ap-5050	43	17	angle	angle	NOUN
ap-5050	43	18	at	at	ADP
ap-5050	43	19	which	which	PRON
ap-5050	43	20	a	a	DET
ap-5050	43	21	particle	particle	NOUN
ap-5050	43	22	rotates	rotate	NOUN
ap-5050	43	23	as	as	ADP
ap-5050	43	24	a	a	DET
ap-5050	43	25	result	result	NOUN
ap-5050	43	26	of	of	ADP
ap-5050	43	27	sliding	slide	VERB
ap-5050	43	28	on	on	ADP
ap-5050	43	29	a	a	DET
ap-5050	43	30	plane	plane	NOUN
ap-5050	43	31	(	(	PUNCT
ap-5050	43	32	a	a	DET
ap-5050	43	33	disk	disk	NOUN
ap-5050	43	34	)	)	PUNCT
ap-5050	43	35	.	.	PUNCT
ap-5050	44	1	the	the	DET
ap-5050	44	2	absolute	absolute	ADJ
ap-5050	44	3	distance	distance	NOUN
ap-5050	44	4	s	s	NOUN
ap-5050	44	5	,	,	PUNCT
ap-5050	44	6	which	which	PRON
ap-5050	44	7	a	a	DET
ap-5050	44	8	particle	particle	NOUN
ap-5050	44	9	covers	cover	VERB
ap-5050	44	10	during	during	ADP
ap-5050	44	11	the	the	DET
ap-5050	44	12	time	time	NOUN
ap-5050	44	13	t	t	PROPN
ap-5050	44	14	,	,	PUNCT
ap-5050	44	15	is	be	AUX
ap-5050	44	16	determined	determine	VERB
ap-5050	44	17	from	from	ADP
ap-5050	44	18	the	the	DET
ap-5050	44	19	following	follow	VERB
ap-5050	44	20	expression	expression	NOUN
ap-5050	44	21	:	:	PUNCT
ap-5050	44	22	s	s	X
ap-5050	44	23	=	=	PUNCT
ap-5050	44	24	r(ωt−	r(ωt−	PROPN
ap-5050	44	25	α	α	NOUN
ap-5050	44	26	)	)	PUNCT
ap-5050	44	27	.	.	PUNCT
ap-5050	45	1	(	(	PUNCT
ap-5050	45	2	1	1	X
ap-5050	45	3	)	)	PUNCT
ap-5050	45	4	let	let	VERB
ap-5050	45	5	us	we	PRON
ap-5050	45	6	consider	consider	VERB
ap-5050	45	7	the	the	DET
ap-5050	45	8	angle	angle	NOUN
ap-5050	45	9	α	α	PRON
ap-5050	45	10	to	to	PART
ap-5050	45	11	be	be	AUX
ap-5050	45	12	a	a	DET
ap-5050	45	13	time	time	NOUN
ap-5050	45	14	-	-	PUNCT
ap-5050	45	15	varying	vary	VERB
ap-5050	45	16	function	function	NOUN
ap-5050	45	17	t	t	NOUN
ap-5050	45	18	:	:	PUNCT
ap-5050	45	19	α	α	PROPN
ap-5050	45	20	=	=	PUNCT
ap-5050	45	21	α(t	α(t	PROPN
ap-5050	45	22	)	)	PUNCT
ap-5050	45	23	.	.	PUNCT
ap-5050	46	1	with	with	ADP
ap-5050	46	2	the	the	DET
ap-5050	46	3	help	help	NOUN
ap-5050	46	4	of	of	ADP
ap-5050	46	5	the	the	DET
ap-5050	46	6	successive	successive	ADJ
ap-5050	46	7	differentiation	differentiation	NOUN
ap-5050	46	8	of	of	ADP
ap-5050	46	9	the	the	DET
ap-5050	46	10	expression	expression	NOUN
ap-5050	46	11	(	(	PUNCT
ap-5050	46	12	1	1	NUM
ap-5050	46	13	)	)	PUNCT
ap-5050	46	14	,	,	PUNCT
ap-5050	46	15	let	let	VERB
ap-5050	46	16	us	we	PRON
ap-5050	46	17	find	find	VERB
ap-5050	46	18	the	the	DET
ap-5050	46	19	figure	figure	NOUN
ap-5050	46	20	2	2	NUM
ap-5050	46	21	.	.	PUNCT
ap-5050	46	22	a	a	DET
ap-5050	46	23	diagram	diagram	NOUN
ap-5050	46	24	of	of	ADP
ap-5050	46	25	forces	force	NOUN
ap-5050	46	26	acting	act	VERB
ap-5050	46	27	on	on	ADP
ap-5050	46	28	the	the	DET
ap-5050	46	29	particle	particle	NOUN
ap-5050	46	30	a	a	PRON
ap-5050	46	31	,	,	PUNCT
ap-5050	46	32	which	which	PRON
ap-5050	46	33	is	be	AUX
ap-5050	46	34	located	locate	VERB
ap-5050	46	35	on	on	ADP
ap-5050	46	36	a	a	DET
ap-5050	46	37	circular	circular	ADJ
ap-5050	46	38	disk	disk	NOUN
ap-5050	46	39	that	that	PRON
ap-5050	46	40	rotates	rotate	VERB
ap-5050	46	41	inside	inside	ADP
ap-5050	46	42	a	a	DET
ap-5050	46	43	cylindrical	cylindrical	ADJ
ap-5050	46	44	cover	cover	NOUN
ap-5050	46	45	.	.	PUNCT
ap-5050	47	1	absolute	absolute	ADJ
ap-5050	47	2	velocity	velocity	NOUN
ap-5050	47	3	va	va	NOUN
ap-5050	47	4	and	and	CCONJ
ap-5050	47	5	the	the	DET
ap-5050	47	6	absolute	absolute	ADJ
ap-5050	47	7	acceleration	acceleration	NOUN
ap-5050	47	8	w	w	NOUN
ap-5050	47	9	of	of	ADP
ap-5050	47	10	a	a	DET
ap-5050	47	11	particle	particle	NOUN
ap-5050	47	12	:	:	PUNCT
ap-5050	47	13	va	va	NOUN
ap-5050	47	14	=	=	NOUN
ap-5050	48	1	ds	ds	ADJ
ap-5050	48	2	dt	dt	X
ap-5050	48	3	=	=	PUNCT
ap-5050	48	4	r(ω	r(ω	ADV
ap-5050	48	5	−	−	PROPN
ap-5050	48	6	α′	α′	NUM
ap-5050	48	7	)	)	PUNCT
ap-5050	48	8	,	,	PUNCT
ap-5050	48	9	(	(	PUNCT
ap-5050	48	10	2	2	X
ap-5050	48	11	)	)	PUNCT
ap-5050	48	12	w	w	NOUN
ap-5050	48	13	=	=	PUNCT
ap-5050	48	14	dva	dva	NOUN
ap-5050	48	15	dt	dt	NOUN
ap-5050	49	1	=	=	PUNCT
ap-5050	49	2	−rα′′.	−rα′′.	NOUN
ap-5050	49	3	(	(	PUNCT
ap-5050	49	4	3	3	NUM
ap-5050	49	5	)	)	PUNCT
ap-5050	49	6	two	two	NUM
ap-5050	49	7	friction	friction	NOUN
ap-5050	49	8	forces	force	NOUN
ap-5050	49	9	,	,	PUNCT
ap-5050	49	10	which	which	PRON
ap-5050	49	11	act	act	VERB
ap-5050	49	12	along	along	ADP
ap-5050	49	13	the	the	DET
ap-5050	49	14	moving	move	VERB
ap-5050	49	15	axis	axis	NOUN
ap-5050	49	16	s	s	NOUN
ap-5050	49	17	in	in	ADP
ap-5050	49	18	opposite	opposite	ADJ
ap-5050	49	19	directions	direction	NOUN
ap-5050	49	20	,	,	PUNCT
ap-5050	49	21	are	be	AUX
ap-5050	49	22	exerted	exert	VERB
ap-5050	49	23	upon	upon	SCONJ
ap-5050	49	24	a	a	DET
ap-5050	49	25	particle	particle	NOUN
ap-5050	49	26	.	.	PUNCT
ap-5050	50	1	the	the	DET
ap-5050	50	2	force	force	NOUN
ap-5050	50	3	f	f	PROPN
ap-5050	50	4	of	of	ADP
ap-5050	50	5	the	the	DET
ap-5050	50	6	particle	particle	NOUN
ap-5050	50	7	friction	friction	NOUN
ap-5050	50	8	on	on	ADP
ap-5050	50	9	a	a	DET
ap-5050	50	10	disk	disk	NOUN
ap-5050	50	11	is	be	AUX
ap-5050	50	12	directed	direct	VERB
ap-5050	50	13	opposite	opposite	ADV
ap-5050	50	14	to	to	ADP
ap-5050	50	15	its	its	PRON
ap-5050	50	16	sliding	slide	VERB
ap-5050	50	17	on	on	ADP
ap-5050	50	18	it	it	PRON
ap-5050	50	19	or	or	CCONJ
ap-5050	50	20	in	in	ADP
ap-5050	50	21	the	the	DET
ap-5050	50	22	direction	direction	NOUN
ap-5050	50	23	of	of	ADP
ap-5050	50	24	the	the	DET
ap-5050	50	25	absolute	absolute	ADJ
ap-5050	50	26	motion	motion	NOUN
ap-5050	50	27	.	.	PUNCT
ap-5050	51	1	its	its	PRON
ap-5050	51	2	value	value	NOUN
ap-5050	51	3	is	be	AUX
ap-5050	51	4	the	the	DET
ap-5050	51	5	product	product	NOUN
ap-5050	51	6	of	of	ADP
ap-5050	51	7	the	the	DET
ap-5050	51	8	coefficient	coefficient	NOUN
ap-5050	51	9	of	of	ADP
ap-5050	51	10	the	the	DET
ap-5050	51	11	particle	particle	NOUN
ap-5050	51	12	friction	friction	NOUN
ap-5050	51	13	f	f	PROPN
ap-5050	51	14	on	on	ADP
ap-5050	51	15	a	a	DET
ap-5050	51	16	disk	disk	NOUN
ap-5050	51	17	by	by	ADP
ap-5050	51	18	disk	disk	NOUN
ap-5050	51	19	reaction	reaction	NOUN
ap-5050	51	20	n	n	PROPN
ap-5050	51	21	=	=	SYM
ap-5050	51	22	mg	mg	PROPN
ap-5050	51	23	.	.	PUNCT
ap-5050	52	1	thus	thus	ADV
ap-5050	52	2	,	,	PUNCT
ap-5050	52	3	f	f	PROPN
ap-5050	52	4	=	=	SYM
ap-5050	52	5	fmg	fmg	PROPN
ap-5050	52	6	.	.	PUNCT
ap-5050	53	1	in	in	ADP
ap-5050	53	2	a	a	DET
ap-5050	53	3	similar	similar	ADJ
ap-5050	53	4	way	way	NOUN
ap-5050	53	5	,	,	PUNCT
ap-5050	53	6	the	the	DET
ap-5050	53	7	force	force	NOUN
ap-5050	53	8	of	of	ADP
ap-5050	53	9	the	the	DET
ap-5050	53	10	particle	particle	NOUN
ap-5050	53	11	friction	friction	NOUN
ap-5050	53	12	fr	fr	NOUN
ap-5050	53	13	on	on	ADP
ap-5050	53	14	the	the	DET
ap-5050	53	15	surface	surface	NOUN
ap-5050	53	16	of	of	ADP
ap-5050	53	17	a	a	DET
ap-5050	53	18	cylindrical	cylindrical	ADJ
ap-5050	53	19	cover	cover	NOUN
ap-5050	53	20	is	be	AUX
ap-5050	53	21	determined	determine	VERB
ap-5050	53	22	.	.	PUNCT
ap-5050	54	1	the	the	DET
ap-5050	54	2	cover	cover	NOUN
ap-5050	54	3	reaction	reaction	NOUN
ap-5050	54	4	on	on	ADP
ap-5050	54	5	a	a	DET
ap-5050	54	6	particle	particle	NOUN
ap-5050	54	7	nr	nr	PROPN
ap-5050	54	8	balances	balance	VERB
ap-5050	54	9	the	the	DET
ap-5050	54	10	value	value	NOUN
ap-5050	54	11	of	of	ADP
ap-5050	54	12	the	the	DET
ap-5050	54	13	centrifugal	centrifugal	ADJ
ap-5050	54	14	force	force	NOUN
ap-5050	54	15	mr(ω−α′)2	mr(ω−α′)2	NOUN
ap-5050	54	16	that	that	PRON
ap-5050	54	17	acts	act	VERB
ap-5050	54	18	on	on	ADP
ap-5050	54	19	the	the	DET
ap-5050	54	20	particle	particle	NOUN
ap-5050	54	21	.	.	PUNCT
ap-5050	55	1	thus	thus	ADV
ap-5050	55	2	,	,	PUNCT
ap-5050	55	3	fr	fr	PROPN
ap-5050	55	4	=	=	PUNCT
ap-5050	55	5	frnr	frnr	PROPN
ap-5050	55	6	=	=	SYM
ap-5050	55	7	frmr(ω−α′)2	frmr(ω−α′)2	NOUN
ap-5050	55	8	.	.	PUNCT
ap-5050	56	1	after	after	ADP
ap-5050	56	2	that	that	PRON
ap-5050	56	3	,	,	PUNCT
ap-5050	56	4	the	the	DET
ap-5050	56	5	equation	equation	NOUN
ap-5050	56	6	mw	mw	VERB
ap-5050	56	7	=	=	PUNCT
ap-5050	56	8	∑	∑	PROPN
ap-5050	56	9	f	f	PROPN
ap-5050	56	10	takes	take	VERB
ap-5050	56	11	the	the	DET
ap-5050	56	12	following	follow	VERB
ap-5050	56	13	form	form	NOUN
ap-5050	56	14	:	:	PUNCT
ap-5050	56	15	−mrα′′	−mrα′′	PROPN
ap-5050	56	16	=	=	SYM
ap-5050	56	17	fmg	fmg	PROPN
ap-5050	56	18	−	−	PROPN
ap-5050	56	19	frmr(ωt−	frmr(ωt−	PROPN
ap-5050	56	20	α′)2	α′)2	PROPN
ap-5050	56	21	.	.	PROPN
ap-5050	57	1	(	(	PUNCT
ap-5050	57	2	4	4	NUM
ap-5050	57	3	)	)	PUNCT
ap-5050	57	4	after	after	ADP
ap-5050	57	5	its	its	PRON
ap-5050	57	6	reduction	reduction	NOUN
ap-5050	57	7	by	by	ADP
ap-5050	57	8	the	the	DET
ap-5050	57	9	mass	mass	NOUN
ap-5050	57	10	m	m	PROPN
ap-5050	57	11	and	and	CCONJ
ap-5050	57	12	its	its	PRON
ap-5050	57	13	simplification	simplification	NOUN
ap-5050	57	14	,	,	PUNCT
ap-5050	57	15	(	(	PUNCT
ap-5050	57	16	4	4	X
ap-5050	57	17	)	)	PUNCT
ap-5050	57	18	is	be	AUX
ap-5050	57	19	written	write	VERB
ap-5050	57	20	as	as	ADP
ap-5050	57	21	:	:	PUNCT
ap-5050	57	22	−	−	PROPN
ap-5050	57	23	α′′	α′′	NOUN
ap-5050	57	24	=	=	SYM
ap-5050	57	25	fg	fg	PROPN
ap-5050	57	26	r	r	NOUN
ap-5050	57	27	−	−	PROPN
ap-5050	57	28	fr(ωt−	fr(ωt−	PROPN
ap-5050	57	29	α′)2	α′)2	PROPN
ap-5050	57	30	.	.	PUNCT
ap-5050	58	1	(	(	PUNCT
ap-5050	58	2	5	5	X
ap-5050	58	3	)	)	PUNCT
ap-5050	58	4	this	this	DET
ap-5050	58	5	equation	equation	NOUN
ap-5050	58	6	can	can	AUX
ap-5050	58	7	be	be	AUX
ap-5050	58	8	analytically	analytically	ADV
ap-5050	58	9	solved	solve	VERB
ap-5050	58	10	.	.	PUNCT
ap-5050	59	1	its	its	PRON
ap-5050	59	2	partial	partial	ADJ
ap-5050	59	3	solution	solution	NOUN
ap-5050	59	4	can	can	AUX
ap-5050	59	5	be	be	AUX
ap-5050	59	6	found	find	VERB
ap-5050	59	7	,	,	PUNCT
ap-5050	59	8	which	which	PRON
ap-5050	59	9	describes	describe	VERB
ap-5050	59	10	the	the	DET
ap-5050	59	11	particle	particle	NOUN
ap-5050	59	12	motion	motion	NOUN
ap-5050	59	13	after	after	ADP
ap-5050	59	14	its	its	PRON
ap-5050	59	15	stabilization	stabilization	NOUN
ap-5050	59	16	.	.	PUNCT
ap-5050	60	1	in	in	ADP
ap-5050	60	2	this	this	DET
ap-5050	60	3	case	case	NOUN
ap-5050	60	4	,	,	PUNCT
ap-5050	60	5	the	the	DET
ap-5050	60	6	angular	angular	ADJ
ap-5050	60	7	velocity	velocity	NOUN
ap-5050	60	8	α′	α′	NUM
ap-5050	60	9	of	of	ADP
ap-5050	60	10	a	a	DET
ap-5050	60	11	particle	particle	NOUN
ap-5050	60	12	sliding	slide	VERB
ap-5050	60	13	will	will	AUX
ap-5050	60	14	be	be	AUX
ap-5050	60	15	stable	stable	ADJ
ap-5050	60	16	,	,	PUNCT
ap-5050	60	17	but	but	CCONJ
ap-5050	60	18	its	its	PRON
ap-5050	60	19	angular	angular	ADJ
ap-5050	60	20	acceleration	acceleration	NOUN
ap-5050	60	21	α′′	α′′	NOUN
ap-5050	60	22	will	will	AUX
ap-5050	60	23	be	be	AUX
ap-5050	60	24	equal	equal	ADJ
ap-5050	60	25	to	to	ADP
ap-5050	60	26	zero	zero	NUM
ap-5050	60	27	.	.	PUNCT
ap-5050	61	1	having	having	AUX
ap-5050	61	2	solved	solve	VERB
ap-5050	61	3	(	(	PUNCT
ap-5050	61	4	5	5	NUM
ap-5050	61	5	)	)	PUNCT
ap-5050	61	6	for	for	ADP
ap-5050	61	7	α′	α′	NUM
ap-5050	61	8	at	at	ADP
ap-5050	61	9	α′′	α′′	NOUN
ap-5050	61	10	=	=	SYM
ap-5050	61	11	0	0	NUM
ap-5050	61	12	,	,	PUNCT
ap-5050	61	13	we	we	PRON
ap-5050	61	14	obtain	obtain	VERB
ap-5050	61	15	:	:	PUNCT
ap-5050	61	16	α′	α′	NUM
ap-5050	62	1	=	=	SYM
ap-5050	62	2	ω	ω	NUM
ap-5050	62	3	−	−	NOUN
ap-5050	62	4	√	√	PROPN
ap-5050	62	5	fg	fg	PROPN
ap-5050	62	6	frr	frr	PROPN
ap-5050	62	7	.	.	PUNCT
ap-5050	63	1	(	(	PUNCT
ap-5050	63	2	6	6	NUM
ap-5050	63	3	)	)	PUNCT
ap-5050	63	4	for	for	ADP
ap-5050	63	5	example	example	NOUN
ap-5050	63	6	,	,	PUNCT
ap-5050	63	7	at	at	ADP
ap-5050	63	8	r	r	NOUN
ap-5050	63	9	=	=	SYM
ap-5050	63	10	0.1	0.1	NUM
ap-5050	63	11	m	m	NOUN
ap-5050	63	12	,	,	PUNCT
ap-5050	63	13	f	f	PROPN
ap-5050	64	1	=	=	NOUN
ap-5050	64	2	fr	fr	PROPN
ap-5050	64	3	=	=	PUNCT
ap-5050	64	4	0.3	0.3	NUM
ap-5050	64	5	and	and	CCONJ
ap-5050	64	6	ω	ω	NUM
ap-5050	64	7	=	=	SYM
ap-5050	64	8	20	20	NUM
ap-5050	64	9	s−1	s−1	PROPN
ap-5050	64	10	using	use	VERB
ap-5050	64	11	the	the	DET
ap-5050	64	12	formula	formula	NOUN
ap-5050	64	13	(	(	PUNCT
ap-5050	64	14	6	6	NUM
ap-5050	64	15	)	)	PUNCT
ap-5050	64	16	,	,	PUNCT
ap-5050	64	17	we	we	PRON
ap-5050	64	18	obtain	obtain	VERB
ap-5050	64	19	:	:	PUNCT
ap-5050	64	20	α′	α′	NUM
ap-5050	64	21	=	=	SYM
ap-5050	64	22	10.1	10.1	NUM
ap-5050	64	23	s−1	s−1	PROPN
ap-5050	64	24	.	.	PUNCT
ap-5050	65	1	thus	thus	ADV
ap-5050	65	2	,	,	PUNCT
ap-5050	65	3	the	the	DET
ap-5050	65	4	angular	angular	ADJ
ap-5050	65	5	velocity	velocity	NOUN
ap-5050	65	6	of	of	ADP
ap-5050	65	7	the	the	DET
ap-5050	65	8	particle	particle	NOUN
ap-5050	65	9	rotation	rotation	NOUN
ap-5050	65	10	in	in	ADP
ap-5050	65	11	the	the	DET
ap-5050	65	12	absolute	absolute	ADJ
ap-5050	65	13	motion	motion	NOUN
ap-5050	65	14	ω−α′	ω−α′	NUM
ap-5050	65	15	=	=	SYM
ap-5050	65	16	9.9	9.9	NUM
ap-5050	65	17	s−1	s−1	PROPN
ap-5050	65	18	will	will	AUX
ap-5050	65	19	be	be	AUX
ap-5050	65	20	twice	twice	ADV
ap-5050	65	21	less	less	ADJ
ap-5050	65	22	68	68	NUM
ap-5050	65	23	vol	vol	NOUN
ap-5050	65	24	.	.	PUNCT
ap-5050	66	1	59	59	NUM
ap-5050	67	1	no	no	NOUN
ap-5050	67	2	.	.	PUNCT
ap-5050	68	1	1/2019	1/2019	NUM
ap-5050	68	2	particle	particle	NOUN
ap-5050	68	3	motion	motion	NOUN
ap-5050	68	4	over	over	ADP
ap-5050	68	5	the	the	DET
ap-5050	68	6	edge	edge	NOUN
ap-5050	68	7	of	of	ADP
ap-5050	68	8	an	an	DET
ap-5050	68	9	inclined	inclined	ADJ
ap-5050	68	10	plane	plane	NOUN
ap-5050	68	11	than	than	ADP
ap-5050	68	12	the	the	DET
ap-5050	68	13	angular	angular	ADJ
ap-5050	68	14	velocity	velocity	NOUN
ap-5050	68	15	of	of	ADP
ap-5050	68	16	the	the	DET
ap-5050	68	17	disk	disk	NOUN
ap-5050	68	18	rotation	rotation	NOUN
ap-5050	68	19	.	.	PUNCT
ap-5050	69	1	the	the	DET
ap-5050	69	2	minimum	minimum	ADJ
ap-5050	69	3	value	value	NOUN
ap-5050	69	4	of	of	ADP
ap-5050	69	5	the	the	DET
ap-5050	69	6	angular	angular	ADJ
ap-5050	69	7	velocity	velocity	NOUN
ap-5050	69	8	of	of	ADP
ap-5050	69	9	the	the	DET
ap-5050	69	10	disk	disk	NOUN
ap-5050	69	11	rotation	rotation	NOUN
ap-5050	69	12	,	,	PUNCT
ap-5050	69	13	at	at	ADP
ap-5050	69	14	which	which	PRON
ap-5050	69	15	the	the	DET
ap-5050	69	16	particle	particle	NOUN
ap-5050	69	17	sliding	slide	VERB
ap-5050	69	18	is	be	AUX
ap-5050	69	19	possible	possible	ADJ
ap-5050	69	20	over	over	ADP
ap-5050	69	21	its	its	PRON
ap-5050	69	22	surface	surface	NOUN
ap-5050	69	23	,	,	PUNCT
ap-5050	69	24	is	be	AUX
ap-5050	69	25	determined	determine	VERB
ap-5050	69	26	from	from	ADP
ap-5050	69	27	the	the	DET
ap-5050	69	28	expression	expression	NOUN
ap-5050	69	29	(	(	PUNCT
ap-5050	69	30	6	6	NUM
ap-5050	69	31	):	):	PUNCT
ap-5050	69	32	ω	ω	PROPN
ap-5050	69	33	>	>	X
ap-5050	69	34	√	√	PROPN
ap-5050	69	35	fg	fg	PROPN
ap-5050	69	36	frr	frr	PROPN
ap-5050	69	37	.	.	PUNCT
ap-5050	70	1	(	(	PUNCT
ap-5050	70	2	7	7	X
ap-5050	70	3	)	)	PUNCT
ap-5050	70	4	for	for	ADP
ap-5050	70	5	the	the	DET
ap-5050	70	6	above	above	ADV
ap-5050	70	7	mentioned	mention	VERB
ap-5050	70	8	parameters	parameter	NOUN
ap-5050	70	9	ω	ω	X
ap-5050	70	10	>	>	X
ap-5050	70	11	9.9	9.9	NUM
ap-5050	70	12	s−1	s−1	PROPN
ap-5050	70	13	.	.	PUNCT
ap-5050	71	1	if	if	SCONJ
ap-5050	71	2	the	the	DET
ap-5050	71	3	angular	angular	ADJ
ap-5050	71	4	velocity	velocity	NOUN
ap-5050	71	5	of	of	ADP
ap-5050	71	6	the	the	DET
ap-5050	71	7	disk	disk	NOUN
ap-5050	71	8	rotation	rotation	NOUN
ap-5050	71	9	is	be	AUX
ap-5050	71	10	less	less	ADJ
ap-5050	71	11	than	than	ADP
ap-5050	71	12	this	this	PRON
ap-5050	71	13	,	,	PUNCT
ap-5050	71	14	a	a	DET
ap-5050	71	15	particle	particle	NOUN
ap-5050	71	16	will	will	AUX
ap-5050	71	17	rotate	rotate	VERB
ap-5050	71	18	together	together	ADV
ap-5050	71	19	with	with	ADP
ap-5050	71	20	it	it	PRON
ap-5050	71	21	without	without	ADP
ap-5050	71	22	sliding	slide	VERB
ap-5050	71	23	.	.	PUNCT
ap-5050	72	1	at	at	ADP
ap-5050	72	2	β	β	PROPN
ap-5050	72	3	6=	6=	ADP
ap-5050	72	4	0	0	NUM
ap-5050	72	5	,	,	PUNCT
ap-5050	72	6	the	the	DET
ap-5050	72	7	absolute	absolute	ADJ
ap-5050	72	8	particle	particle	NOUN
ap-5050	72	9	motion	motion	NOUN
ap-5050	72	10	will	will	AUX
ap-5050	72	11	be	be	AUX
ap-5050	72	12	spatial	spatial	ADJ
ap-5050	72	13	.	.	PUNCT
ap-5050	73	1	in	in	ADP
ap-5050	73	2	order	order	NOUN
ap-5050	73	3	to	to	PART
ap-5050	73	4	find	find	VERB
ap-5050	73	5	the	the	DET
ap-5050	73	6	pattern	pattern	NOUN
ap-5050	73	7	of	of	ADP
ap-5050	73	8	the	the	DET
ap-5050	73	9	sliding	slide	VERB
ap-5050	73	10	angle	angle	NOUN
ap-5050	73	11	change	change	NOUN
ap-5050	73	12	α	α	X
ap-5050	73	13	=	=	SYM
ap-5050	73	14	α(t	α(t	PROPN
ap-5050	73	15	)	)	PUNCT
ap-5050	73	16	,	,	PUNCT
ap-5050	73	17	let	let	VERB
ap-5050	73	18	us	we	PRON
ap-5050	73	19	use	use	VERB
ap-5050	73	20	fixed	fix	VERB
ap-5050	73	21	oxyz	oxyz	PROPN
ap-5050	73	22	coordinates	coordinate	NOUN
ap-5050	73	23	.	.	PUNCT
ap-5050	74	1	the	the	DET
ap-5050	74	2	differential	differential	ADJ
ap-5050	74	3	equation	equation	NOUN
ap-5050	74	4	of	of	ADP
ap-5050	74	5	motion	motion	NOUN
ap-5050	74	6	is	be	AUX
ap-5050	74	7	written	write	VERB
ap-5050	74	8	in	in	ADP
ap-5050	74	9	projections	projection	NOUN
ap-5050	74	10	onto	onto	ADP
ap-5050	74	11	the	the	DET
ap-5050	74	12	axes	axis	NOUN
ap-5050	74	13	of	of	ADP
ap-5050	74	14	this	this	DET
ap-5050	74	15	coordinate	coordinate	NOUN
ap-5050	74	16	system	system	NOUN
ap-5050	74	17	.	.	PUNCT
ap-5050	75	1	the	the	DET
ap-5050	75	2	parametrical	parametrical	ADJ
ap-5050	75	3	equations	equation	NOUN
ap-5050	75	4	of	of	ADP
ap-5050	75	5	an	an	DET
ap-5050	75	6	ellipse	ellipse	NOUN
ap-5050	75	7	that	that	PRON
ap-5050	75	8	is	be	AUX
ap-5050	75	9	created	create	VERB
ap-5050	75	10	as	as	ADP
ap-5050	75	11	a	a	DET
ap-5050	75	12	result	result	NOUN
ap-5050	75	13	of	of	ADP
ap-5050	75	14	the	the	DET
ap-5050	75	15	intersection	intersection	NOUN
ap-5050	75	16	of	of	ADP
ap-5050	75	17	an	an	DET
ap-5050	75	18	inclined	inclined	ADJ
ap-5050	75	19	plane	plane	NOUN
ap-5050	75	20	and	and	CCONJ
ap-5050	75	21	a	a	DET
ap-5050	75	22	vertical	vertical	ADJ
ap-5050	75	23	cylinder	cylinder	NOUN
ap-5050	75	24	with	with	ADP
ap-5050	75	25	radius	radius	NOUN
ap-5050	75	26	r	r	NOUN
ap-5050	75	27	,	,	PUNCT
ap-5050	75	28	are	be	AUX
ap-5050	75	29	written	write	VERB
ap-5050	75	30	as	as	ADP
ap-5050	75	31	:	:	PUNCT
ap-5050	75	32	x	x	SYM
ap-5050	75	33	=	=	SYM
ap-5050	75	34	r	r	NOUN
ap-5050	75	35	cosα	cosα	NOUN
ap-5050	75	36	,	,	PUNCT
ap-5050	75	37	y	y	PROPN
ap-5050	75	38	=	=	SYM
ap-5050	75	39	r	r	NOUN
ap-5050	75	40	sinα	sinα	NOUN
ap-5050	75	41	,	,	PUNCT
ap-5050	75	42	z	z	NOUN
ap-5050	76	1	=	=	PUNCT
ap-5050	76	2	r	r	NOUN
ap-5050	76	3	tg	tg	PROPN
ap-5050	76	4	β	β	PROPN
ap-5050	76	5	cosα	cosα	PROPN
ap-5050	76	6	,	,	PUNCT
ap-5050	76	7	(	(	PUNCT
ap-5050	76	8	8)	8)	NUM
ap-5050	76	9	where	where	SCONJ
ap-5050	76	10	β	β	X
ap-5050	76	11	—	—	PUNCT
ap-5050	76	12	the	the	DET
ap-5050	76	13	angle	angle	NOUN
ap-5050	76	14	of	of	ADP
ap-5050	76	15	the	the	DET
ap-5050	76	16	plane	plane	NOUN
ap-5050	76	17	inclination	inclination	NOUN
ap-5050	76	18	(	(	PUNCT
ap-5050	76	19	figure	figure	NOUN
ap-5050	76	20	1b	1b	NUM
ap-5050	76	21	)	)	PUNCT
ap-5050	76	22	.	.	PUNCT
ap-5050	77	1	when	when	SCONJ
ap-5050	77	2	a	a	DET
ap-5050	77	3	plane	plane	NOUN
ap-5050	77	4	segment	segment	NOUN
ap-5050	77	5	rotates	rotate	VERB
ap-5050	77	6	with	with	ADP
ap-5050	77	7	the	the	DET
ap-5050	77	8	angular	angular	ADJ
ap-5050	77	9	velocity	velocity	NOUN
ap-5050	77	10	ω	ω	PROPN
ap-5050	77	11	,	,	PUNCT
ap-5050	77	12	a	a	DET
ap-5050	77	13	particle	particle	NOUN
ap-5050	77	14	in	in	ADP
ap-5050	77	15	an	an	DET
ap-5050	77	16	absolute	absolute	ADJ
ap-5050	77	17	motion	motion	NOUN
ap-5050	77	18	has	have	VERB
ap-5050	77	19	to	to	PART
ap-5050	77	20	rotate	rotate	VERB
ap-5050	77	21	in	in	ADP
ap-5050	77	22	an	an	DET
ap-5050	77	23	ellipse	ellipse	NOUN
ap-5050	77	24	(	(	PUNCT
ap-5050	77	25	8)	8)	NUM
ap-5050	77	26	.	.	PUNCT
ap-5050	78	1	during	during	ADP
ap-5050	78	2	the	the	DET
ap-5050	78	3	time	time	NOUN
ap-5050	78	4	t	t	PROPN
ap-5050	78	5	,	,	PUNCT
ap-5050	78	6	an	an	DET
ap-5050	78	7	ellipse	ellipse	NOUN
ap-5050	78	8	rotates	rotate	VERB
ap-5050	78	9	through	through	ADP
ap-5050	78	10	the	the	DET
ap-5050	78	11	angle	angle	NOUN
ap-5050	78	12	ωt	ωt	ADP
ap-5050	78	13	in	in	ADP
ap-5050	78	14	the	the	DET
ap-5050	78	15	direction	direction	NOUN
ap-5050	78	16	opposite	opposite	ADV
ap-5050	78	17	to	to	ADP
ap-5050	78	18	the	the	DET
ap-5050	78	19	particle	particle	NOUN
ap-5050	78	20	sliding	slide	VERB
ap-5050	78	21	through	through	ADP
ap-5050	78	22	the	the	DET
ap-5050	78	23	angle	angle	NOUN
ap-5050	78	24	α	α	NOUN
ap-5050	78	25	.	.	PUNCT
ap-5050	79	1	having	having	AUX
ap-5050	79	2	considered	consider	VERB
ap-5050	79	3	the	the	DET
ap-5050	79	4	angle	angle	NOUN
ap-5050	79	5	α	α	PRON
ap-5050	79	6	to	to	PART
ap-5050	79	7	be	be	AUX
ap-5050	79	8	sufficient	sufficient	ADJ
ap-5050	79	9	,	,	PUNCT
ap-5050	79	10	let	let	VERB
ap-5050	79	11	us	we	PRON
ap-5050	79	12	find	find	VERB
ap-5050	79	13	the	the	DET
ap-5050	79	14	parametrical	parametrical	ADJ
ap-5050	79	15	equations	equation	NOUN
ap-5050	79	16	of	of	ADP
ap-5050	79	17	an	an	DET
ap-5050	79	18	absolute	absolute	ADJ
ap-5050	79	19	particle	particle	NOUN
ap-5050	79	20	motion	motion	NOUN
ap-5050	79	21	.	.	PUNCT
ap-5050	80	1	for	for	ADP
ap-5050	80	2	this	this	DET
ap-5050	80	3	purpose	purpose	NOUN
ap-5050	80	4	,	,	PUNCT
ap-5050	80	5	let	let	VERB
ap-5050	80	6	us	we	PRON
ap-5050	80	7	turn	turn	VERB
ap-5050	80	8	the	the	DET
ap-5050	80	9	ellipse	ellipse	NOUN
ap-5050	80	10	(	(	PUNCT
ap-5050	80	11	8)	8)	NUM
ap-5050	80	12	through	through	ADP
ap-5050	80	13	the	the	DET
ap-5050	80	14	angle	angle	NOUN
ap-5050	80	15	−ωt	−ωt	NOUN
ap-5050	80	16	.	.	PUNCT
ap-5050	81	1	the	the	DET
ap-5050	81	2	coordinate	coordinate	NOUN
ap-5050	81	3	z	z	NOUN
ap-5050	81	4	does	do	AUX
ap-5050	81	5	not	not	PART
ap-5050	81	6	depend	depend	VERB
ap-5050	81	7	on	on	ADP
ap-5050	81	8	this	this	DET
ap-5050	81	9	turn	turn	NOUN
ap-5050	81	10	,	,	PUNCT
ap-5050	81	11	that	that	PRON
ap-5050	81	12	is	be	AUX
ap-5050	81	13	why	why	SCONJ
ap-5050	81	14	,	,	PUNCT
ap-5050	81	15	it	it	PRON
ap-5050	81	16	remains	remain	VERB
ap-5050	81	17	unchanged	unchanged	ADJ
ap-5050	81	18	.	.	PUNCT
ap-5050	82	1	after	after	ADP
ap-5050	82	2	such	such	DET
ap-5050	82	3	a	a	DET
ap-5050	82	4	turn	turn	NOUN
ap-5050	82	5	,	,	PUNCT
ap-5050	82	6	we	we	PRON
ap-5050	82	7	obtain	obtain	VERB
ap-5050	82	8	parametrical	parametrical	ADJ
ap-5050	82	9	equations	equation	NOUN
ap-5050	82	10	of	of	ADP
ap-5050	82	11	the	the	DET
ap-5050	82	12	absolute	absolute	ADJ
ap-5050	82	13	motion	motion	NOUN
ap-5050	82	14	of	of	ADP
ap-5050	82	15	a	a	DET
ap-5050	82	16	particle	particle	NOUN
ap-5050	82	17	:	:	PUNCT
ap-5050	82	18	xa	xa	PROPN
ap-5050	82	19	=	=	PUNCT
ap-5050	82	20	r	r	PROPN
ap-5050	82	21	cosα	cosα	PROPN
ap-5050	82	22	cos(−ωt)−r	cos(−ωt)−r	PROPN
ap-5050	82	23	sinα	sinα	PROPN
ap-5050	82	24	sin(−ωt	sin(−ωt	PROPN
ap-5050	82	25	)	)	PUNCT
ap-5050	83	1	=	=	SYM
ap-5050	83	2	r	r	NOUN
ap-5050	83	3	cos(ωt−	cos(ωt−	NOUN
ap-5050	83	4	α	α	NOUN
ap-5050	83	5	)	)	PUNCT
ap-5050	83	6	,	,	PUNCT
ap-5050	83	7	ya	ya	NOUN
ap-5050	84	1	=	=	PUNCT
ap-5050	84	2	r	r	NOUN
ap-5050	84	3	cosα	cosα	NOUN
ap-5050	84	4	sin(−ωt)−r	sin(−ωt)−r	PROPN
ap-5050	84	5	sinα	sinα	NOUN
ap-5050	84	6	cos(−ωt	cos(−ωt	NOUN
ap-5050	84	7	)	)	PUNCT
ap-5050	85	1	=	=	SYM
ap-5050	86	1	−r	−r	PROPN
ap-5050	86	2	sin(ωt−	sin(ωt−	NOUN
ap-5050	86	3	α	α	NOUN
ap-5050	86	4	)	)	PUNCT
ap-5050	86	5	,	,	PUNCT
ap-5050	86	6	za	za	PROPN
ap-5050	86	7	=	=	PUNCT
ap-5050	86	8	−r	−r	PROPN
ap-5050	86	9	tg	tg	PROPN
ap-5050	86	10	β	β	PROPN
ap-5050	86	11	cosα	cosα	PROPN
ap-5050	86	12	.	.	PUNCT
ap-5050	87	1	(	(	PUNCT
ap-5050	87	2	9	9	X
ap-5050	87	3	)	)	PUNCT
ap-5050	87	4	having	having	AUX
ap-5050	87	5	differentiated	differentiate	VERB
ap-5050	87	6	(	(	PUNCT
ap-5050	87	7	9	9	NUM
ap-5050	87	8	)	)	PUNCT
ap-5050	87	9	,	,	PUNCT
ap-5050	87	10	we	we	PRON
ap-5050	87	11	obtain	obtain	VERB
ap-5050	87	12	the	the	DET
ap-5050	87	13	projections	projection	NOUN
ap-5050	87	14	of	of	ADP
ap-5050	87	15	the	the	DET
ap-5050	87	16	absolute	absolute	ADJ
ap-5050	87	17	velocity	velocity	NOUN
ap-5050	87	18	of	of	ADP
ap-5050	87	19	a	a	DET
ap-5050	87	20	particle	particle	NOUN
ap-5050	87	21	:	:	PUNCT
ap-5050	87	22	x′a	x′a	PUNCT
ap-5050	87	23	=	=	X
ap-5050	87	24	−r(ω	−r(ω	VERB
ap-5050	87	25	−	−	NOUN
ap-5050	87	26	α′	α′	NUM
ap-5050	87	27	)	)	PUNCT
ap-5050	87	28	sin(ωt−	sin(ωt−	NOUN
ap-5050	87	29	α	α	NOUN
ap-5050	87	30	)	)	PUNCT
ap-5050	87	31	,	,	PUNCT
ap-5050	87	32	y′a	y′a	PROPN
ap-5050	87	33	=	=	SYM
ap-5050	87	34	−r(ω	−r(ω	VERB
ap-5050	87	35	−	−	PROPN
ap-5050	87	36	α′	α′	NUM
ap-5050	87	37	)	)	PUNCT
ap-5050	87	38	cos(ωt−	cos(ωt−	NOUN
ap-5050	87	39	α	α	NOUN
ap-5050	87	40	)	)	PUNCT
ap-5050	87	41	,	,	PUNCT
ap-5050	87	42	z′a	z′a	X
ap-5050	87	43	=	=	SYM
ap-5050	87	44	−rα′	−rα′	NOUN
ap-5050	87	45	tg	tg	NUM
ap-5050	87	46	β	β	PROPN
ap-5050	87	47	sinα	sinα	PROPN
ap-5050	87	48	.	.	PUNCT
ap-5050	88	1	(	(	PUNCT
ap-5050	88	2	10	10	NUM
ap-5050	88	3	)	)	PUNCT
ap-5050	88	4	its	its	PRON
ap-5050	88	5	value	value	NOUN
ap-5050	88	6	is	be	AUX
ap-5050	88	7	found	find	VERB
ap-5050	88	8	as	as	ADP
ap-5050	88	9	a	a	DET
ap-5050	88	10	geometric	geometric	ADJ
ap-5050	88	11	sum	sum	NOUN
ap-5050	88	12	of	of	ADP
ap-5050	88	13	the	the	DET
ap-5050	88	14	projections	projection	NOUN
ap-5050	88	15	(	(	PUNCT
ap-5050	88	16	10	10	NUM
ap-5050	88	17	):	):	PUNCT
ap-5050	88	18	va	va	NOUN
ap-5050	88	19	=	=	PUNCT
ap-5050	88	20	√	√	PROPN
ap-5050	88	21	(	(	PUNCT
ap-5050	88	22	x′a)2	x′a)2	PROPN
ap-5050	88	23	+	+	CCONJ
ap-5050	88	24	(	(	PUNCT
ap-5050	88	25	y′a)2	y′a)2	PROPN
ap-5050	88	26	+	+	CCONJ
ap-5050	88	27	(	(	PUNCT
ap-5050	88	28	z′a)2	z′a)2	NOUN
ap-5050	88	29	=	=	SYM
ap-5050	88	30	r	r	NOUN
ap-5050	88	31	√	√	NUM
ap-5050	88	32	(	(	PUNCT
ap-5050	88	33	ω	ω	NOUN
ap-5050	88	34	−	−	PROPN
ap-5050	88	35	α′)2	α′)2	PROPN
ap-5050	88	36	+	+	CCONJ
ap-5050	88	37	(	(	PUNCT
ap-5050	88	38	α′)2	α′)2	NOUN
ap-5050	88	39	tg2	tg2	ADJ
ap-5050	88	40	β	β	X
ap-5050	88	41	sin2	sin2	NOUN
ap-5050	88	42	α	α	PRON
ap-5050	88	43	.	.	PUNCT
ap-5050	89	1	(	(	PUNCT
ap-5050	89	2	11	11	NUM
ap-5050	89	3	)	)	PUNCT
ap-5050	89	4	let	let	VERB
ap-5050	89	5	us	we	PRON
ap-5050	89	6	find	find	VERB
ap-5050	89	7	the	the	DET
ap-5050	89	8	projections	projection	NOUN
ap-5050	89	9	of	of	ADP
ap-5050	89	10	the	the	DET
ap-5050	89	11	unit	unit	NOUN
ap-5050	89	12	vector	vector	NOUN
ap-5050	89	13	,	,	PUNCT
ap-5050	89	14	which	which	PRON
ap-5050	89	15	sets	set	VERB
ap-5050	89	16	the	the	DET
ap-5050	89	17	direction	direction	NOUN
ap-5050	89	18	of	of	ADP
ap-5050	89	19	the	the	DET
ap-5050	89	20	absolute	absolute	ADJ
ap-5050	89	21	velocity	velocity	NOUN
ap-5050	89	22	of	of	ADP
ap-5050	89	23	a	a	DET
ap-5050	89	24	particle	particle	NOUN
ap-5050	89	25	,	,	PUNCT
ap-5050	89	26	by	by	ADP
ap-5050	89	27	dividing	divide	VERB
ap-5050	89	28	the	the	DET
ap-5050	89	29	expressions	expression	NOUN
ap-5050	89	30	(	(	PUNCT
ap-5050	89	31	10	10	NUM
ap-5050	89	32	)	)	PUNCT
ap-5050	89	33	by	by	ADP
ap-5050	89	34	the	the	DET
ap-5050	89	35	velocity	velocity	NOUN
ap-5050	89	36	value	value	NOUN
ap-5050	89	37	(	(	PUNCT
ap-5050	89	38	11	11	NUM
ap-5050	89	39	):	):	PUNCT
ap-5050	89	40	tv	tv	NOUN
ap-5050	89	41	ax	ax	NOUN
ap-5050	89	42	=	=	NOUN
ap-5050	90	1	−	−	PROPN
ap-5050	90	2	(	(	PUNCT
ap-5050	90	3	ω	ω	NOUN
ap-5050	90	4	−	−	NOUN
ap-5050	90	5	α′	α′	NUM
ap-5050	90	6	)	)	PUNCT
ap-5050	90	7	sin(ωt−	sin(ωt−	NOUN
ap-5050	90	8	α	α	NOUN
ap-5050	90	9	)	)	PUNCT
ap-5050	90	10	a	a	PRON
ap-5050	90	11	,	,	PUNCT
ap-5050	90	12	tv	tv	NOUN
ap-5050	90	13	ay	ay	NOUN
ap-5050	91	1	=	=	PUNCT
ap-5050	91	2	−	−	PROPN
ap-5050	91	3	(	(	PUNCT
ap-5050	91	4	ω	ω	NOUN
ap-5050	91	5	−	−	NOUN
ap-5050	91	6	α′	α′	NUM
ap-5050	91	7	)	)	PUNCT
ap-5050	91	8	cos(ωt−	cos(ωt−	NOUN
ap-5050	91	9	α	α	NOUN
ap-5050	91	10	)	)	PUNCT
ap-5050	91	11	a	a	PRON
ap-5050	91	12	,	,	PUNCT
ap-5050	91	13	tv	tv	NOUN
ap-5050	91	14	az	az	NOUN
ap-5050	91	15	=	=	PUNCT
ap-5050	92	1	α′	α′	NUM
ap-5050	92	2	tg	tg	PROPN
ap-5050	92	3	β	β	PROPN
ap-5050	92	4	sinα	sinα	PROPN
ap-5050	92	5	a	a	DET
ap-5050	92	6	,	,	PUNCT
ap-5050	92	7	(	(	PUNCT
ap-5050	92	8	12	12	NUM
ap-5050	92	9	)	)	PUNCT
ap-5050	92	10	where	where	SCONJ
ap-5050	92	11	a	a	DET
ap-5050	92	12	=	=	NOUN
ap-5050	92	13	√	√	PROPN
ap-5050	92	14	(	(	PUNCT
ap-5050	92	15	ω	ω	NOUN
ap-5050	92	16	−	−	PROPN
ap-5050	92	17	α′)2	α′)2	PROPN
ap-5050	92	18	+	+	CCONJ
ap-5050	92	19	(	(	PUNCT
ap-5050	92	20	α′)2	α′)2	NOUN
ap-5050	92	21	tg2	tg2	ADJ
ap-5050	92	22	β	β	X
ap-5050	92	23	sin2	sin2	NOUN
ap-5050	92	24	α	α	X
ap-5050	92	25	.	.	PUNCT
ap-5050	93	1	as	as	ADP
ap-5050	93	2	a	a	DET
ap-5050	93	3	result	result	NOUN
ap-5050	93	4	of	of	ADP
ap-5050	93	5	the	the	DET
ap-5050	93	6	differentiation	differentiation	NOUN
ap-5050	93	7	of	of	ADP
ap-5050	93	8	(	(	PUNCT
ap-5050	93	9	10	10	NUM
ap-5050	93	10	)	)	PUNCT
ap-5050	93	11	,	,	PUNCT
ap-5050	93	12	we	we	PRON
ap-5050	93	13	obtain	obtain	VERB
ap-5050	93	14	the	the	DET
ap-5050	93	15	projections	projection	NOUN
ap-5050	93	16	of	of	ADP
ap-5050	93	17	the	the	DET
ap-5050	93	18	absolute	absolute	ADJ
ap-5050	93	19	acceleration	acceleration	NOUN
ap-5050	93	20	w	w	NOUN
ap-5050	93	21	of	of	ADP
ap-5050	93	22	a	a	DET
ap-5050	93	23	particle	particle	NOUN
ap-5050	93	24	:	:	PUNCT
ap-5050	93	25	x′′a	x′′a	PROPN
ap-5050	93	26	=	=	PUNCT
ap-5050	93	27	rα′′	rα′′	VERB
ap-5050	93	28	sin(ωt−	sin(ωt−	NOUN
ap-5050	93	29	α)−r(ω	α)−r(ω	SYM
ap-5050	93	30	−	−	PROPN
ap-5050	94	1	α′)2	α′)2	PROPN
ap-5050	94	2	cos(ωt−	cos(ωt−	NOUN
ap-5050	94	3	α	α	NOUN
ap-5050	94	4	)	)	PUNCT
ap-5050	94	5	,	,	PUNCT
ap-5050	94	6	y′′a	y′′a	PROPN
ap-5050	94	7	=	=	PUNCT
ap-5050	94	8	rα′′	rα′′	PROPN
ap-5050	94	9	cos(ωt−	cos(ωt−	NOUN
ap-5050	94	10	α	α	NOUN
ap-5050	94	11	)	)	PUNCT
ap-5050	95	1	+	+	PROPN
ap-5050	95	2	r(ω	r(ω	ADV
ap-5050	95	3	−	−	PUNCT
ap-5050	95	4	α′)2	α′)2	PROPN
ap-5050	95	5	sin(ωt−	sin(ωt−	NOUN
ap-5050	95	6	α	α	NOUN
ap-5050	95	7	)	)	PUNCT
ap-5050	95	8	,	,	PUNCT
ap-5050	95	9	z′′a	z′′a	PROPN
ap-5050	95	10	=	=	PUNCT
ap-5050	95	11	rα′′	rα′′	VERB
ap-5050	95	12	tg	tg	PROPN
ap-5050	95	13	β	β	PROPN
ap-5050	96	1	sinα+r(α′)2	sinα+r(α′)2	INTJ
ap-5050	96	2	tg	tg	INTJ
ap-5050	96	3	β	β	PROPN
ap-5050	96	4	cosα	cosα	PROPN
ap-5050	96	5	.	.	PUNCT
ap-5050	97	1	(	(	PUNCT
ap-5050	97	2	13	13	NUM
ap-5050	97	3	)	)	PUNCT
ap-5050	97	4	let	let	VERB
ap-5050	97	5	us	we	PRON
ap-5050	97	6	write	write	VERB
ap-5050	97	7	the	the	DET
ap-5050	97	8	equation	equation	NOUN
ap-5050	97	9	mw	mw	NOUN
ap-5050	97	10	=	=	PUNCT
ap-5050	97	11	∑	∑	PROPN
ap-5050	97	12	f	f	PROPN
ap-5050	97	13	in	in	ADP
ap-5050	97	14	projections	projection	NOUN
ap-5050	97	15	onto	onto	ADP
ap-5050	97	16	the	the	DET
ap-5050	97	17	axes	axis	NOUN
ap-5050	97	18	of	of	ADP
ap-5050	97	19	the	the	DET
ap-5050	97	20	oxyz	oxyz	NOUN
ap-5050	97	21	coordinate	coordinate	NOUN
ap-5050	97	22	system	system	NOUN
ap-5050	97	23	.	.	PUNCT
ap-5050	98	1	for	for	ADP
ap-5050	98	2	this	this	DET
ap-5050	98	3	purpose	purpose	NOUN
ap-5050	98	4	,	,	PUNCT
ap-5050	98	5	it	it	PRON
ap-5050	98	6	is	be	AUX
ap-5050	98	7	necessary	necessary	ADJ
ap-5050	98	8	to	to	PART
ap-5050	98	9	determine	determine	VERB
ap-5050	98	10	the	the	DET
ap-5050	98	11	forces	force	NOUN
ap-5050	98	12	,	,	PUNCT
ap-5050	98	13	that	that	PRON
ap-5050	98	14	act	act	VERB
ap-5050	98	15	on	on	ADP
ap-5050	98	16	a	a	DET
ap-5050	98	17	particle	particle	NOUN
ap-5050	98	18	as	as	ADV
ap-5050	98	19	well	well	ADV
ap-5050	98	20	as	as	ADP
ap-5050	98	21	their	their	PRON
ap-5050	98	22	direction	direction	NOUN
ap-5050	98	23	.	.	PUNCT
ap-5050	99	1	let	let	VERB
ap-5050	99	2	us	we	PRON
ap-5050	99	3	find	find	VERB
ap-5050	99	4	the	the	DET
ap-5050	99	5	direction	direction	NOUN
ap-5050	99	6	of	of	ADP
ap-5050	99	7	the	the	DET
ap-5050	99	8	reaction	reaction	NOUN
ap-5050	99	9	force	force	NOUN
ap-5050	99	10	n	n	PROPN
ap-5050	99	11	of	of	ADP
ap-5050	99	12	a	a	DET
ap-5050	99	13	flat	flat	ADJ
ap-5050	99	14	segment	segment	NOUN
ap-5050	99	15	and	and	CCONJ
ap-5050	99	16	the	the	DET
ap-5050	99	17	reaction	reaction	NOUN
ap-5050	99	18	force	force	NOUN
ap-5050	99	19	nr	nr	PROPN
ap-5050	99	20	of	of	ADP
ap-5050	99	21	the	the	DET
ap-5050	99	22	inner	inner	ADJ
ap-5050	99	23	surface	surface	NOUN
ap-5050	99	24	of	of	ADP
ap-5050	99	25	a	a	DET
ap-5050	99	26	cylinder	cylinder	NOUN
ap-5050	99	27	(	(	PUNCT
ap-5050	99	28	figure	figure	NOUN
ap-5050	99	29	1b	1b	NUM
ap-5050	99	30	)	)	PUNCT
ap-5050	99	31	.	.	PUNCT
ap-5050	100	1	the	the	DET
ap-5050	100	2	vector	vector	NOUN
ap-5050	100	3	force	force	NOUN
ap-5050	100	4	of	of	ADP
ap-5050	100	5	the	the	DET
ap-5050	100	6	reaction	reaction	NOUN
ap-5050	100	7	n	n	NUM
ap-5050	100	8	is	be	AUX
ap-5050	100	9	projected	project	VERB
ap-5050	100	10	onto	onto	ADP
ap-5050	100	11	two	two	NUM
ap-5050	100	12	axes	axis	NOUN
ap-5050	100	13	,	,	PUNCT
ap-5050	100	14	namely	namely	ADV
ap-5050	100	15	,	,	PUNCT
ap-5050	100	16	ox	ox	NOUN
ap-5050	100	17	and	and	CCONJ
ap-5050	100	18	oz	oz	INTJ
ap-5050	100	19	.	.	PUNCT
ap-5050	100	20	let	let	VERB
ap-5050	100	21	us	we	PRON
ap-5050	100	22	write	write	VERB
ap-5050	100	23	its	its	PRON
ap-5050	100	24	projections	projection	NOUN
ap-5050	100	25	on	on	ADP
ap-5050	100	26	coordinate	coordinate	NOUN
ap-5050	100	27	axes	axis	NOUN
ap-5050	100	28	through	through	ADP
ap-5050	100	29	the	the	DET
ap-5050	100	30	angle	angle	NOUN
ap-5050	100	31	β	β	NOUN
ap-5050	101	1	:	:	PUNCT
ap-5050	101	2	nx	nx	PROPN
ap-5050	101	3	=	=	SYM
ap-5050	101	4	n	n	PROPN
ap-5050	101	5	sin	sin	VERB
ap-5050	101	6	β	β	NOUN
ap-5050	101	7	,	,	PUNCT
ap-5050	101	8	ny	ny	PROPN
ap-5050	101	9	=	=	SYM
ap-5050	101	10	0	0	NUM
ap-5050	101	11	,	,	PUNCT
ap-5050	101	12	nz	nz	NOUN
ap-5050	101	13	=	=	SYM
ap-5050	101	14	n	n	NUM
ap-5050	101	15	cosβ	cosβ	NOUN
ap-5050	101	16	.	.	PUNCT
ap-5050	102	1	(	(	PUNCT
ap-5050	102	2	14	14	NUM
ap-5050	102	3	)	)	PUNCT
ap-5050	102	4	the	the	DET
ap-5050	102	5	projections	projection	NOUN
ap-5050	102	6	(	(	PUNCT
ap-5050	102	7	14	14	NUM
ap-5050	102	8	)	)	PUNCT
ap-5050	102	9	are	be	AUX
ap-5050	102	10	written	write	VERB
ap-5050	102	11	without	without	ADP
ap-5050	102	12	taking	take	VERB
ap-5050	102	13	into	into	ADP
ap-5050	102	14	consideration	consideration	NOUN
ap-5050	102	15	the	the	DET
ap-5050	102	16	rotating	rotate	VERB
ap-5050	102	17	motion	motion	NOUN
ap-5050	102	18	of	of	ADP
ap-5050	102	19	a	a	DET
ap-5050	102	20	plane	plane	NOUN
ap-5050	102	21	segment	segment	NOUN
ap-5050	102	22	.	.	PUNCT
ap-5050	103	1	in	in	ADP
ap-5050	103	2	order	order	NOUN
ap-5050	103	3	to	to	PART
ap-5050	103	4	exert	exert	VERB
ap-5050	103	5	the	the	DET
ap-5050	103	6	force	force	NOUN
ap-5050	103	7	n	n	CCONJ
ap-5050	103	8	in	in	ADP
ap-5050	103	9	the	the	DET
ap-5050	103	10	point	point	NOUN
ap-5050	103	11	of	of	ADP
ap-5050	103	12	the	the	DET
ap-5050	103	13	particle	particle	NOUN
ap-5050	103	14	location	location	NOUN
ap-5050	103	15	,	,	PUNCT
ap-5050	103	16	the	the	DET
ap-5050	103	17	projections	projection	NOUN
ap-5050	103	18	(	(	PUNCT
ap-5050	103	19	14	14	NUM
ap-5050	103	20	)	)	PUNCT
ap-5050	103	21	must	must	AUX
ap-5050	103	22	be	be	AUX
ap-5050	103	23	turned	turn	VERB
ap-5050	103	24	through	through	ADP
ap-5050	103	25	the	the	DET
ap-5050	103	26	angle	angle	NOUN
ap-5050	103	27	−ωt	−ωt	NOUN
ap-5050	103	28	about	about	ADP
ap-5050	103	29	oz	oz	NOUN
ap-5050	103	30	axis	axis	NOUN
ap-5050	103	31	.	.	PUNCT
ap-5050	104	1	after	after	ADP
ap-5050	104	2	this	this	PRON
ap-5050	104	3	,	,	PUNCT
ap-5050	104	4	they	they	PRON
ap-5050	104	5	take	take	VERB
ap-5050	104	6	the	the	DET
ap-5050	104	7	following	follow	VERB
ap-5050	104	8	form	form	NOUN
ap-5050	104	9	:	:	PUNCT
ap-5050	104	10	nωx	nωx	PROPN
ap-5050	104	11	=	=	PUNCT
ap-5050	104	12	n	n	PRON
ap-5050	104	13	sin	sin	VERB
ap-5050	104	14	β	β	PROPN
ap-5050	104	15	cosωt	cosωt	PROPN
ap-5050	104	16	,	,	PUNCT
ap-5050	104	17	nωy	nωy	NOUN
ap-5050	104	18	=	=	SYM
ap-5050	104	19	−n	−n	ADV
ap-5050	104	20	sin	sin	VERB
ap-5050	104	21	β	β	PROPN
ap-5050	104	22	sinωt	sinωt	NOUN
ap-5050	104	23	,	,	PUNCT
ap-5050	104	24	nωz	nωz	NOUN
ap-5050	104	25	=	=	SYM
ap-5050	104	26	n	n	NUM
ap-5050	104	27	cosβ	cosβ	NOUN
ap-5050	104	28	.	.	PUNCT
ap-5050	105	1	(	(	PUNCT
ap-5050	105	2	15	15	NUM
ap-5050	105	3	)	)	PUNCT
ap-5050	105	4	the	the	DET
ap-5050	105	5	reaction	reaction	NOUN
ap-5050	105	6	nr	nr	PROPN
ap-5050	105	7	is	be	AUX
ap-5050	105	8	directed	direct	VERB
ap-5050	105	9	towards	towards	ADP
ap-5050	105	10	the	the	DET
ap-5050	105	11	centre	centre	NOUN
ap-5050	105	12	of	of	ADP
ap-5050	105	13	the	the	DET
ap-5050	105	14	cylinder	cylinder	NOUN
ap-5050	105	15	perpendicular	perpendicular	NOUN
ap-5050	105	16	to	to	ADP
ap-5050	105	17	its	its	PRON
ap-5050	105	18	surface	surface	NOUN
ap-5050	105	19	,	,	PUNCT
ap-5050	105	20	that	that	PRON
ap-5050	105	21	is	be	AUX
ap-5050	105	22	to	to	PART
ap-5050	105	23	say	say	VERB
ap-5050	105	24	,	,	PUNCT
ap-5050	105	25	perpendicular	perpendicular	ADJ
ap-5050	105	26	to	to	ADP
ap-5050	105	27	the	the	DET
ap-5050	105	28	circle	circle	NOUN
ap-5050	105	29	,	,	PUNCT
ap-5050	105	30	which	which	PRON
ap-5050	105	31	is	be	AUX
ap-5050	105	32	set	set	VERB
ap-5050	105	33	by	by	ADP
ap-5050	105	34	the	the	DET
ap-5050	105	35	first	first	ADJ
ap-5050	105	36	two	two	NUM
ap-5050	105	37	equations	equation	NOUN
ap-5050	105	38	in	in	ADP
ap-5050	105	39	(	(	PUNCT
ap-5050	105	40	8)	8)	NUM
ap-5050	105	41	.	.	PUNCT
ap-5050	106	1	the	the	DET
ap-5050	106	2	projections	projection	NOUN
ap-5050	106	3	of	of	ADP
ap-5050	106	4	the	the	DET
ap-5050	106	5	reaction	reaction	NOUN
ap-5050	106	6	force	force	NOUN
ap-5050	106	7	on	on	ADP
ap-5050	106	8	the	the	DET
ap-5050	106	9	coordinate	coordinate	NOUN
ap-5050	106	10	axes	axis	NOUN
ap-5050	106	11	are	be	AUX
ap-5050	106	12	written	write	VERB
ap-5050	106	13	as	as	ADP
ap-5050	106	14	:	:	PUNCT
ap-5050	106	15	nrx	nrx	NOUN
ap-5050	106	16	=	=	SYM
ap-5050	106	17	−nr	−nr	PROPN
ap-5050	106	18	cosα	cosα	PROPN
ap-5050	106	19	,	,	PUNCT
ap-5050	106	20	nry	nry	PROPN
ap-5050	106	21	=	=	SYM
ap-5050	106	22	−nr	−nr	PROPN
ap-5050	106	23	sinα	sinα	NOUN
ap-5050	106	24	,	,	PUNCT
ap-5050	106	25	nrz	nrz	NOUN
ap-5050	106	26	=	=	NOUN
ap-5050	107	1	0	0	X
ap-5050	107	2	.	.	PUNCT
ap-5050	108	1	(	(	PUNCT
ap-5050	108	2	16	16	NUM
ap-5050	108	3	)	)	PUNCT
ap-5050	108	4	after	after	ADP
ap-5050	108	5	the	the	DET
ap-5050	108	6	projections	projection	NOUN
ap-5050	108	7	(	(	PUNCT
ap-5050	108	8	16	16	NUM
ap-5050	108	9	)	)	PUNCT
ap-5050	108	10	are	be	AUX
ap-5050	108	11	turned	turn	VERB
ap-5050	108	12	through	through	ADP
ap-5050	108	13	the	the	DET
ap-5050	108	14	angle	angle	NOUN
ap-5050	108	15	−ωt	−ωt	NOUN
ap-5050	108	16	about	about	ADP
ap-5050	108	17	oz	oz	ADP
ap-5050	108	18	axis	axis	NOUN
ap-5050	108	19	,	,	PUNCT
ap-5050	108	20	we	we	PRON
ap-5050	108	21	obtain	obtain	VERB
ap-5050	108	22	:	:	PUNCT
ap-5050	108	23	nrωx	nrωx	NOUN
ap-5050	108	24	=	=	SYM
ap-5050	108	25	−n	−n	NOUN
ap-5050	108	26	cos(ωt−	cos(ωt−	PROPN
ap-5050	108	27	α	α	NOUN
ap-5050	108	28	)	)	PUNCT
ap-5050	108	29	,	,	PUNCT
ap-5050	108	30	nrωy	nrωy	NOUN
ap-5050	108	31	=	=	PUNCT
ap-5050	108	32	0n	0n	PROPN
ap-5050	108	33	sin(ωt−	sin(ωt−	NOUN
ap-5050	108	34	α	α	NOUN
ap-5050	108	35	)	)	PUNCT
ap-5050	108	36	,	,	PUNCT
ap-5050	108	37	nrωz	nrωz	NOUN
ap-5050	108	38	=	=	SYM
ap-5050	108	39	0	0	X
ap-5050	108	40	.	.	PUNCT
ap-5050	109	1	(	(	PUNCT
ap-5050	109	2	17	17	NUM
ap-5050	109	3	)	)	PUNCT
ap-5050	109	4	weight	weight	NOUN
ap-5050	109	5	force	force	NOUN
ap-5050	109	6	of	of	ADP
ap-5050	109	7	a	a	DET
ap-5050	109	8	particle	particle	NOUN
ap-5050	109	9	mg	mg	PROPN
ap-5050	109	10	is	be	AUX
ap-5050	109	11	down	down	ADV
ap-5050	109	12	-	-	PUNCT
ap-5050	109	13	directed	direct	VERB
ap-5050	109	14	and	and	CCONJ
ap-5050	109	15	does	do	AUX
ap-5050	109	16	not	not	PART
ap-5050	109	17	depend	depend	VERB
ap-5050	109	18	on	on	ADP
ap-5050	109	19	the	the	DET
ap-5050	109	20	rotation	rotation	NOUN
ap-5050	109	21	angle	angle	NOUN
ap-5050	109	22	of	of	ADP
ap-5050	109	23	a	a	DET
ap-5050	109	24	plane	plane	NOUN
ap-5050	109	25	69	69	NUM
ap-5050	109	26	s.	s.	PROPN
ap-5050	109	27	f.	f.	PROPN
ap-5050	109	28	pylypaka	pylypaka	PROPN
ap-5050	109	29	,	,	PUNCT
ap-5050	109	30	m.	m.	PROPN
ap-5050	109	31	b.	b.	PROPN
ap-5050	109	32	klendii	klendii	PROPN
ap-5050	109	33	,	,	PUNCT
ap-5050	109	34	v.	v.	PROPN
ap-5050	109	35	m.	m.	PROPN
ap-5050	109	36	nesvidomin	nesvidomin	PROPN
ap-5050	109	37	,	,	PUNCT
ap-5050	109	38	v.	v.	PROPN
ap-5050	109	39	i.	i.	PROPN
ap-5050	109	40	trokhaniak	trokhaniak	PROPN
ap-5050	109	41	acta	acta	PROPN
ap-5050	109	42	polytechnica	polytechnica	PROPN
ap-5050	109	43	segment	segment	NOUN
ap-5050	109	44	.	.	PUNCT
ap-5050	110	1	let	let	VERB
ap-5050	110	2	us	we	PRON
ap-5050	110	3	write	write	VERB
ap-5050	110	4	its	its	PRON
ap-5050	110	5	projections	projection	NOUN
ap-5050	110	6	on	on	ADP
ap-5050	110	7	the	the	DET
ap-5050	110	8	coordinate	coordinate	NOUN
ap-5050	110	9	axes	axis	NOUN
ap-5050	110	10	:	:	PUNCT
ap-5050	110	11	(	(	PUNCT
ap-5050	110	12	0	0	NUM
ap-5050	110	13	;	;	PUNCT
ap-5050	110	14	0;−mg	0;−mg	NUM
ap-5050	110	15	)	)	PUNCT
ap-5050	110	16	.	.	PUNCT
ap-5050	111	1	(	(	PUNCT
ap-5050	111	2	18	18	NUM
ap-5050	111	3	)	)	PUNCT
ap-5050	111	4	during	during	ADP
ap-5050	111	5	an	an	DET
ap-5050	111	6	absolute	absolute	ADJ
ap-5050	111	7	particle	particle	NOUN
ap-5050	111	8	motion	motion	NOUN
ap-5050	111	9	,	,	PUNCT
ap-5050	111	10	it	it	PRON
ap-5050	111	11	slides	slide	VERB
ap-5050	111	12	both	both	PRON
ap-5050	111	13	on	on	ADP
ap-5050	111	14	a	a	DET
ap-5050	111	15	flat	flat	ADJ
ap-5050	111	16	segment	segment	NOUN
ap-5050	111	17	and	and	CCONJ
ap-5050	111	18	on	on	ADP
ap-5050	111	19	the	the	DET
ap-5050	111	20	wall	wall	NOUN
ap-5050	111	21	of	of	ADP
ap-5050	111	22	a	a	DET
ap-5050	111	23	cylindrical	cylindrical	ADJ
ap-5050	111	24	cover	cover	NOUN
ap-5050	111	25	.	.	PUNCT
ap-5050	112	1	in	in	ADP
ap-5050	112	2	both	both	DET
ap-5050	112	3	cases	case	NOUN
ap-5050	112	4	,	,	PUNCT
ap-5050	112	5	the	the	DET
ap-5050	112	6	value	value	NOUN
ap-5050	112	7	of	of	ADP
ap-5050	112	8	the	the	DET
ap-5050	112	9	friction	friction	NOUN
ap-5050	112	10	force	force	NOUN
ap-5050	112	11	is	be	AUX
ap-5050	112	12	determined	determine	VERB
ap-5050	112	13	as	as	ADP
ap-5050	112	14	the	the	DET
ap-5050	112	15	product	product	NOUN
ap-5050	112	16	of	of	ADP
ap-5050	112	17	the	the	DET
ap-5050	112	18	reaction	reaction	NOUN
ap-5050	112	19	force	force	NOUN
ap-5050	112	20	and	and	CCONJ
ap-5050	112	21	the	the	DET
ap-5050	112	22	correspondent	correspondent	NOUN
ap-5050	112	23	friction	friction	NOUN
ap-5050	112	24	coefficient	coefficient	NOUN
ap-5050	112	25	:	:	PUNCT
ap-5050	112	26	f	f	X
ap-5050	112	27	=	=	PUNCT
ap-5050	112	28	fn	fn	PROPN
ap-5050	112	29	and	and	CCONJ
ap-5050	112	30	fr	fr	NOUN
ap-5050	113	1	=	=	ADJ
ap-5050	113	2	frnr	frnr	PROPN
ap-5050	113	3	.	.	PUNCT
ap-5050	114	1	the	the	DET
ap-5050	114	2	force	force	NOUN
ap-5050	114	3	f	f	PROPN
ap-5050	114	4	is	be	AUX
ap-5050	114	5	directed	direct	VERB
ap-5050	114	6	opposite	opposite	ADV
ap-5050	114	7	to	to	ADP
ap-5050	114	8	the	the	DET
ap-5050	114	9	direction	direction	NOUN
ap-5050	114	10	of	of	ADP
ap-5050	114	11	sliding	slide	VERB
ap-5050	114	12	,	,	PUNCT
ap-5050	114	13	that	that	PRON
ap-5050	114	14	is	be	AUX
ap-5050	114	15	to	to	PART
ap-5050	114	16	say	say	VERB
ap-5050	114	17	,	,	PUNCT
ap-5050	114	18	opposite	opposite	ADJ
ap-5050	114	19	to	to	ADP
ap-5050	114	20	the	the	DET
ap-5050	114	21	vector	vector	NOUN
ap-5050	114	22	of	of	ADP
ap-5050	114	23	the	the	DET
ap-5050	114	24	absolute	absolute	ADJ
ap-5050	114	25	velocity	velocity	NOUN
ap-5050	114	26	of	of	ADP
ap-5050	114	27	particle	particle	NOUN
ap-5050	114	28	motion	motion	NOUN
ap-5050	114	29	.	.	PUNCT
ap-5050	115	1	the	the	DET
ap-5050	115	2	projections	projection	NOUN
ap-5050	115	3	of	of	ADP
ap-5050	115	4	this	this	DET
ap-5050	115	5	vector	vector	NOUN
ap-5050	115	6	are	be	AUX
ap-5050	115	7	determined	determine	VERB
ap-5050	115	8	from	from	ADP
ap-5050	115	9	differentiation	differentiation	NOUN
ap-5050	115	10	of	of	ADP
ap-5050	115	11	(	(	PUNCT
ap-5050	115	12	8)	8)	NUM
ap-5050	115	13	:	:	PUNCT
ap-5050	115	14	x′	x′	PROPN
ap-5050	115	15	=	=	SYM
ap-5050	115	16	−rα′	−rα′	NOUN
ap-5050	115	17	sinα	sinα	NOUN
ap-5050	115	18	,	,	PUNCT
ap-5050	115	19	y′	y′	X
ap-5050	115	20	=	=	SYM
ap-5050	115	21	rα′	rα′	NOUN
ap-5050	115	22	cosα	cosα	NOUN
ap-5050	115	23	,	,	PUNCT
ap-5050	115	24	z′	z′	NUM
ap-5050	115	25	=	=	PUNCT
ap-5050	115	26	rα′	rα′	NOUN
ap-5050	115	27	tg	tg	PROPN
ap-5050	115	28	β	β	PROPN
ap-5050	115	29	sinα	sinα	PROPN
ap-5050	115	30	(	(	PUNCT
ap-5050	115	31	19	19	NUM
ap-5050	115	32	)	)	PUNCT
ap-5050	115	33	let	let	VERB
ap-5050	115	34	us	we	PRON
ap-5050	115	35	find	find	VERB
ap-5050	115	36	the	the	DET
ap-5050	115	37	value	value	NOUN
ap-5050	115	38	of	of	ADP
ap-5050	115	39	the	the	DET
ap-5050	115	40	relative	relative	ADJ
ap-5050	115	41	velocity	velocity	NOUN
ap-5050	115	42	of	of	ADP
ap-5050	115	43	the	the	DET
ap-5050	115	44	particle	particle	NOUN
ap-5050	115	45	motion	motion	NOUN
ap-5050	115	46	:	:	PUNCT
ap-5050	116	1	v	v	X
ap-5050	116	2	=	=	SYM
ap-5050	116	3	√	√	PROPN
ap-5050	116	4	(	(	PUNCT
ap-5050	116	5	x′)2	x′)2	PROPN
ap-5050	117	1	+	+	PUNCT
ap-5050	118	1	(	(	PUNCT
ap-5050	118	2	y′)2	y′)2	PROPN
ap-5050	118	3	+	+	PROPN
ap-5050	118	4	(	(	PUNCT
ap-5050	118	5	z′)2	z′)2	PROPN
ap-5050	118	6	=	=	PUNCT
ap-5050	118	7	rα′	rα′	NOUN
ap-5050	118	8	√	√	NOUN
ap-5050	118	9	1	1	NUM
ap-5050	118	10	+	+	CCONJ
ap-5050	118	11	tg2	tg2	PROPN
ap-5050	118	12	β	β	PROPN
ap-5050	118	13	sin2	sin2	PROPN
ap-5050	118	14	α	α	PRON
ap-5050	118	15	.	.	PUNCT
ap-5050	119	1	(	(	PUNCT
ap-5050	119	2	20	20	NUM
ap-5050	119	3	)	)	PUNCT
ap-5050	119	4	the	the	DET
ap-5050	119	5	projections	projection	NOUN
ap-5050	119	6	of	of	ADP
ap-5050	119	7	a	a	DET
ap-5050	119	8	unit	unit	NOUN
ap-5050	119	9	directing	direct	VERB
ap-5050	119	10	vector	vector	NOUN
ap-5050	119	11	of	of	ADP
ap-5050	119	12	relative	relative	ADJ
ap-5050	119	13	velocity	velocity	NOUN
ap-5050	119	14	can	can	AUX
ap-5050	119	15	be	be	AUX
ap-5050	119	16	determined	determine	VERB
ap-5050	119	17	from	from	ADP
ap-5050	119	18	dividing	divide	VERB
ap-5050	119	19	the	the	DET
ap-5050	119	20	projections	projection	NOUN
ap-5050	119	21	(	(	PUNCT
ap-5050	119	22	19	19	NUM
ap-5050	119	23	)	)	PUNCT
ap-5050	119	24	of	of	ADP
ap-5050	119	25	this	this	DET
ap-5050	119	26	velocity	velocity	NOUN
ap-5050	119	27	by	by	ADP
ap-5050	119	28	its	its	PRON
ap-5050	119	29	absolute	absolute	ADJ
ap-5050	119	30	value	value	NOUN
ap-5050	119	31	(	(	PUNCT
ap-5050	119	32	20	20	NUM
ap-5050	119	33	):	):	PUNCT
ap-5050	119	34	tv	tv	NOUN
ap-5050	119	35	x	x	PUNCT
ap-5050	120	1	=	=	PUNCT
ap-5050	120	2	−	−	PROPN
ap-5050	120	3	sinα	sinα	PROPN
ap-5050	120	4	b	b	PROPN
ap-5050	120	5	,	,	PUNCT
ap-5050	120	6	tv	tv	NOUN
ap-5050	120	7	y	y	NOUN
ap-5050	120	8	=	=	PUNCT
ap-5050	120	9	cosα	cosα	PROPN
ap-5050	120	10	b	b	PROPN
ap-5050	120	11	,	,	PUNCT
ap-5050	120	12	tv	tv	NOUN
ap-5050	120	13	z	z	NOUN
ap-5050	120	14	=	=	PUNCT
ap-5050	120	15	tg	tg	PROPN
ap-5050	120	16	β	β	PROPN
ap-5050	120	17	sinα	sinα	PROPN
ap-5050	120	18	b	b	PROPN
ap-5050	120	19	,	,	PUNCT
ap-5050	120	20	(	(	PUNCT
ap-5050	120	21	21	21	NUM
ap-5050	120	22	)	)	PUNCT
ap-5050	120	23	where	where	SCONJ
ap-5050	120	24	b	b	X
ap-5050	120	25	=	=	NOUN
ap-5050	120	26	√	√	ADP
ap-5050	120	27	1	1	NUM
ap-5050	120	28	+	+	CCONJ
ap-5050	120	29	tg2	tg2	PROPN
ap-5050	120	30	β	β	PROPN
ap-5050	120	31	sin2	sin2	NOUN
ap-5050	120	32	α	α	X
ap-5050	120	33	.	.	PUNCT
ap-5050	121	1	after	after	ADP
ap-5050	121	2	the	the	DET
ap-5050	121	3	vector	vector	NOUN
ap-5050	121	4	(	(	PUNCT
ap-5050	121	5	21	21	NUM
ap-5050	121	6	)	)	PUNCT
ap-5050	121	7	is	be	AUX
ap-5050	121	8	turned	turn	VERB
ap-5050	121	9	through	through	ADP
ap-5050	121	10	the	the	DET
ap-5050	121	11	angle	angle	NOUN
ap-5050	121	12	−ωt	−ωt	NOUN
ap-5050	121	13	,	,	PUNCT
ap-5050	121	14	so	so	SCONJ
ap-5050	121	15	that	that	SCONJ
ap-5050	121	16	it	it	PRON
ap-5050	121	17	is	be	AUX
ap-5050	121	18	exerted	exert	VERB
ap-5050	121	19	to	to	ADP
ap-5050	121	20	a	a	DET
ap-5050	121	21	particle	particle	NOUN
ap-5050	121	22	,	,	PUNCT
ap-5050	121	23	we	we	PRON
ap-5050	121	24	obtain	obtain	VERB
ap-5050	121	25	:	:	PUNCT
ap-5050	121	26	tv	tv	NOUN
ap-5050	121	27	ωx	ωx	NOUN
ap-5050	121	28	=	=	PUNCT
ap-5050	121	29	sin(ωt−	sin(ωt−	NOUN
ap-5050	121	30	α	α	NOUN
ap-5050	121	31	)	)	PUNCT
ap-5050	121	32	b	b	PROPN
ap-5050	121	33	,	,	PUNCT
ap-5050	121	34	tv	tv	NOUN
ap-5050	121	35	ωy	ωy	PROPN
ap-5050	121	36	=	=	SYM
ap-5050	121	37	cos(ωt−	cos(ωt−	PROPN
ap-5050	121	38	α	α	NOUN
ap-5050	121	39	)	)	PUNCT
ap-5050	121	40	b	b	PROPN
ap-5050	121	41	,	,	PUNCT
ap-5050	121	42	tv	tv	NOUN
ap-5050	121	43	ωz	ωz	PUNCT
ap-5050	122	1	=	=	PUNCT
ap-5050	122	2	tg	tg	PROPN
ap-5050	122	3	β	β	PROPN
ap-5050	122	4	sinα	sinα	PROPN
ap-5050	122	5	b	b	PROPN
ap-5050	122	6	,	,	PUNCT
ap-5050	122	7	(	(	PUNCT
ap-5050	122	8	22	22	NUM
ap-5050	122	9	)	)	PUNCT
ap-5050	122	10	here	here	ADV
ap-5050	122	11	,	,	PUNCT
ap-5050	122	12	it	it	PRON
ap-5050	122	13	is	be	AUX
ap-5050	122	14	possible	possible	ADJ
ap-5050	122	15	to	to	PART
ap-5050	122	16	write	write	VERB
ap-5050	122	17	the	the	DET
ap-5050	122	18	projections	projection	NOUN
ap-5050	122	19	of	of	ADP
ap-5050	122	20	the	the	DET
ap-5050	122	21	friction	friction	NOUN
ap-5050	122	22	force	force	NOUN
ap-5050	122	23	f	f	PROPN
ap-5050	122	24	,	,	PUNCT
ap-5050	122	25	taking	take	VERB
ap-5050	122	26	into	into	ADP
ap-5050	122	27	account	account	NOUN
ap-5050	122	28	that	that	SCONJ
ap-5050	122	29	it	it	PRON
ap-5050	122	30	is	be	AUX
ap-5050	122	31	directed	direct	VERB
ap-5050	122	32	opposite	opposite	ADV
ap-5050	122	33	to	to	ADP
ap-5050	122	34	the	the	DET
ap-5050	122	35	direction	direction	NOUN
ap-5050	122	36	of	of	ADP
ap-5050	122	37	the	the	DET
ap-5050	122	38	vector	vector	NOUN
ap-5050	122	39	(	(	PUNCT
ap-5050	122	40	22	22	NUM
ap-5050	122	41	):	):	PUNCT
ap-5050	122	42	fωx	fωx	NOUN
ap-5050	122	43	=	=	NOUN
ap-5050	122	44	−fn	−fn	X
ap-5050	122	45	b	b	PROPN
ap-5050	122	46	sin(ωt−	sin(ωt−	NOUN
ap-5050	122	47	α	α	NOUN
ap-5050	122	48	)	)	PUNCT
ap-5050	122	49	,	,	PUNCT
ap-5050	122	50	fωy	fωy	NOUN
ap-5050	122	51	=	=	PUNCT
ap-5050	122	52	−fn	−fn	X
ap-5050	122	53	b	b	PROPN
ap-5050	122	54	cos(ωt−	cos(ωt−	NOUN
ap-5050	122	55	α	α	NOUN
ap-5050	122	56	)	)	PUNCT
ap-5050	122	57	,	,	PUNCT
ap-5050	122	58	fωz	fωz	X
ap-5050	122	59	=	=	PUNCT
ap-5050	122	60	−fn	−fn	X
ap-5050	122	61	b	b	X
ap-5050	122	62	tg	tg	PROPN
ap-5050	122	63	β	β	PROPN
ap-5050	122	64	sinα	sinα	PROPN
ap-5050	122	65	,	,	PUNCT
ap-5050	122	66	(	(	PUNCT
ap-5050	122	67	23	23	NUM
ap-5050	122	68	)	)	PUNCT
ap-5050	122	69	the	the	DET
ap-5050	122	70	friction	friction	NOUN
ap-5050	122	71	force	force	NOUN
ap-5050	122	72	fr	fr	PROPN
ap-5050	122	73	is	be	AUX
ap-5050	122	74	directed	direct	VERB
ap-5050	122	75	opposite	opposite	ADV
ap-5050	122	76	to	to	ADP
ap-5050	122	77	the	the	DET
ap-5050	122	78	direction	direction	NOUN
ap-5050	122	79	of	of	ADP
ap-5050	122	80	the	the	DET
ap-5050	122	81	absolute	absolute	ADJ
ap-5050	122	82	velocity	velocity	NOUN
ap-5050	122	83	,	,	PUNCT
ap-5050	122	84	that	that	PRON
ap-5050	122	85	is	be	AUX
ap-5050	122	86	to	to	PART
ap-5050	122	87	say	say	VERB
ap-5050	122	88	,	,	PUNCT
ap-5050	122	89	the	the	DET
ap-5050	122	90	vector	vector	NOUN
ap-5050	122	91	(	(	PUNCT
ap-5050	122	92	12	12	NUM
ap-5050	122	93	)	)	PUNCT
ap-5050	122	94	.	.	PUNCT
ap-5050	123	1	there	there	PRON
ap-5050	123	2	is	be	VERB
ap-5050	123	3	no	no	DET
ap-5050	123	4	need	need	NOUN
ap-5050	123	5	to	to	PART
ap-5050	123	6	turn	turn	VERB
ap-5050	123	7	the	the	DET
ap-5050	123	8	vector	vector	NOUN
ap-5050	123	9	(	(	PUNCT
ap-5050	123	10	12	12	NUM
ap-5050	123	11	)	)	PUNCT
ap-5050	123	12	through	through	ADP
ap-5050	123	13	the	the	DET
ap-5050	123	14	angle	angle	NOUN
ap-5050	123	15	−ωt	−ωt	NOUN
ap-5050	123	16	,	,	PUNCT
ap-5050	123	17	since	since	SCONJ
ap-5050	123	18	the	the	DET
ap-5050	123	19	cylinder	cylinder	NOUN
ap-5050	123	20	is	be	AUX
ap-5050	123	21	fixed	fix	VERB
ap-5050	123	22	and	and	CCONJ
ap-5050	123	23	the	the	DET
ap-5050	123	24	position	position	NOUN
ap-5050	123	25	of	of	ADP
ap-5050	123	26	a	a	DET
ap-5050	123	27	particle	particle	NOUN
ap-5050	123	28	in	in	ADP
ap-5050	123	29	an	an	DET
ap-5050	123	30	absolute	absolute	ADJ
ap-5050	123	31	motion	motion	NOUN
ap-5050	123	32	is	be	AUX
ap-5050	123	33	determined	determine	VERB
ap-5050	123	34	relative	relative	ADJ
ap-5050	123	35	to	to	ADP
ap-5050	123	36	a	a	DET
ap-5050	123	37	fixed	fix	VERB
ap-5050	123	38	coordinate	coordinate	NOUN
ap-5050	123	39	system	system	NOUN
ap-5050	123	40	as	as	ADV
ap-5050	123	41	well	well	ADV
ap-5050	123	42	.	.	PUNCT
ap-5050	124	1	taking	take	VERB
ap-5050	124	2	this	this	PRON
ap-5050	124	3	into	into	ADP
ap-5050	124	4	account	account	NOUN
ap-5050	124	5	,	,	PUNCT
ap-5050	124	6	the	the	DET
ap-5050	124	7	projections	projection	NOUN
ap-5050	124	8	of	of	ADP
ap-5050	124	9	the	the	DET
ap-5050	124	10	force	force	NOUN
ap-5050	124	11	fr	fr	PROPN
ap-5050	124	12	are	be	AUX
ap-5050	124	13	written	write	VERB
ap-5050	124	14	as	as	SCONJ
ap-5050	124	15	follows	follow	VERB
ap-5050	124	16	:	:	PUNCT
ap-5050	125	1	frx	frx	PROPN
ap-5050	125	2	=	=	PUNCT
ap-5050	125	3	frnr	frnr	PROPN
ap-5050	125	4	a	a	DET
ap-5050	125	5	(	(	PUNCT
ap-5050	125	6	ω	ω	NOUN
ap-5050	125	7	−	−	NOUN
ap-5050	125	8	α′	α′	NUM
ap-5050	125	9	)	)	PUNCT
ap-5050	125	10	sin(ωt−	sin(ωt−	NOUN
ap-5050	125	11	α	α	NOUN
ap-5050	125	12	)	)	PUNCT
ap-5050	125	13	,	,	PUNCT
ap-5050	125	14	fry	fry	NOUN
ap-5050	125	15	=	=	SYM
ap-5050	125	16	frnr	frnr	NOUN
ap-5050	125	17	a	a	DET
ap-5050	125	18	(	(	PUNCT
ap-5050	125	19	ω	ω	NOUN
ap-5050	125	20	−	−	NOUN
ap-5050	125	21	α′	α′	NUM
ap-5050	125	22	)	)	PUNCT
ap-5050	125	23	cos(ωt−	cos(ωt−	NOUN
ap-5050	125	24	α	α	NOUN
ap-5050	125	25	)	)	PUNCT
ap-5050	125	26	,	,	PUNCT
ap-5050	125	27	frz	frz	PROPN
ap-5050	125	28	=	=	PROPN
ap-5050	126	1	−frnr	−frnr	PROPN
ap-5050	126	2	a	a	DET
ap-5050	126	3	α′	α′	NUM
ap-5050	126	4	tg	tg	PROPN
ap-5050	126	5	β	β	PROPN
ap-5050	126	6	sinα	sinα	PROPN
ap-5050	126	7	,	,	PUNCT
ap-5050	126	8	(	(	PUNCT
ap-5050	126	9	24	24	NUM
ap-5050	126	10	)	)	PUNCT
ap-5050	126	11	here	here	ADV
ap-5050	126	12	,	,	PUNCT
ap-5050	126	13	it	it	PRON
ap-5050	126	14	is	be	AUX
ap-5050	126	15	possible	possible	ADJ
ap-5050	126	16	to	to	PART
ap-5050	126	17	write	write	VERB
ap-5050	126	18	the	the	DET
ap-5050	126	19	equationmw	equationmw	ADJ
ap-5050	126	20	=	=	PUNCT
ap-5050	126	21	∑	∑	PUNCT
ap-5050	126	22	f	f	PROPN
ap-5050	126	23	in	in	ADP
ap-5050	126	24	projections	projection	NOUN
ap-5050	126	25	on	on	ADP
ap-5050	126	26	oxyz	oxyz	NOUN
ap-5050	126	27	coordinate	coordinate	NOUN
ap-5050	126	28	axes	axis	NOUN
ap-5050	126	29	:	:	PUNCT
ap-5050	126	30	mx′′a	mx′′a	X
ap-5050	126	31	=	=	PUNCT
ap-5050	126	32	nωx	nωx	PROPN
ap-5050	127	1	+	+	PUNCT
ap-5050	127	2	nrωx	nrωx	NOUN
ap-5050	127	3	+	+	CCONJ
ap-5050	127	4	fx	fx	NOUN
ap-5050	127	5	+	+	CCONJ
ap-5050	127	6	frx	frx	PROPN
ap-5050	127	7	,	,	PUNCT
ap-5050	127	8	my′′a	my′′a	PROPN
ap-5050	127	9	=	=	SYM
ap-5050	127	10	nωy	nωy	NOUN
ap-5050	127	11	+	+	NOUN
ap-5050	127	12	nrωy	nrωy	VERB
ap-5050	127	13	+	+	CCONJ
ap-5050	127	14	fy	fy	PROPN
ap-5050	127	15	+	+	CCONJ
ap-5050	127	16	fry	fry	NOUN
ap-5050	127	17	,	,	PUNCT
ap-5050	127	18	mz′′a	mz′′a	X
ap-5050	127	19	=	=	SYM
ap-5050	127	20	nωz	nωz	VERB
ap-5050	127	21	+	+	NOUN
ap-5050	127	22	nrωz	nrωz	NOUN
ap-5050	127	23	+	+	CCONJ
ap-5050	127	24	fz	fz	NOUN
ap-5050	127	25	+	+	CCONJ
ap-5050	127	26	frz	frz	PROPN
ap-5050	127	27	−mg	−mg	PROPN
ap-5050	127	28	.	.	PUNCT
ap-5050	128	1	(	(	PUNCT
ap-5050	128	2	25	25	NUM
ap-5050	128	3	)	)	PUNCT
ap-5050	128	4	let	let	VERB
ap-5050	128	5	us	we	PRON
ap-5050	128	6	substitute	substitute	VERB
ap-5050	128	7	the	the	DET
ap-5050	128	8	expressions	expression	NOUN
ap-5050	128	9	of	of	ADP
ap-5050	128	10	the	the	DET
ap-5050	128	11	absolute	absolute	ADJ
ap-5050	128	12	acceleration	acceleration	NOUN
ap-5050	128	13	(	(	PUNCT
ap-5050	128	14	13	13	NUM
ap-5050	128	15	)	)	PUNCT
ap-5050	128	16	and	and	CCONJ
ap-5050	128	17	the	the	DET
ap-5050	128	18	expressions	expression	NOUN
ap-5050	128	19	of	of	ADP
ap-5050	128	20	exerted	exert	VERB
ap-5050	128	21	forces	force	NOUN
ap-5050	128	22	(	(	PUNCT
ap-5050	128	23	14	14	NUM
ap-5050	128	24	)	)	PUNCT
ap-5050	128	25	,	,	PUNCT
ap-5050	128	26	(	(	PUNCT
ap-5050	128	27	15	15	NUM
ap-5050	128	28	)	)	PUNCT
ap-5050	128	29	,	,	PUNCT
ap-5050	128	30	(	(	PUNCT
ap-5050	128	31	23	23	NUM
ap-5050	128	32	)	)	PUNCT
ap-5050	128	33	and	and	CCONJ
ap-5050	128	34	(	(	PUNCT
ap-5050	128	35	24	24	NUM
ap-5050	128	36	)	)	PUNCT
ap-5050	128	37	into	into	ADP
ap-5050	128	38	(	(	PUNCT
ap-5050	128	39	25	25	NUM
ap-5050	128	40	)	)	PUNCT
ap-5050	128	41	.	.	PUNCT
ap-5050	129	1	as	as	ADP
ap-5050	129	2	a	a	DET
ap-5050	129	3	result	result	NOUN
ap-5050	129	4	,	,	PUNCT
ap-5050	129	5	we	we	PRON
ap-5050	129	6	obtain	obtain	VERB
ap-5050	129	7	the	the	DET
ap-5050	129	8	system	system	NOUN
ap-5050	129	9	of	of	ADP
ap-5050	129	10	three	three	NUM
ap-5050	129	11	differential	differential	ADJ
ap-5050	129	12	second	second	ADJ
ap-5050	129	13	-	-	PUNCT
ap-5050	129	14	order	order	NOUN
ap-5050	129	15	equations	equation	NOUN
ap-5050	129	16	with	with	ADP
ap-5050	129	17	three	three	NUM
ap-5050	129	18	unknown	unknown	ADJ
ap-5050	129	19	functions	function	NOUN
ap-5050	129	20	α	α	X
ap-5050	129	21	=	=	SYM
ap-5050	129	22	α(t	α(t	PROPN
ap-5050	129	23	)	)	PUNCT
ap-5050	129	24	,	,	PUNCT
ap-5050	129	25	n	n	PROPN
ap-5050	129	26	=	=	SYM
ap-5050	129	27	n(t	n(t	PROPN
ap-5050	129	28	)	)	PUNCT
ap-5050	129	29	,	,	PUNCT
ap-5050	129	30	nr	nr	NOUN
ap-5050	129	31	=	=	NOUN
ap-5050	129	32	nr(t	nr(t	X
ap-5050	129	33	):	):	PUNCT
ap-5050	129	34	m	m	VERB
ap-5050	129	35	(	(	PUNCT
ap-5050	129	36	rα′′	rα′′	PROPN
ap-5050	129	37	sin(ωt−	sin(ωt−	PROPN
ap-5050	129	38	α)−r(ω	α)−r(ω	SYM
ap-5050	129	39	−	−	PROPN
ap-5050	129	40	α′)2	α′)2	PROPN
ap-5050	129	41	cos(ωt−	cos(ωt−	NOUN
ap-5050	129	42	α	α	NOUN
ap-5050	129	43	)	)	PUNCT
ap-5050	129	44	)	)	PUNCT
ap-5050	130	1	=	=	SYM
ap-5050	131	1	n	n	PRON
ap-5050	131	2	sin	sin	VERB
ap-5050	131	3	β	β	X
ap-5050	131	4	cosωt−nr	cosωt−nr	NOUN
ap-5050	131	5	cos(ωt−	cos(ωt−	NOUN
ap-5050	131	6	α	α	NOUN
ap-5050	131	7	)	)	PUNCT
ap-5050	132	1	−	−	PROPN
ap-5050	132	2	fn	fn	NOUN
ap-5050	132	3	b	b	PROPN
ap-5050	132	4	sin(ωt−	sin(ωt−	NOUN
ap-5050	132	5	α	α	NOUN
ap-5050	132	6	)	)	PUNCT
ap-5050	132	7	+	+	CCONJ
ap-5050	132	8	frnr	frnr	PRON
ap-5050	132	9	a	a	DET
ap-5050	132	10	(	(	PUNCT
ap-5050	132	11	ω	ω	NOUN
ap-5050	132	12	−	−	NOUN
ap-5050	132	13	α′	α′	NUM
ap-5050	132	14	)	)	PUNCT
ap-5050	132	15	sin(ωt−	sin(ωt−	NOUN
ap-5050	132	16	α	α	NOUN
ap-5050	132	17	)	)	PUNCT
ap-5050	132	18	,	,	PUNCT
ap-5050	132	19	m	m	VERB
ap-5050	132	20	(	(	PUNCT
ap-5050	132	21	rα′′	rα′′	PROPN
ap-5050	132	22	cos(ωt−	cos(ωt−	NOUN
ap-5050	132	23	α	α	NOUN
ap-5050	132	24	)	)	PUNCT
ap-5050	132	25	+	+	PROPN
ap-5050	132	26	r(ω	r(ω	ADV
ap-5050	132	27	−	−	PUNCT
ap-5050	132	28	α′)2	α′)2	PROPN
ap-5050	132	29	sin(ωt−	sin(ωt−	NOUN
ap-5050	132	30	α	α	NOUN
ap-5050	132	31	)	)	PUNCT
ap-5050	132	32	)	)	PUNCT
ap-5050	133	1	=	=	SYM
ap-5050	134	1	n	n	ADP
ap-5050	134	2	sin	sin	VERB
ap-5050	134	3	β	β	X
ap-5050	134	4	sinωt−nr	sinωt−nr	VERB
ap-5050	134	5	sin(ωt−	sin(ωt−	NOUN
ap-5050	134	6	α	α	NOUN
ap-5050	134	7	)	)	PUNCT
ap-5050	134	8	−	−	PROPN
ap-5050	134	9	fn	fn	PROPN
ap-5050	134	10	b	b	PROPN
ap-5050	134	11	cos(ωt−	cos(ωt−	PROPN
ap-5050	134	12	α	α	NOUN
ap-5050	134	13	)	)	PUNCT
ap-5050	135	1	+	+	CCONJ
ap-5050	135	2	frnr	frnr	PRON
ap-5050	135	3	a	a	DET
ap-5050	135	4	(	(	PUNCT
ap-5050	135	5	ω	ω	NOUN
ap-5050	135	6	−	−	NOUN
ap-5050	135	7	α′	α′	NUM
ap-5050	135	8	)	)	PUNCT
ap-5050	135	9	cos(ωt−	cos(ωt−	NOUN
ap-5050	135	10	α	α	NOUN
ap-5050	135	11	)	)	PUNCT
ap-5050	135	12	,	,	PUNCT
ap-5050	135	13	m	m	VERB
ap-5050	135	14	(	(	PUNCT
ap-5050	135	15	rα′′	rα′′	NOUN
ap-5050	135	16	tg	tg	PROPN
ap-5050	135	17	β	β	PROPN
ap-5050	135	18	sinα+r(α′)2	sinα+r(α′)2	INTJ
ap-5050	135	19	tg	tg	ADP
ap-5050	135	20	β	β	X
ap-5050	135	21	cosα	cosα	NOUN
ap-5050	135	22	)	)	PUNCT
ap-5050	135	23	=	=	PUNCT
ap-5050	136	1	n	n	NOUN
ap-5050	136	2	cosβ	cosβ	NOUN
ap-5050	136	3	−	−	PROPN
ap-5050	137	1	fn	fn	NOUN
ap-5050	137	2	b	b	PROPN
ap-5050	137	3	tg	tg	PROPN
ap-5050	137	4	β	β	PROPN
ap-5050	137	5	sinα−	sinα−	VERB
ap-5050	137	6	frnr	frnr	ADV
ap-5050	137	7	a	a	DET
ap-5050	137	8	α′	α′	NUM
ap-5050	137	9	tg	tg	PROPN
ap-5050	137	10	β	β	PROPN
ap-5050	137	11	sinα−mg	sinα−mg	PROPN
ap-5050	137	12	.	.	PUNCT
ap-5050	138	1	(	(	PUNCT
ap-5050	138	2	26	26	NUM
ap-5050	138	3	)	)	PUNCT
ap-5050	138	4	having	having	AUX
ap-5050	138	5	solved	solve	VERB
ap-5050	138	6	(	(	PUNCT
ap-5050	138	7	26	26	NUM
ap-5050	138	8	)	)	PUNCT
ap-5050	138	9	for	for	ADP
ap-5050	138	10	α′′	α′′	NOUN
ap-5050	138	11	,	,	PUNCT
ap-5050	138	12	n	n	PROPN
ap-5050	138	13	and	and	CCONJ
ap-5050	138	14	nr	nr	PROPN
ap-5050	138	15	,	,	PUNCT
ap-5050	138	16	we	we	PRON
ap-5050	138	17	obtain	obtain	VERB
ap-5050	138	18	:	:	PUNCT
ap-5050	138	19	α′′	α′′	NOUN
ap-5050	138	20	=	=	SYM
ap-5050	138	21	1	1	NUM
ap-5050	138	22	mr	mr	PROPN
ap-5050	138	23	(	(	PUNCT
ap-5050	138	24	frnr	frnr	PROPN
ap-5050	138	25	a	a	DET
ap-5050	138	26	(	(	PUNCT
ap-5050	138	27	ω	ω	NOUN
ap-5050	138	28	−	−	PROPN
ap-5050	138	29	α′)−	α′)−	PROPN
ap-5050	138	30	fn	fn	PROPN
ap-5050	138	31	b	b	PROPN
ap-5050	139	1	+	+	CCONJ
ap-5050	139	2	nr	nr	PRON
ap-5050	139	3	−mr(ω	−mr(ω	ADJ
ap-5050	139	4	−	−	PROPN
ap-5050	139	5	α′)2	α′)2	PROPN
ap-5050	139	6	cotg(ωt−	cotg(ωt−	PROPN
ap-5050	139	7	α	α	NUM
ap-5050	139	8	)	)	PUNCT
ap-5050	139	9	−	−	NOUN
ap-5050	140	1	n	n	PRON
ap-5050	140	2	sin	sin	VERB
ap-5050	140	3	β	β	PROPN
ap-5050	140	4	sinωt	sinωt	PROPN
ap-5050	140	5	cos(ωt−	cos(ωt−	PROPN
ap-5050	140	6	α	α	NOUN
ap-5050	140	7	)	)	PUNCT
ap-5050	140	8	)	)	PUNCT
ap-5050	140	9	,	,	PUNCT
ap-5050	140	10	(	(	PUNCT
ap-5050	140	11	27	27	NUM
ap-5050	140	12	)	)	PUNCT
ap-5050	140	13	n	n	NOUN
ap-5050	140	14	=	=	SYM
ap-5050	140	15	d−1	d−1	PROPN
ap-5050	140	16	(	(	PUNCT
ap-5050	140	17	−4mga	−4mga	PROPN
ap-5050	140	18	cosβ	cosβ	NOUN
ap-5050	140	19	−	−	PROPN
ap-5050	140	20	4mr	4mr	ADJ
ap-5050	140	21	sin	sin	NOUN
ap-5050	140	22	β	β	X
ap-5050	140	23	(	(	PUNCT
ap-5050	140	24	(	(	PUNCT
ap-5050	140	25	α′)2a	α′)2a	NOUN
ap-5050	140	26	cosα+	cosα+	NOUN
ap-5050	140	27	frω(ω	frω(ω	PROPN
ap-5050	140	28	−	−	PROPN
ap-5050	140	29	α′)2	α′)2	PROPN
ap-5050	140	30	sinα	sinα	NOUN
ap-5050	140	31	)	)	PUNCT
ap-5050	140	32	)	)	PUNCT
ap-5050	140	33	,	,	PUNCT
ap-5050	140	34	(	(	PUNCT
ap-5050	140	35	28	28	NUM
ap-5050	140	36	)	)	PUNCT
ap-5050	140	37	nr	nr	NOUN
ap-5050	140	38	=	=	NOUN
ap-5050	140	39	d−1ma	d−1ma	NOUN
ap-5050	140	40	(	(	PUNCT
ap-5050	140	41	crω(ω	crω(ω	ADP
ap-5050	140	42	−	−	ADP
ap-5050	140	43	2α′	2α′	NUM
ap-5050	140	44	)	)	PUNCT
ap-5050	141	1	−r	−r	PROPN
ap-5050	141	2	(	(	PUNCT
ap-5050	141	3	3ω2	3ω2	NUM
ap-5050	141	4	−	−	NUM
ap-5050	141	5	6α′ω	6α′ω	NUM
ap-5050	142	1	+	+	CCONJ
ap-5050	142	2	4(α′)2)−	4(α′)2)−	NUM
ap-5050	142	3	2	2	NUM
ap-5050	142	4	g	g	NOUN
ap-5050	142	5	sin	sin	NOUN
ap-5050	142	6	2β	2β	NOUN
ap-5050	142	7	cosα	cosα	NOUN
ap-5050	142	8	)	)	PUNCT
ap-5050	142	9	,	,	PUNCT
ap-5050	142	10	(	(	PUNCT
ap-5050	142	11	29	29	NUM
ap-5050	142	12	)	)	PUNCT
ap-5050	143	1	where	where	SCONJ
ap-5050	143	2	c	c	NOUN
ap-5050	143	3	=	=	SYM
ap-5050	143	4	cos	cos	ADP
ap-5050	143	5	2α	2α	PROPN
ap-5050	143	6	−	−	PROPN
ap-5050	143	7	2	2	NUM
ap-5050	143	8	cos	cos	ADP
ap-5050	143	9	2β	2β	NOUN
ap-5050	143	10	cos2	cos2	NOUN
ap-5050	143	11	α	α	NOUN
ap-5050	143	12	and	and	CCONJ
ap-5050	143	13	d	d	NOUN
ap-5050	143	14	=	=	PUNCT
ap-5050	143	15	a(c	a(c	PROPN
ap-5050	143	16	−	−	NOUN
ap-5050	143	17	3	3	NUM
ap-5050	143	18	)	)	PUNCT
ap-5050	143	19	+	+	NOUN
ap-5050	143	20	2frω	2frω	NUM
ap-5050	143	21	sin2	sin2	NOUN
ap-5050	143	22	β	β	X
ap-5050	143	23	sin	sin	NOUN
ap-5050	143	24	2α	2α	NOUN
ap-5050	143	25	.	.	PUNCT
ap-5050	144	1	having	having	AUX
ap-5050	144	2	substituted	substitute	VERB
ap-5050	144	3	(	(	PUNCT
ap-5050	144	4	28	28	NUM
ap-5050	144	5	)	)	PUNCT
ap-5050	144	6	and	and	CCONJ
ap-5050	144	7	(	(	PUNCT
ap-5050	144	8	29	29	NUM
ap-5050	144	9	)	)	PUNCT
ap-5050	144	10	into	into	ADP
ap-5050	144	11	(	(	PUNCT
ap-5050	144	12	27	27	NUM
ap-5050	144	13	)	)	PUNCT
ap-5050	144	14	,	,	PUNCT
ap-5050	144	15	the	the	DET
ap-5050	144	16	particle	particle	NOUN
ap-5050	144	17	mass	mass	NOUN
ap-5050	144	18	m	m	NOUN
ap-5050	144	19	reduces	reduce	VERB
ap-5050	144	20	and	and	CCONJ
ap-5050	144	21	we	we	PRON
ap-5050	144	22	obtain	obtain	VERB
ap-5050	144	23	a	a	DET
ap-5050	144	24	differential	differential	ADJ
ap-5050	144	25	second	second	ADJ
ap-5050	144	26	-	-	PUNCT
ap-5050	144	27	order	order	NOUN
ap-5050	144	28	equation	equation	NOUN
ap-5050	144	29	,	,	PUNCT
ap-5050	144	30	which	which	PRON
ap-5050	144	31	can	can	AUX
ap-5050	144	32	be	be	AUX
ap-5050	144	33	solved	solve	VERB
ap-5050	144	34	using	use	VERB
ap-5050	144	35	numerical	numerical	ADJ
ap-5050	144	36	methods	method	NOUN
ap-5050	144	37	.	.	PUNCT
ap-5050	145	1	at	at	ADP
ap-5050	145	2	β	β	X
ap-5050	145	3	=	=	SYM
ap-5050	145	4	0	0	NUM
ap-5050	145	5	,	,	PUNCT
ap-5050	145	6	the	the	DET
ap-5050	145	7	expressions	expression	NOUN
ap-5050	145	8	(	(	PUNCT
ap-5050	145	9	27)–(29	27)–(29	NUM
ap-5050	145	10	)	)	PUNCT
ap-5050	145	11	take	take	VERB
ap-5050	145	12	the	the	DET
ap-5050	145	13	following	follow	VERB
ap-5050	145	14	forms	form	NOUN
ap-5050	145	15	:	:	PUNCT
ap-5050	145	16	α′′	α′′	NOUN
ap-5050	145	17	=	=	SYM
ap-5050	145	18	frnr	frnr	PROPN
ap-5050	145	19	−	−	PROPN
ap-5050	145	20	fn	fn	NOUN
ap-5050	145	21	mr	mr	PROPN
ap-5050	145	22	+	+	PROPN
ap-5050	145	23	nr	nr	PRON
ap-5050	145	24	−mr(ω	−mr(ω	ADJ
ap-5050	145	25	−	−	PROPN
ap-5050	145	26	α′)2	α′)2	PROPN
ap-5050	145	27	mr	mr	PROPN
ap-5050	145	28	cotg(ωt−	cotg(ωt−	PROPN
ap-5050	145	29	α	α	PROPN
ap-5050	145	30	)	)	PUNCT
ap-5050	145	31	,	,	PUNCT
ap-5050	145	32	(	(	PUNCT
ap-5050	145	33	30	30	NUM
ap-5050	145	34	)	)	PUNCT
ap-5050	145	35	n	n	NOUN
ap-5050	145	36	=	=	SYM
ap-5050	145	37	mg	mg	PROPN
ap-5050	145	38	,	,	PUNCT
ap-5050	145	39	(	(	PUNCT
ap-5050	145	40	31	31	NUM
ap-5050	145	41	)	)	PUNCT
ap-5050	146	1	n	n	NOUN
ap-5050	146	2	=	=	SYM
ap-5050	146	3	mr(ω	mr(ω	PROPN
ap-5050	146	4	−	−	PROPN
ap-5050	146	5	α′)2	α′)2	PROPN
ap-5050	146	6	.	.	PROPN
ap-5050	147	1	(	(	PUNCT
ap-5050	147	2	32	32	NUM
ap-5050	147	3	)	)	PUNCT
ap-5050	147	4	having	having	AUX
ap-5050	147	5	substituted	substitute	VERB
ap-5050	147	6	(	(	PUNCT
ap-5050	147	7	31	31	NUM
ap-5050	147	8	)	)	PUNCT
ap-5050	147	9	and	and	CCONJ
ap-5050	147	10	(	(	PUNCT
ap-5050	147	11	32	32	NUM
ap-5050	147	12	)	)	PUNCT
ap-5050	147	13	into	into	ADP
ap-5050	147	14	(	(	PUNCT
ap-5050	147	15	30	30	NUM
ap-5050	147	16	)	)	PUNCT
ap-5050	147	17	,	,	PUNCT
ap-5050	147	18	after	after	ADP
ap-5050	147	19	a	a	DET
ap-5050	147	20	simplification	simplification	NOUN
ap-5050	147	21	,	,	PUNCT
ap-5050	147	22	we	we	PRON
ap-5050	147	23	obtain	obtain	VERB
ap-5050	147	24	the	the	DET
ap-5050	147	25	differential	differential	ADJ
ap-5050	147	26	equation	equation	NOUN
ap-5050	147	27	(	(	PUNCT
ap-5050	147	28	5	5	NUM
ap-5050	147	29	)	)	PUNCT
ap-5050	147	30	.	.	PUNCT
ap-5050	148	1	70	70	NUM
ap-5050	148	2	vol	vol	NOUN
ap-5050	148	3	.	.	PUNCT
ap-5050	149	1	59	59	NUM
ap-5050	149	2	no	no	NOUN
ap-5050	149	3	.	.	PUNCT
ap-5050	150	1	1/2019	1/2019	NUM
ap-5050	150	2	particle	particle	NOUN
ap-5050	150	3	motion	motion	NOUN
ap-5050	150	4	over	over	ADP
ap-5050	150	5	the	the	DET
ap-5050	150	6	edge	edge	NOUN
ap-5050	150	7	of	of	ADP
ap-5050	150	8	an	an	DET
ap-5050	150	9	inclined	inclined	ADJ
ap-5050	150	10	plane	plane	NOUN
ap-5050	150	11	thus	thus	ADV
ap-5050	150	12	,	,	PUNCT
ap-5050	150	13	in	in	ADP
ap-5050	150	14	case	case	NOUN
ap-5050	150	15	,	,	PUNCT
ap-5050	150	16	when	when	SCONJ
ap-5050	150	17	β	β	X
ap-5050	150	18	=	=	SYM
ap-5050	150	19	0	0	NUM
ap-5050	150	20	,	,	PUNCT
ap-5050	150	21	all	all	DET
ap-5050	150	22	the	the	DET
ap-5050	150	23	three	three	NUM
ap-5050	150	24	equations	equation	NOUN
ap-5050	150	25	(	(	PUNCT
ap-5050	150	26	30	30	NUM
ap-5050	150	27	)	)	PUNCT
ap-5050	150	28	–	–	PUNCT
ap-5050	150	29	(	(	PUNCT
ap-5050	150	30	32	32	NUM
ap-5050	150	31	)	)	PUNCT
ap-5050	150	32	completely	completely	ADV
ap-5050	150	33	coincide	coincide	VERB
ap-5050	150	34	with	with	ADP
ap-5050	150	35	the	the	DET
ap-5050	150	36	expressions	expression	NOUN
ap-5050	150	37	obtained	obtain	VERB
ap-5050	150	38	earlier	early	ADV
ap-5050	150	39	,	,	PUNCT
ap-5050	150	40	when	when	SCONJ
ap-5050	150	41	the	the	DET
ap-5050	150	42	differential	differential	ADJ
ap-5050	150	43	equation	equation	NOUN
ap-5050	150	44	of	of	ADP
ap-5050	150	45	an	an	DET
ap-5050	150	46	absolute	absolute	ADJ
ap-5050	150	47	particle	particle	NOUN
ap-5050	150	48	motion	motion	NOUN
ap-5050	150	49	was	be	AUX
ap-5050	150	50	determined	determine	VERB
ap-5050	150	51	in	in	ADP
ap-5050	150	52	the	the	DET
ap-5050	150	53	projection	projection	NOUN
ap-5050	150	54	on	on	ADP
ap-5050	150	55	a	a	DET
ap-5050	150	56	moving	move	VERB
ap-5050	150	57	axis	axis	NOUN
ap-5050	150	58	.	.	PUNCT
ap-5050	151	1	3	3	X
ap-5050	151	2	.	.	X
ap-5050	151	3	results	result	VERB
ap-5050	151	4	the	the	DET
ap-5050	151	5	solution	solution	NOUN
ap-5050	151	6	of	of	ADP
ap-5050	151	7	the	the	DET
ap-5050	151	8	differential	differential	ADJ
ap-5050	151	9	equation	equation	NOUN
ap-5050	151	10	(	(	PUNCT
ap-5050	151	11	27	27	NUM
ap-5050	151	12	)	)	PUNCT
ap-5050	151	13	was	be	AUX
ap-5050	151	14	performed	perform	VERB
ap-5050	151	15	with	with	ADP
ap-5050	151	16	the	the	DET
ap-5050	151	17	help	help	NOUN
ap-5050	151	18	of	of	ADP
ap-5050	151	19	numerical	numerical	ADJ
ap-5050	151	20	methods	method	NOUN
ap-5050	151	21	.	.	PUNCT
ap-5050	152	1	the	the	DET
ap-5050	152	2	investigations	investigation	NOUN
ap-5050	152	3	for	for	ADP
ap-5050	152	4	a	a	DET
ap-5050	152	5	case	case	NOUN
ap-5050	152	6	,	,	PUNCT
ap-5050	152	7	when	when	SCONJ
ap-5050	152	8	β	β	X
ap-5050	152	9	=	=	SYM
ap-5050	152	10	0	0	NUM
ap-5050	152	11	,	,	PUNCT
ap-5050	152	12	r	r	NOUN
ap-5050	152	13	=	=	SYM
ap-5050	152	14	0.1	0.1	NUM
ap-5050	152	15	m	m	NOUN
ap-5050	152	16	,	,	PUNCT
ap-5050	152	17	f	f	PROPN
ap-5050	152	18	=	=	NOUN
ap-5050	152	19	fr	fr	PROPN
ap-5050	152	20	=	=	PUNCT
ap-5050	152	21	0.3	0.3	NUM
ap-5050	152	22	,	,	PUNCT
ap-5050	152	23	ω	ω	NOUN
ap-5050	152	24	=	=	SYM
ap-5050	152	25	20	20	NUM
ap-5050	152	26	s−1	s−1	PROPN
ap-5050	152	27	and	and	CCONJ
ap-5050	152	28	when	when	SCONJ
ap-5050	152	29	the	the	DET
ap-5050	152	30	initial	initial	ADJ
ap-5050	152	31	integrating	integrating	NOUN
ap-5050	152	32	conditions	condition	NOUN
ap-5050	152	33	are	be	AUX
ap-5050	152	34	α′	α′	NUM
ap-5050	152	35	=	=	SYM
ap-5050	152	36	0	0	NUM
ap-5050	152	37	,	,	PUNCT
ap-5050	152	38	α	α	NOUN
ap-5050	152	39	=	=	SYM
ap-5050	152	40	0	0	NUM
ap-5050	152	41	,	,	PUNCT
ap-5050	152	42	were	be	AUX
ap-5050	152	43	conducted	conduct	VERB
ap-5050	152	44	and	and	CCONJ
ap-5050	152	45	the	the	DET
ap-5050	152	46	obtained	obtain	VERB
ap-5050	152	47	results	result	NOUN
ap-5050	152	48	are	be	AUX
ap-5050	152	49	presented	present	VERB
ap-5050	152	50	in	in	ADP
ap-5050	152	51	figure	figure	NOUN
ap-5050	152	52	3	3	NUM
ap-5050	152	53	.	.	PUNCT
ap-5050	153	1	the	the	DET
ap-5050	153	2	curve	curve	NOUN
ap-5050	153	3	in	in	ADP
ap-5050	153	4	figure	figure	NOUN
ap-5050	153	5	3a	3a	PROPN
ap-5050	153	6	shows	show	VERB
ap-5050	153	7	that	that	SCONJ
ap-5050	153	8	the	the	DET
ap-5050	153	9	angular	angular	ADJ
ap-5050	153	10	velocity	velocity	NOUN
ap-5050	153	11	of	of	ADP
ap-5050	153	12	the	the	DET
ap-5050	153	13	sliding	slide	VERB
ap-5050	153	14	after	after	SCONJ
ap-5050	153	15	the	the	DET
ap-5050	153	16	motion	motion	NOUN
ap-5050	153	17	stabilization	stabilization	NOUN
ap-5050	153	18	is	be	AUX
ap-5050	153	19	about	about	ADV
ap-5050	153	20	10	10	NUM
ap-5050	153	21	s−1	s−1	PROPN
ap-5050	153	22	.	.	PUNCT
ap-5050	154	1	as	as	ADP
ap-5050	154	2	a	a	DET
ap-5050	154	3	result	result	NOUN
ap-5050	154	4	of	of	ADP
ap-5050	154	5	the	the	DET
ap-5050	154	6	analytical	analytical	ADJ
ap-5050	154	7	solution	solution	NOUN
ap-5050	154	8	,	,	PUNCT
ap-5050	154	9	the	the	DET
ap-5050	154	10	exact	exact	ADJ
ap-5050	154	11	value	value	NOUN
ap-5050	154	12	of	of	ADP
ap-5050	154	13	α′	α′	NUM
ap-5050	154	14	=	=	SYM
ap-5050	154	15	10.1	10.1	NUM
ap-5050	154	16	s−1	s−1	PROPN
ap-5050	154	17	was	be	AUX
ap-5050	154	18	obtained	obtain	VERB
ap-5050	154	19	,	,	PUNCT
ap-5050	154	20	which	which	PRON
ap-5050	154	21	is	be	AUX
ap-5050	154	22	mentioned	mention	VERB
ap-5050	154	23	at	at	ADP
ap-5050	154	24	the	the	DET
ap-5050	154	25	beginning	beginning	NOUN
ap-5050	154	26	of	of	ADP
ap-5050	154	27	the	the	DET
ap-5050	154	28	paper	paper	NOUN
ap-5050	154	29	.	.	PUNCT
ap-5050	155	1	the	the	DET
ap-5050	155	2	deduced	deduce	VERB
ap-5050	155	3	equations	equation	NOUN
ap-5050	155	4	also	also	ADV
ap-5050	155	5	work	work	VERB
ap-5050	155	6	at	at	ADP
ap-5050	155	7	ω	ω	PROPN
ap-5050	155	8	=	=	SYM
ap-5050	155	9	0	0	PROPN
ap-5050	155	10	,	,	PUNCT
ap-5050	155	11	that	that	PRON
ap-5050	155	12	is	be	AUX
ap-5050	155	13	to	to	PART
ap-5050	155	14	say	say	VERB
ap-5050	155	15	,	,	PUNCT
ap-5050	155	16	when	when	SCONJ
ap-5050	155	17	there	there	PRON
ap-5050	155	18	is	be	VERB
ap-5050	155	19	no	no	DET
ap-5050	155	20	rotating	rotate	VERB
ap-5050	155	21	motion	motion	NOUN
ap-5050	155	22	of	of	ADP
ap-5050	155	23	a	a	DET
ap-5050	155	24	plane	plane	NOUN
ap-5050	155	25	segment	segment	NOUN
ap-5050	155	26	.	.	PUNCT
ap-5050	156	1	if	if	SCONJ
ap-5050	156	2	the	the	DET
ap-5050	156	3	angle	angle	NOUN
ap-5050	156	4	β	β	X
ap-5050	156	5	is	be	AUX
ap-5050	156	6	bigger	big	ADJ
ap-5050	156	7	than	than	ADP
ap-5050	156	8	the	the	DET
ap-5050	156	9	friction	friction	NOUN
ap-5050	156	10	angle	angle	NOUN
ap-5050	156	11	,	,	PUNCT
ap-5050	156	12	a	a	DET
ap-5050	156	13	particle	particle	NOUN
ap-5050	156	14	moves	move	NOUN
ap-5050	156	15	uniformly	uniformly	ADV
ap-5050	156	16	accelerated	accelerate	VERB
ap-5050	156	17	on	on	ADP
ap-5050	156	18	an	an	DET
ap-5050	156	19	inclined	inclined	ADJ
ap-5050	156	20	plane	plane	NOUN
ap-5050	156	21	.	.	PUNCT
ap-5050	157	1	in	in	ADP
ap-5050	157	2	our	our	PRON
ap-5050	157	3	case	case	NOUN
ap-5050	157	4	,	,	PUNCT
ap-5050	157	5	particle	particle	NOUN
ap-5050	157	6	motion	motion	NOUN
ap-5050	157	7	must	must	AUX
ap-5050	157	8	be	be	AUX
ap-5050	157	9	different	different	ADJ
ap-5050	157	10	,	,	PUNCT
ap-5050	157	11	since	since	SCONJ
ap-5050	157	12	,	,	PUNCT
ap-5050	157	13	if	if	SCONJ
ap-5050	157	14	an	an	DET
ap-5050	157	15	ellipse	ellipse	NOUN
ap-5050	157	16	moves	move	VERB
ap-5050	157	17	,	,	PUNCT
ap-5050	157	18	the	the	DET
ap-5050	157	19	angle	angle	NOUN
ap-5050	157	20	between	between	ADP
ap-5050	157	21	a	a	DET
ap-5050	157	22	velocity	velocity	NOUN
ap-5050	157	23	vector	vector	NOUN
ap-5050	157	24	and	and	CCONJ
ap-5050	157	25	a	a	DET
ap-5050	157	26	horizontal	horizontal	ADJ
ap-5050	157	27	plane	plane	NOUN
ap-5050	157	28	is	be	AUX
ap-5050	157	29	alternate	alternate	ADJ
ap-5050	157	30	,	,	PUNCT
ap-5050	157	31	besides	besides	ADV
ap-5050	157	32	,	,	PUNCT
ap-5050	157	33	the	the	DET
ap-5050	157	34	friction	friction	NOUN
ap-5050	157	35	force	force	NOUN
ap-5050	157	36	from	from	ADP
ap-5050	157	37	a	a	DET
ap-5050	157	38	cylinder	cylinder	NOUN
ap-5050	157	39	wall	wall	NOUN
ap-5050	157	40	acts	act	VERB
ap-5050	157	41	on	on	ADP
ap-5050	157	42	a	a	DET
ap-5050	157	43	particle	particle	NOUN
ap-5050	157	44	.	.	PUNCT
ap-5050	158	1	figure	figure	NOUN
ap-5050	158	2	4	4	NUM
ap-5050	158	3	represents	represent	VERB
ap-5050	158	4	the	the	DET
ap-5050	158	5	curves	curve	NOUN
ap-5050	158	6	of	of	ADP
ap-5050	158	7	the	the	DET
ap-5050	158	8	relative	relative	ADJ
ap-5050	158	9	velocity	velocity	NOUN
ap-5050	158	10	and	and	CCONJ
ap-5050	158	11	the	the	DET
ap-5050	158	12	height	height	NOUN
ap-5050	158	13	of	of	ADP
ap-5050	158	14	the	the	DET
ap-5050	158	15	particle	particle	NOUN
ap-5050	158	16	fall	fall	NOUN
ap-5050	158	17	movement	movement	NOUN
ap-5050	158	18	.	.	PUNCT
ap-5050	159	1	the	the	DET
ap-5050	159	2	initial	initial	ADJ
ap-5050	159	3	value	value	NOUN
ap-5050	159	4	of	of	ADP
ap-5050	159	5	the	the	DET
ap-5050	159	6	angle	angle	NOUN
ap-5050	159	7	is	be	AUX
ap-5050	159	8	α	α	NOUN
ap-5050	159	9	=	=	PROPN
ap-5050	159	10	90	90	NUM
ap-5050	159	11	°	°	NOUN
ap-5050	159	12	,	,	PUNCT
ap-5050	159	13	which	which	PRON
ap-5050	159	14	corresponds	correspond	VERB
ap-5050	159	15	to	to	ADP
ap-5050	159	16	the	the	DET
ap-5050	159	17	position	position	NOUN
ap-5050	159	18	of	of	ADP
ap-5050	159	19	a	a	DET
ap-5050	159	20	particle	particle	NOUN
ap-5050	159	21	in	in	ADP
ap-5050	159	22	the	the	DET
ap-5050	159	23	middle	middle	ADJ
ap-5050	159	24	point	point	NOUN
ap-5050	159	25	through	through	ADP
ap-5050	159	26	the	the	DET
ap-5050	159	27	height	height	NOUN
ap-5050	159	28	of	of	ADP
ap-5050	159	29	a	a	DET
ap-5050	159	30	segment	segment	NOUN
ap-5050	159	31	.	.	PUNCT
ap-5050	160	1	the	the	DET
ap-5050	160	2	curves	curve	NOUN
ap-5050	160	3	show	show	VERB
ap-5050	160	4	that	that	SCONJ
ap-5050	160	5	,	,	PUNCT
ap-5050	160	6	at	at	ADP
ap-5050	160	7	first	first	ADV
ap-5050	160	8	,	,	PUNCT
ap-5050	160	9	a	a	DET
ap-5050	160	10	particle	particle	NOUN
ap-5050	160	11	builds	build	VERB
ap-5050	160	12	up	up	ADP
ap-5050	160	13	speed	speed	NOUN
ap-5050	160	14	and	and	CCONJ
ap-5050	160	15	then	then	ADV
ap-5050	160	16	it	it	PRON
ap-5050	160	17	slows	slow	VERB
ap-5050	160	18	down	down	ADP
ap-5050	160	19	its	its	PRON
ap-5050	160	20	movement	movement	NOUN
ap-5050	160	21	and	and	CCONJ
ap-5050	160	22	stops	stop	NOUN
ap-5050	160	23	.	.	PUNCT
ap-5050	161	1	if	if	SCONJ
ap-5050	161	2	a	a	DET
ap-5050	161	3	segment	segment	NOUN
ap-5050	161	4	rotates	rotate	VERB
ap-5050	161	5	with	with	ADP
ap-5050	161	6	a	a	DET
ap-5050	161	7	low	low	ADJ
ap-5050	161	8	angular	angular	ADJ
ap-5050	161	9	velocity	velocity	NOUN
ap-5050	161	10	,	,	PUNCT
ap-5050	161	11	e.g.	e.g.	ADV
ap-5050	161	12	ω	ω	X
ap-5050	161	13	=	=	SYM
ap-5050	161	14	5	5	NUM
ap-5050	161	15	s−1	s−1	PROPN
ap-5050	161	16	,	,	PUNCT
ap-5050	161	17	the	the	DET
ap-5050	161	18	fall	fall	NOUN
ap-5050	161	19	movement	movement	NOUN
ap-5050	161	20	of	of	ADP
ap-5050	161	21	a	a	DET
ap-5050	161	22	particle	particle	NOUN
ap-5050	161	23	is	be	AUX
ap-5050	161	24	different	different	ADJ
ap-5050	161	25	.	.	PUNCT
ap-5050	162	1	similar	similar	ADJ
ap-5050	162	2	curves	curve	NOUN
ap-5050	162	3	for	for	ADP
ap-5050	162	4	such	such	ADJ
ap-5050	162	5	case	case	NOUN
ap-5050	162	6	are	be	AUX
ap-5050	162	7	presented	present	VERB
ap-5050	162	8	in	in	ADP
ap-5050	162	9	figure	figure	NOUN
ap-5050	162	10	5	5	NUM
ap-5050	162	11	.	.	PUNCT
ap-5050	163	1	the	the	DET
ap-5050	163	2	curves	curve	NOUN
ap-5050	163	3	in	in	ADP
ap-5050	163	4	figure	figure	NOUN
ap-5050	163	5	5	5	NUM
ap-5050	163	6	show	show	VERB
ap-5050	163	7	that	that	SCONJ
ap-5050	163	8	there	there	PRON
ap-5050	163	9	is	be	VERB
ap-5050	163	10	more	more	ADJ
ap-5050	163	11	time	time	NOUN
ap-5050	163	12	needed	need	VERB
ap-5050	163	13	for	for	SCONJ
ap-5050	163	14	a	a	DET
ap-5050	163	15	particle	particle	NOUN
ap-5050	163	16	to	to	PART
ap-5050	163	17	stop	stop	VERB
ap-5050	163	18	,	,	PUNCT
ap-5050	163	19	here	here	ADV
ap-5050	163	20	,	,	PUNCT
ap-5050	163	21	at	at	ADP
ap-5050	163	22	certain	certain	ADJ
ap-5050	163	23	moments	moment	NOUN
ap-5050	163	24	,	,	PUNCT
ap-5050	163	25	the	the	DET
ap-5050	163	26	direction	direction	NOUN
ap-5050	163	27	of	of	ADP
ap-5050	163	28	the	the	DET
ap-5050	163	29	sliding	slide	VERB
ap-5050	163	30	velocity	velocity	NOUN
ap-5050	163	31	changes	change	NOUN
ap-5050	163	32	for	for	ADP
ap-5050	163	33	the	the	DET
ap-5050	163	34	opposite	opposite	ADJ
ap-5050	163	35	one	one	NUM
ap-5050	163	36	.	.	PUNCT
ap-5050	164	1	this	this	PRON
ap-5050	164	2	means	mean	VERB
ap-5050	164	3	that	that	SCONJ
ap-5050	164	4	a	a	DET
ap-5050	164	5	particle	particle	NOUN
ap-5050	164	6	performs	perform	VERB
ap-5050	164	7	oscillations	oscillation	NOUN
ap-5050	164	8	near	near	ADP
ap-5050	164	9	the	the	DET
ap-5050	164	10	low	low	ADJ
ap-5050	164	11	point	point	NOUN
ap-5050	164	12	of	of	ADP
ap-5050	164	13	an	an	DET
ap-5050	164	14	ellipse	ellipse	NOUN
ap-5050	164	15	and	and	CCONJ
ap-5050	164	16	this	this	DET
ap-5050	164	17	oscillatory	oscillatory	ADJ
ap-5050	164	18	motion	motion	NOUN
ap-5050	164	19	gradually	gradually	ADV
ap-5050	164	20	declines	decline	VERB
ap-5050	164	21	.	.	PUNCT
ap-5050	165	1	if	if	SCONJ
ap-5050	165	2	the	the	DET
ap-5050	165	3	angular	angular	ADJ
ap-5050	165	4	velocity	velocity	NOUN
ap-5050	165	5	of	of	ADP
ap-5050	165	6	the	the	DET
ap-5050	165	7	segment	segment	NOUN
ap-5050	165	8	rotation	rotation	NOUN
ap-5050	165	9	increases	increase	NOUN
ap-5050	165	10	,	,	PUNCT
ap-5050	165	11	a	a	DET
ap-5050	165	12	particle	particle	NOUN
ap-5050	165	13	begins	begin	VERB
ap-5050	165	14	to	to	PART
ap-5050	165	15	slide	slide	VERB
ap-5050	165	16	in	in	ADP
ap-5050	165	17	an	an	DET
ap-5050	165	18	ellipse	ellipse	NOUN
ap-5050	165	19	passing	pass	VERB
ap-5050	165	20	through	through	ADP
ap-5050	165	21	the	the	DET
ap-5050	165	22	lowest	low	ADJ
ap-5050	165	23	and	and	CCONJ
ap-5050	165	24	the	the	DET
ap-5050	165	25	highest	high	ADJ
ap-5050	165	26	points	point	NOUN
ap-5050	165	27	in	in	ADP
ap-5050	165	28	a	a	DET
ap-5050	165	29	sequence	sequence	NOUN
ap-5050	165	30	(	(	PUNCT
ap-5050	165	31	figure	figure	NOUN
ap-5050	165	32	6	6	NUM
ap-5050	165	33	)	)	PUNCT
ap-5050	165	34	.	.	PUNCT
ap-5050	166	1	having	having	AUX
ap-5050	166	2	analysed	analyse	VERB
ap-5050	166	3	the	the	DET
ap-5050	166	4	curves	curve	NOUN
ap-5050	166	5	with	with	ADP
ap-5050	166	6	the	the	DET
ap-5050	166	7	help	help	NOUN
ap-5050	166	8	of	of	ADP
ap-5050	166	9	the	the	DET
ap-5050	166	10	similar	similar	ADJ
ap-5050	166	11	values	value	NOUN
ap-5050	166	12	of	of	ADP
ap-5050	166	13	the	the	DET
ap-5050	166	14	time	time	NOUN
ap-5050	166	15	t	t	PROPN
ap-5050	166	16	,	,	PUNCT
ap-5050	166	17	it	it	PRON
ap-5050	166	18	can	can	AUX
ap-5050	166	19	be	be	AUX
ap-5050	166	20	concluded	conclude	VERB
ap-5050	166	21	that	that	SCONJ
ap-5050	166	22	a	a	DET
ap-5050	166	23	particle	particle	NOUN
ap-5050	166	24	has	have	VERB
ap-5050	166	25	its	its	PRON
ap-5050	166	26	highest	high	ADJ
ap-5050	166	27	sliding	slide	VERB
ap-5050	166	28	velocity	velocity	NOUN
ap-5050	166	29	near	near	ADP
ap-5050	166	30	the	the	DET
ap-5050	166	31	lowest	low	ADJ
ap-5050	166	32	point	point	NOUN
ap-5050	166	33	and	and	CCONJ
ap-5050	166	34	its	its	PRON
ap-5050	166	35	lowest	low	ADJ
ap-5050	166	36	speed	speed	NOUN
ap-5050	166	37	near	near	ADP
ap-5050	166	38	the	the	DET
ap-5050	166	39	highest	high	ADJ
ap-5050	166	40	point	point	NOUN
ap-5050	166	41	.	.	PUNCT
ap-5050	167	1	the	the	DET
ap-5050	167	2	pattern	pattern	NOUN
ap-5050	167	3	of	of	ADP
ap-5050	167	4	the	the	DET
ap-5050	167	5	height	height	NOUN
ap-5050	167	6	change	change	NOUN
ap-5050	167	7	(	(	PUNCT
ap-5050	167	8	figure	figure	NOUN
ap-5050	167	9	6b	6b	NUM
ap-5050	167	10	)	)	PUNCT
ap-5050	167	11	shows	show	VERB
ap-5050	167	12	that	that	SCONJ
ap-5050	167	13	a	a	DET
ap-5050	167	14	particle	particle	NOUN
ap-5050	167	15	moves	move	VERB
ap-5050	167	16	upwards	upwards	ADV
ap-5050	167	17	slower	slow	ADJ
ap-5050	167	18	than	than	SCONJ
ap-5050	167	19	it	it	PRON
ap-5050	167	20	moves	move	VERB
ap-5050	167	21	downwards	downward	NOUN
ap-5050	167	22	.	.	PUNCT
ap-5050	168	1	let	let	VERB
ap-5050	168	2	us	we	PRON
ap-5050	168	3	increase	increase	VERB
ap-5050	168	4	the	the	DET
ap-5050	168	5	angle	angle	NOUN
ap-5050	168	6	β	β	NOUN
ap-5050	168	7	of	of	ADP
ap-5050	168	8	the	the	DET
ap-5050	168	9	plane	plane	NOUN
ap-5050	168	10	inclination	inclination	NOUN
ap-5050	168	11	to	to	ADP
ap-5050	168	12	35	35	NUM
ap-5050	168	13	°	°	NOUN
ap-5050	168	14	without	without	ADP
ap-5050	168	15	changing	change	VERB
ap-5050	168	16	any	any	DET
ap-5050	168	17	other	other	ADJ
ap-5050	168	18	parameters	parameter	NOUN
ap-5050	168	19	.	.	PUNCT
ap-5050	169	1	in	in	ADP
ap-5050	169	2	this	this	DET
ap-5050	169	3	case	case	NOUN
ap-5050	169	4	,	,	PUNCT
ap-5050	169	5	a	a	DET
ap-5050	169	6	particle	particle	NOUN
ap-5050	169	7	in	in	ADP
ap-5050	169	8	a	a	DET
ap-5050	169	9	relative	relative	ADJ
ap-5050	169	10	motion	motion	NOUN
ap-5050	169	11	will	will	AUX
ap-5050	169	12	go	go	VERB
ap-5050	169	13	upwards	upwards	ADV
ap-5050	169	14	and	and	CCONJ
ap-5050	169	15	will	will	AUX
ap-5050	169	16	stop	stop	VERB
ap-5050	169	17	near	near	ADP
ap-5050	169	18	the	the	DET
ap-5050	169	19	highest	high	ADJ
ap-5050	169	20	point	point	NOUN
ap-5050	169	21	(	(	PUNCT
ap-5050	169	22	figure	figure	NOUN
ap-5050	169	23	7a	7a	NUM
ap-5050	169	24	)	)	PUNCT
ap-5050	169	25	.	.	PUNCT
ap-5050	170	1	after	after	ADP
ap-5050	170	2	its	its	PRON
ap-5050	170	3	stop	stop	NOUN
ap-5050	170	4	in	in	ADP
ap-5050	170	5	the	the	DET
ap-5050	170	6	relative	relative	ADJ
ap-5050	170	7	motion	motion	NOUN
ap-5050	170	8	,	,	PUNCT
ap-5050	170	9	it	it	PRON
ap-5050	170	10	will	will	AUX
ap-5050	170	11	describe	describe	VERB
ap-5050	170	12	a	a	DET
ap-5050	170	13	circle	circle	NOUN
ap-5050	170	14	in	in	ADP
ap-5050	170	15	an	an	DET
ap-5050	170	16	absolute	absolute	ADJ
ap-5050	170	17	motion	motion	NOUN
ap-5050	170	18	(	(	PUNCT
ap-5050	170	19	figure	figure	NOUN
ap-5050	170	20	7b	7b	NUM
ap-5050	170	21	)	)	PUNCT
ap-5050	170	22	.	.	PUNCT
ap-5050	171	1	the	the	DET
ap-5050	171	2	fact	fact	NOUN
ap-5050	171	3	that	that	SCONJ
ap-5050	171	4	a	a	DET
ap-5050	171	5	particle	particle	NOUN
ap-5050	171	6	stops	stop	NOUN
ap-5050	171	7	can	can	AUX
ap-5050	171	8	be	be	AUX
ap-5050	171	9	explained	explain	VERB
ap-5050	171	10	by	by	ADP
ap-5050	171	11	the	the	DET
ap-5050	171	12	fact	fact	NOUN
ap-5050	171	13	that	that	SCONJ
ap-5050	171	14	when	when	SCONJ
ap-5050	171	15	going	go	VERB
ap-5050	171	16	upwards	upwards	ADV
ap-5050	171	17	,	,	PUNCT
ap-5050	171	18	there	there	PRON
ap-5050	171	19	are	be	VERB
ap-5050	171	20	inertial	inertial	ADJ
ap-5050	171	21	forces	force	NOUN
ap-5050	171	22	that	that	PRON
ap-5050	171	23	make	make	VERB
ap-5050	171	24	a	a	DET
ap-5050	171	25	particle	particle	NOUN
ap-5050	171	26	move	move	NOUN
ap-5050	171	27	further	far	ADV
ap-5050	171	28	upwards	upwards	ADV
ap-5050	171	29	and	and	CCONJ
ap-5050	171	30	the	the	DET
ap-5050	171	31	weight	weight	NOUN
ap-5050	171	32	force	force	NOUN
ap-5050	171	33	of	of	ADP
ap-5050	171	34	a	a	DET
ap-5050	171	35	particle	particle	NOUN
ap-5050	171	36	is	be	AUX
ap-5050	171	37	not	not	PART
ap-5050	171	38	enough	enough	ADJ
ap-5050	171	39	to	to	PART
ap-5050	171	40	overcome	overcome	VERB
ap-5050	171	41	them	they	PRON
ap-5050	171	42	.	.	PUNCT
ap-5050	172	1	since	since	SCONJ
ap-5050	172	2	a	a	DET
ap-5050	172	3	particle	particle	NOUN
ap-5050	172	4	can	can	AUX
ap-5050	172	5	not	not	PART
ap-5050	172	6	move	move	VERB
ap-5050	172	7	further	far	ADV
ap-5050	172	8	upwards	upwards	ADV
ap-5050	172	9	,	,	PUNCT
ap-5050	172	10	it	it	PRON
ap-5050	172	11	“	"	PUNCT
ap-5050	172	12	sticks	stick	NOUN
ap-5050	172	13	”	"	PUNCT
ap-5050	172	14	.	.	PUNCT
ap-5050	173	1	it	it	PRON
ap-5050	173	2	can	can	AUX
ap-5050	173	3	be	be	AUX
ap-5050	173	4	assumed	assume	VERB
ap-5050	173	5	,	,	PUNCT
ap-5050	173	6	that	that	SCONJ
ap-5050	173	7	such	such	ADJ
ap-5050	173	8	particle	particle	NOUN
ap-5050	173	9	“	"	PUNCT
ap-5050	173	10	sticking	sticking	NOUN
ap-5050	173	11	”	"	PUNCT
ap-5050	173	12	can	can	AUX
ap-5050	173	13	be	be	AUX
ap-5050	173	14	overcome	overcome	VERB
ap-5050	173	15	by	by	ADP
ap-5050	173	16	increasing	increase	VERB
ap-5050	173	17	the	the	DET
ap-5050	173	18	angular	angular	ADJ
ap-5050	173	19	velocity	velocity	NOUN
ap-5050	173	20	?	?	PUNCT
ap-5050	173	21	.	.	PUNCT
ap-5050	174	1	indeed	indeed	ADV
ap-5050	174	2	,	,	PUNCT
ap-5050	174	3	when	when	SCONJ
ap-5050	174	4	the	the	DET
ap-5050	174	5	angular	angular	ADJ
ap-5050	174	6	velocity	velocity	NOUN
ap-5050	174	7	ω	ω	PROPN
ap-5050	174	8	is	be	AUX
ap-5050	174	9	increased	increase	VERB
ap-5050	174	10	to	to	ADP
ap-5050	174	11	24	24	NUM
ap-5050	174	12	s−1	s−1	PROPN
ap-5050	174	13	,	,	PUNCT
ap-5050	174	14	there	there	PRON
ap-5050	174	15	will	will	AUX
ap-5050	174	16	be	be	AUX
ap-5050	174	17	no	no	DET
ap-5050	174	18	“	"	PUNCT
ap-5050	174	19	sticking	stick	VERB
ap-5050	174	20	”	"	PUNCT
ap-5050	174	21	,	,	PUNCT
ap-5050	174	22	but	but	CCONJ
ap-5050	174	23	,	,	PUNCT
ap-5050	174	24	at	at	ADP
ap-5050	174	25	certain	certain	ADJ
ap-5050	174	26	moments	moment	NOUN
ap-5050	174	27	of	of	ADP
ap-5050	174	28	the	the	DET
ap-5050	174	29	particle	particle	NOUN
ap-5050	174	30	sliding	sliding	NOUN
ap-5050	174	31	,	,	PUNCT
ap-5050	174	32	the	the	DET
ap-5050	174	33	reaction	reaction	NOUN
ap-5050	174	34	n	n	PRON
ap-5050	174	35	of	of	ADP
ap-5050	174	36	the	the	DET
ap-5050	174	37	surfaces	surface	NOUN
ap-5050	174	38	will	will	AUX
ap-5050	174	39	become	become	VERB
ap-5050	174	40	less	less	ADJ
ap-5050	174	41	than	than	ADP
ap-5050	174	42	zero	zero	NUM
ap-5050	174	43	.	.	PUNCT
ap-5050	175	1	in	in	ADP
ap-5050	175	2	figure	figure	NOUN
ap-5050	175	3	8	8	NUM
ap-5050	175	4	there	there	PRON
ap-5050	175	5	are	be	VERB
ap-5050	175	6	two	two	NUM
ap-5050	175	7	curves	curve	NOUN
ap-5050	175	8	synchronized	synchronize	VERB
ap-5050	175	9	in	in	ADP
ap-5050	175	10	time	time	NOUN
ap-5050	175	11	:	:	PUNCT
ap-5050	175	12	the	the	DET
ap-5050	175	13	segment	segment	NOUN
ap-5050	175	14	surface	surface	NOUN
ap-5050	175	15	reaction	reaction	NOUN
ap-5050	175	16	n	n	CCONJ
ap-5050	175	17	at	at	ADP
ap-5050	175	18	the	the	DET
ap-5050	175	19	particle	particle	NOUN
ap-5050	175	20	mass	mass	PROPN
ap-5050	175	21	m	m	PROPN
ap-5050	175	22	=	=	NOUN
ap-5050	175	23	0.01	0.01	NUM
ap-5050	175	24	kg	kg	NOUN
ap-5050	175	25	and	and	CCONJ
ap-5050	175	26	the	the	DET
ap-5050	175	27	height	height	NOUN
ap-5050	175	28	z	z	NOUN
ap-5050	175	29	change	change	NOUN
ap-5050	175	30	.	.	PUNCT
ap-5050	176	1	straight	straight	ADJ
ap-5050	176	2	vertical	vertical	ADJ
ap-5050	176	3	lines	line	NOUN
ap-5050	176	4	of	of	ADP
ap-5050	176	5	the	the	DET
ap-5050	176	6	curves	curve	NOUN
ap-5050	176	7	show	show	VERB
ap-5050	176	8	the	the	DET
ap-5050	176	9	parts	part	NOUN
ap-5050	176	10	where	where	SCONJ
ap-5050	176	11	the	the	DET
ap-5050	176	12	reaction	reaction	NOUN
ap-5050	176	13	n	n	VERB
ap-5050	176	14	is	be	AUX
ap-5050	176	15	equal	equal	ADJ
ap-5050	176	16	to	to	ADP
ap-5050	176	17	zero	zero	NUM
ap-5050	176	18	or	or	CCONJ
ap-5050	176	19	less	less	ADJ
ap-5050	176	20	than	than	ADP
ap-5050	176	21	zero	zero	NUM
ap-5050	176	22	.	.	PUNCT
ap-5050	177	1	this	this	PRON
ap-5050	177	2	happens	happen	VERB
ap-5050	177	3	at	at	ADP
ap-5050	177	4	the	the	DET
ap-5050	177	5	moment	moment	NOUN
ap-5050	177	6	when	when	SCONJ
ap-5050	177	7	a	a	DET
ap-5050	177	8	particle	particle	NOUN
ap-5050	177	9	begins	begin	VERB
ap-5050	177	10	its	its	PRON
ap-5050	177	11	fall	fall	NOUN
ap-5050	177	12	movement	movement	NOUN
ap-5050	177	13	.	.	PUNCT
ap-5050	178	1	during	during	ADP
ap-5050	178	2	this	this	DET
ap-5050	178	3	time	time	NOUN
ap-5050	178	4	,	,	PUNCT
ap-5050	178	5	the	the	DET
ap-5050	178	6	particle	particle	NOUN
ap-5050	178	7	detaches	detach	VERB
ap-5050	178	8	from	from	ADP
ap-5050	178	9	a	a	DET
ap-5050	178	10	plane	plane	NOUN
ap-5050	178	11	.	.	PUNCT
ap-5050	179	1	a	a	DET
ap-5050	179	2	differential	differential	ADJ
ap-5050	179	3	equation	equation	NOUN
ap-5050	179	4	sufficiently	sufficiently	ADV
ap-5050	179	5	describes	describe	VERB
ap-5050	179	6	the	the	DET
ap-5050	179	7	particle	particle	NOUN
ap-5050	179	8	motion	motion	NOUN
ap-5050	179	9	only	only	ADV
ap-5050	179	10	at	at	ADP
ap-5050	179	11	positive	positive	ADJ
ap-5050	179	12	values	value	NOUN
ap-5050	179	13	of	of	ADP
ap-5050	179	14	the	the	DET
ap-5050	179	15	reaction	reaction	NOUN
ap-5050	179	16	n	n	NOUN
ap-5050	179	17	.	.	PUNCT
ap-5050	180	1	the	the	DET
ap-5050	180	2	physical	physical	ADJ
ap-5050	180	3	essence	essence	NOUN
ap-5050	180	4	of	of	ADP
ap-5050	180	5	such	such	ADJ
ap-5050	180	6	effect	effect	NOUN
ap-5050	180	7	can	can	AUX
ap-5050	180	8	be	be	AUX
ap-5050	180	9	explained	explain	VERB
ap-5050	180	10	by	by	ADP
ap-5050	180	11	the	the	DET
ap-5050	180	12	fact	fact	NOUN
ap-5050	180	13	that	that	SCONJ
ap-5050	180	14	,	,	PUNCT
ap-5050	180	15	if	if	SCONJ
ap-5050	180	16	angular	angular	ADJ
ap-5050	180	17	velocity	velocity	NOUN
ap-5050	180	18	is	be	AUX
ap-5050	180	19	increased	increase	VERB
ap-5050	180	20	,	,	PUNCT
ap-5050	180	21	inertial	inertial	ADJ
ap-5050	180	22	force	force	NOUN
ap-5050	180	23	increases	increase	NOUN
ap-5050	180	24	and	and	CCONJ
ap-5050	180	25	it	it	PRON
ap-5050	180	26	overcomes	overcome	VERB
ap-5050	180	27	the	the	DET
ap-5050	180	28	particle	particle	NOUN
ap-5050	180	29	weight	weight	NOUN
ap-5050	180	30	force	force	NOUN
ap-5050	180	31	,	,	PUNCT
ap-5050	180	32	but	but	CCONJ
ap-5050	180	33	here	here	ADV
ap-5050	180	34	,	,	PUNCT
ap-5050	180	35	it	it	PRON
ap-5050	180	36	detaches	detach	VERB
ap-5050	180	37	a	a	DET
ap-5050	180	38	particle	particle	NOUN
ap-5050	180	39	from	from	ADP
ap-5050	180	40	a	a	DET
ap-5050	180	41	plane	plane	NOUN
ap-5050	180	42	.	.	PUNCT
ap-5050	181	1	let	let	VERB
ap-5050	181	2	us	we	PRON
ap-5050	181	3	increase	increase	VERB
ap-5050	181	4	the	the	DET
ap-5050	181	5	radius	radius	NOUN
ap-5050	181	6	r	r	NOUN
ap-5050	181	7	of	of	ADP
ap-5050	181	8	a	a	DET
ap-5050	181	9	limiting	limit	VERB
ap-5050	181	10	cylinder	cylinder	NOUN
ap-5050	181	11	to	to	ADP
ap-5050	181	12	0.25	0.25	NUM
ap-5050	181	13	m	m	NOUN
ap-5050	181	14	without	without	ADP
ap-5050	181	15	changing	change	VERB
ap-5050	181	16	any	any	DET
ap-5050	181	17	other	other	ADJ
ap-5050	181	18	parameters	parameter	NOUN
ap-5050	181	19	.	.	PUNCT
ap-5050	182	1	the	the	DET
ap-5050	182	2	area	area	NOUN
ap-5050	182	3	of	of	ADP
ap-5050	182	4	the	the	DET
ap-5050	182	5	unpredictable	unpredictable	ADJ
ap-5050	182	6	behaviour	behaviour	NOUN
ap-5050	182	7	of	of	ADP
ap-5050	182	8	a	a	DET
ap-5050	182	9	particle	particle	NOUN
ap-5050	182	10	increases	increase	NOUN
ap-5050	182	11	and	and	CCONJ
ap-5050	182	12	begins	begin	VERB
ap-5050	182	13	even	even	ADV
ap-5050	182	14	before	before	ADP
ap-5050	182	15	the	the	DET
ap-5050	182	16	moment	moment	NOUN
ap-5050	182	17	when	when	SCONJ
ap-5050	182	18	a	a	DET
ap-5050	182	19	particle	particle	NOUN
ap-5050	182	20	reaches	reach	VERB
ap-5050	182	21	its	its	PRON
ap-5050	182	22	highest	high	ADJ
ap-5050	182	23	point	point	NOUN
ap-5050	182	24	at	at	ADP
ap-5050	182	25	its	its	PRON
ap-5050	182	26	upward	upward	ADJ
ap-5050	182	27	movement	movement	NOUN
ap-5050	182	28	(	(	PUNCT
ap-5050	182	29	figure	figure	NOUN
ap-5050	182	30	9	9	NUM
ap-5050	182	31	)	)	PUNCT
ap-5050	182	32	.	.	PUNCT
ap-5050	183	1	this	this	PRON
ap-5050	183	2	implies	imply	VERB
ap-5050	183	3	that	that	SCONJ
ap-5050	183	4	the	the	DET
ap-5050	183	5	increase	increase	NOUN
ap-5050	183	6	of	of	ADP
ap-5050	183	7	the	the	DET
ap-5050	183	8	design	design	NOUN
ap-5050	183	9	parameters	parameter	NOUN
ap-5050	183	10	(	(	PUNCT
ap-5050	183	11	the	the	DET
ap-5050	183	12	angle	angle	NOUN
ap-5050	183	13	β	β	X
ap-5050	183	14	of	of	ADP
ap-5050	183	15	the	the	DET
ap-5050	183	16	plane	plane	NOUN
ap-5050	183	17	inclination	inclination	NOUN
ap-5050	183	18	,	,	PUNCT
ap-5050	183	19	the	the	DET
ap-5050	183	20	radius	radius	NOUN
ap-5050	183	21	r	r	NOUN
ap-5050	183	22	of	of	ADP
ap-5050	183	23	a	a	DET
ap-5050	183	24	limiting	limit	VERB
ap-5050	183	25	cylinder	cylinder	NOUN
ap-5050	183	26	)	)	PUNCT
ap-5050	183	27	or	or	CCONJ
ap-5050	183	28	the	the	DET
ap-5050	183	29	technological	technological	ADJ
ap-5050	183	30	ones	one	NOUN
ap-5050	183	31	(	(	PUNCT
ap-5050	183	32	the	the	DET
ap-5050	183	33	increase	increase	NOUN
ap-5050	183	34	of	of	ADP
ap-5050	183	35	the	the	DET
ap-5050	183	36	angular	angular	ADJ
ap-5050	183	37	velocity	velocity	NOUN
ap-5050	183	38	ω	ω	PROPN
ap-5050	183	39	of	of	ADP
ap-5050	183	40	plane	plane	NOUN
ap-5050	183	41	rotation	rotation	NOUN
ap-5050	183	42	)	)	PUNCT
ap-5050	183	43	causes	cause	VERB
ap-5050	183	44	a	a	DET
ap-5050	183	45	situation	situation	NOUN
ap-5050	183	46	when	when	SCONJ
ap-5050	183	47	the	the	DET
ap-5050	183	48	particle	particle	NOUN
ap-5050	183	49	motion	motion	NOUN
ap-5050	183	50	in	in	ADP
ap-5050	183	51	an	an	DET
ap-5050	183	52	ellipse	ellipse	NOUN
ap-5050	183	53	can	can	AUX
ap-5050	183	54	not	not	PART
ap-5050	183	55	be	be	AUX
ap-5050	183	56	provided	provide	VERB
ap-5050	183	57	along	along	ADP
ap-5050	183	58	the	the	DET
ap-5050	183	59	whole	whole	ADJ
ap-5050	183	60	trajectory	trajectory	NOUN
ap-5050	183	61	.	.	PUNCT
ap-5050	184	1	there	there	PRON
ap-5050	184	2	is	be	VERB
ap-5050	184	3	either	either	CCONJ
ap-5050	184	4	the	the	DET
ap-5050	184	5	particle	particle	NOUN
ap-5050	184	6	“	"	PUNCT
ap-5050	184	7	sticking	stick	VERB
ap-5050	184	8	”	"	PUNCT
ap-5050	184	9	or	or	CCONJ
ap-5050	184	10	its	its	PRON
ap-5050	184	11	detachment	detachment	NOUN
ap-5050	184	12	from	from	ADP
ap-5050	184	13	a	a	DET
ap-5050	184	14	plane	plane	NOUN
ap-5050	184	15	.	.	PUNCT
ap-5050	185	1	let	let	VERB
ap-5050	185	2	us	we	PRON
ap-5050	185	3	determine	determine	VERB
ap-5050	185	4	the	the	DET
ap-5050	185	5	role	role	NOUN
ap-5050	185	6	of	of	ADP
ap-5050	185	7	the	the	DET
ap-5050	185	8	coefficient	coefficient	NOUN
ap-5050	185	9	f	f	PROPN
ap-5050	185	10	of	of	ADP
ap-5050	185	11	the	the	DET
ap-5050	185	12	particle	particle	NOUN
ap-5050	185	13	friction	friction	NOUN
ap-5050	185	14	on	on	ADP
ap-5050	185	15	the	the	DET
ap-5050	185	16	surface	surface	NOUN
ap-5050	185	17	of	of	ADP
ap-5050	185	18	a	a	DET
ap-5050	185	19	flat	flat	ADJ
ap-5050	185	20	segment	segment	NOUN
ap-5050	185	21	and	and	CCONJ
ap-5050	185	22	the	the	DET
ap-5050	185	23	coefficient	coefficient	NOUN
ap-5050	185	24	fr	fr	NOUN
ap-5050	185	25	of	of	ADP
ap-5050	185	26	the	the	DET
ap-5050	185	27	particle	particle	NOUN
ap-5050	185	28	friction	friction	NOUN
ap-5050	185	29	on	on	ADP
ap-5050	185	30	the	the	DET
ap-5050	185	31	surface	surface	NOUN
ap-5050	185	32	of	of	ADP
ap-5050	185	33	a	a	DET
ap-5050	185	34	limiting	limit	VERB
ap-5050	185	35	cylinder	cylinder	NOUN
ap-5050	185	36	.	.	PUNCT
ap-5050	186	1	the	the	DET
ap-5050	186	2	value	value	NOUN
ap-5050	186	3	of	of	ADP
ap-5050	186	4	these	these	DET
ap-5050	186	5	coefficients	coefficient	NOUN
ap-5050	186	6	plays	play	VERB
ap-5050	186	7	a	a	DET
ap-5050	186	8	part	part	NOUN
ap-5050	186	9	in	in	ADP
ap-5050	186	10	the	the	DET
ap-5050	186	11	particle	particle	NOUN
ap-5050	186	12	motion	motion	NOUN
ap-5050	186	13	in	in	ADP
ap-5050	186	14	an	an	DET
ap-5050	186	15	ellipse	ellipse	NOUN
ap-5050	186	16	.	.	PUNCT
ap-5050	187	1	let	let	VERB
ap-5050	187	2	us	we	PRON
ap-5050	187	3	determine	determine	VERB
ap-5050	187	4	this	this	DET
ap-5050	187	5	motion	motion	NOUN
ap-5050	187	6	by	by	ADP
ap-5050	187	7	the	the	DET
ap-5050	187	8	dependence	dependence	NOUN
ap-5050	187	9	z	z	NOUN
ap-5050	187	10	=	=	SYM
ap-5050	187	11	z(t	z(t	NOUN
ap-5050	187	12	)	)	PUNCT
ap-5050	187	13	,	,	PUNCT
ap-5050	187	14	that	that	PRON
ap-5050	187	15	is	be	AUX
ap-5050	187	16	to	to	PART
ap-5050	187	17	say	say	VERB
ap-5050	187	18	,	,	PUNCT
ap-5050	187	19	by	by	ADP
ap-5050	187	20	the	the	DET
ap-5050	187	21	regularity	regularity	NOUN
ap-5050	187	22	of	of	ADP
ap-5050	187	23	the	the	DET
ap-5050	187	24	particle	particle	NOUN
ap-5050	187	25	upward	upward	ADJ
ap-5050	187	26	movement	movement	NOUN
ap-5050	187	27	and	and	CCONJ
ap-5050	187	28	particle	particle	NOUN
ap-5050	187	29	fall	fall	NOUN
ap-5050	187	30	movement	movement	NOUN
ap-5050	187	31	.	.	PUNCT
ap-5050	188	1	this	this	DET
ap-5050	188	2	regularity	regularity	NOUN
ap-5050	188	3	is	be	AUX
ap-5050	188	4	the	the	DET
ap-5050	188	5	same	same	ADJ
ap-5050	188	6	for	for	ADP
ap-5050	188	7	the	the	DET
ap-5050	188	8	relative	relative	ADJ
ap-5050	188	9	motion	motion	NOUN
ap-5050	188	10	and	and	CCONJ
ap-5050	188	11	the	the	DET
ap-5050	188	12	absolute	absolute	ADJ
ap-5050	188	13	motion	motion	NOUN
ap-5050	188	14	.	.	PUNCT
ap-5050	189	1	to	to	PART
ap-5050	189	2	put	put	VERB
ap-5050	189	3	that	that	PRON
ap-5050	189	4	into	into	ADP
ap-5050	189	5	context	context	NOUN
ap-5050	189	6	,	,	PUNCT
ap-5050	189	7	let	let	VERB
ap-5050	189	8	us	we	PRON
ap-5050	189	9	take	take	VERB
ap-5050	189	10	the	the	DET
ap-5050	189	11	curve	curve	NOUN
ap-5050	189	12	shown	show	VERB
ap-5050	189	13	in	in	ADP
ap-5050	189	14	figure	figure	NOUN
ap-5050	189	15	6b	6b	NOUN
ap-5050	189	16	and	and	CCONJ
ap-5050	189	17	decrease	decrease	VERB
ap-5050	189	18	the	the	DET
ap-5050	189	19	friction	friction	NOUN
ap-5050	189	20	coefficient	coefficient	NOUN
ap-5050	189	21	f	f	PROPN
ap-5050	189	22	for	for	ADP
ap-5050	189	23	0.1	0.1	NUM
ap-5050	189	24	.	.	PUNCT
ap-5050	190	1	let	let	VERB
ap-5050	190	2	us	we	PRON
ap-5050	190	3	construct	construct	VERB
ap-5050	190	4	the	the	DET
ap-5050	190	5	analogical	analogical	ADJ
ap-5050	190	6	curve	curve	NOUN
ap-5050	190	7	for	for	ADP
ap-5050	190	8	the	the	DET
ap-5050	190	9	process	process	NOUN
ap-5050	190	10	lasting	last	VERB
ap-5050	190	11	for	for	ADP
ap-5050	190	12	5	5	NUM
ap-5050	190	13	s.	s.	PROPN
ap-5050	190	14	this	this	DET
ap-5050	190	15	curve	curve	NOUN
ap-5050	190	16	is	be	AUX
ap-5050	190	17	presented	present	VERB
ap-5050	190	18	in	in	ADP
ap-5050	190	19	figure	figure	NOUN
ap-5050	190	20	10	10	NUM
ap-5050	190	21	(	(	PUNCT
ap-5050	190	22	at	at	ADP
ap-5050	190	23	the	the	DET
ap-5050	190	24	top	top	NOUN
ap-5050	190	25	)	)	PUNCT
ap-5050	190	26	,	,	PUNCT
ap-5050	190	27	which	which	PRON
ap-5050	190	28	is	be	AUX
ap-5050	190	29	synchronized	synchronize	VERB
ap-5050	190	30	in	in	ADP
ap-5050	190	31	time	time	NOUN
ap-5050	190	32	with	with	ADP
ap-5050	190	33	the	the	DET
ap-5050	190	34	surface	surface	NOUN
ap-5050	190	35	reaction	reaction	NOUN
ap-5050	190	36	curve	curve	NOUN
ap-5050	190	37	(	(	PUNCT
ap-5050	190	38	at	at	ADP
ap-5050	190	39	the	the	DET
ap-5050	190	40	bottom	bottom	NOUN
ap-5050	190	41	)	)	PUNCT
ap-5050	190	42	in	in	ADP
ap-5050	190	43	a	a	DET
ap-5050	190	44	similar	similar	ADJ
ap-5050	190	45	way	way	NOUN
ap-5050	190	46	to	to	ADP
ap-5050	190	47	the	the	DET
ap-5050	190	48	previous	previous	ADJ
ap-5050	190	49	examples	example	NOUN
ap-5050	190	50	.	.	PUNCT
ap-5050	191	1	71	71	NUM
ap-5050	191	2	s.	s.	PROPN
ap-5050	191	3	f.	f.	PROPN
ap-5050	191	4	pylypaka	pylypaka	PROPN
ap-5050	191	5	,	,	PUNCT
ap-5050	191	6	m.	m.	PROPN
ap-5050	191	7	b.	b.	PROPN
ap-5050	191	8	klendii	klendii	PROPN
ap-5050	191	9	,	,	PUNCT
ap-5050	191	10	v.	v.	PROPN
ap-5050	191	11	m.	m.	PROPN
ap-5050	191	12	nesvidomin	nesvidomin	PROPN
ap-5050	191	13	,	,	PUNCT
ap-5050	191	14	v.	v.	PROPN
ap-5050	191	15	i.	i.	PROPN
ap-5050	191	16	trokhaniak	trokhaniak	PROPN
ap-5050	191	17	acta	acta	PROPN
ap-5050	191	18	polytechnica	polytechnica	PROPN
ap-5050	191	19	figure	figure	NOUN
ap-5050	191	20	3	3	NUM
ap-5050	191	21	.	.	PUNCT
ap-5050	191	22	(	(	PUNCT
ap-5050	191	23	a	a	X
ap-5050	191	24	)	)	PUNCT
ap-5050	191	25	sliding	slide	VERB
ap-5050	191	26	angular	angular	ADJ
ap-5050	191	27	velocity	velocity	NOUN
ap-5050	191	28	curve	curve	NOUN
ap-5050	191	29	;	;	PUNCT
ap-5050	191	30	(	(	PUNCT
ap-5050	191	31	b	b	X
ap-5050	191	32	)	)	PUNCT
ap-5050	191	33	the	the	DET
ap-5050	191	34	curve	curve	NOUN
ap-5050	191	35	of	of	ADP
ap-5050	191	36	the	the	DET
ap-5050	191	37	relative	relative	ADJ
ap-5050	191	38	velocity	velocity	NOUN
ap-5050	191	39	of	of	ADP
ap-5050	191	40	particle	particle	NOUN
ap-5050	191	41	sliding	slide	VERB
ap-5050	191	42	in	in	ADP
ap-5050	191	43	a	a	DET
ap-5050	191	44	circle	circle	NOUN
ap-5050	191	45	.	.	PUNCT
ap-5050	192	1	figure	figure	NOUN
ap-5050	192	2	4	4	NUM
ap-5050	192	3	.	.	PUNCT
ap-5050	192	4	kinematic	kinematic	ADJ
ap-5050	192	5	parameter	parameter	NOUN
ap-5050	192	6	curves	curve	NOUN
ap-5050	192	7	for	for	ADP
ap-5050	192	8	particle	particle	NOUN
ap-5050	192	9	fall	fall	NOUN
ap-5050	192	10	movement	movement	NOUN
ap-5050	192	11	in	in	ADP
ap-5050	192	12	an	an	DET
ap-5050	192	13	ellipse	ellipse	NOUN
ap-5050	192	14	of	of	ADP
ap-5050	192	15	a	a	DET
ap-5050	192	16	fixed	fix	VERB
ap-5050	192	17	plane	plane	NOUN
ap-5050	192	18	at	at	ADP
ap-5050	192	19	β	β	X
ap-5050	192	20	=	=	SYM
ap-5050	192	21	30	30	NUM
ap-5050	192	22	°	°	NUM
ap-5050	192	23	,	,	PUNCT
ap-5050	192	24	r	r	NOUN
ap-5050	192	25	=	=	SYM
ap-5050	192	26	0.1	0.1	NUM
ap-5050	192	27	m	m	NOUN
ap-5050	192	28	,	,	PUNCT
ap-5050	192	29	f	f	PROPN
ap-5050	193	1	=	=	NOUN
ap-5050	193	2	fr	fr	PROPN
ap-5050	193	3	=	=	PUNCT
ap-5050	193	4	0.3	0.3	NUM
ap-5050	193	5	,	,	PUNCT
ap-5050	193	6	ω	ω	X
ap-5050	193	7	=	=	SYM
ap-5050	193	8	0	0	NUM
ap-5050	193	9	:	:	PUNCT
ap-5050	193	10	(	(	PUNCT
ap-5050	193	11	a	a	X
ap-5050	193	12	)	)	PUNCT
ap-5050	193	13	relative	relative	ADJ
ap-5050	193	14	velocity	velocity	NOUN
ap-5050	193	15	curve	curve	NOUN
ap-5050	193	16	;	;	PUNCT
ap-5050	193	17	(	(	PUNCT
ap-5050	193	18	b	b	X
ap-5050	193	19	)	)	PUNCT
ap-5050	193	20	the	the	DET
ap-5050	193	21	height	height	NOUN
ap-5050	193	22	of	of	ADP
ap-5050	193	23	particle	particle	NOUN
ap-5050	193	24	fall	fall	NOUN
ap-5050	193	25	movement	movement	PROPN
ap-5050	193	26	curve	curve	NOUN
ap-5050	193	27	.	.	PUNCT
ap-5050	194	1	figure	figure	NOUN
ap-5050	194	2	5	5	NUM
ap-5050	194	3	.	.	PUNCT
ap-5050	194	4	kinematic	kinematic	ADJ
ap-5050	194	5	parameter	parameter	NOUN
ap-5050	194	6	curves	curve	NOUN
ap-5050	194	7	for	for	ADP
ap-5050	194	8	particle	particle	NOUN
ap-5050	194	9	fall	fall	NOUN
ap-5050	194	10	movement	movement	NOUN
ap-5050	194	11	in	in	ADP
ap-5050	194	12	an	an	DET
ap-5050	194	13	ellipse	ellipse	NOUN
ap-5050	194	14	,	,	PUNCT
ap-5050	194	15	which	which	PRON
ap-5050	194	16	rotates	rotate	VERB
ap-5050	194	17	with	with	ADP
ap-5050	194	18	low	low	ADJ
ap-5050	194	19	angular	angular	ADJ
ap-5050	194	20	velocity	velocity	NOUN
ap-5050	194	21	,	,	PUNCT
ap-5050	194	22	at	at	ADP
ap-5050	194	23	β	β	X
ap-5050	194	24	=	=	SYM
ap-5050	194	25	30	30	NUM
ap-5050	194	26	°	°	NUM
ap-5050	194	27	,	,	PUNCT
ap-5050	194	28	r	r	NOUN
ap-5050	194	29	=	=	SYM
ap-5050	194	30	0.1	0.1	NUM
ap-5050	194	31	m	m	NOUN
ap-5050	194	32	,	,	PUNCT
ap-5050	195	1	f	f	PROPN
ap-5050	196	1	=	=	NOUN
ap-5050	196	2	fr	fr	PROPN
ap-5050	196	3	=	=	PUNCT
ap-5050	196	4	0.3	0.3	NUM
ap-5050	196	5	,	,	PUNCT
ap-5050	196	6	ω	ω	NOUN
ap-5050	196	7	=	=	SYM
ap-5050	196	8	5	5	NUM
ap-5050	196	9	s−1	s−1	PROPN
ap-5050	196	10	:	:	PUNCT
ap-5050	196	11	(	(	PUNCT
ap-5050	196	12	a	a	X
ap-5050	196	13	)	)	PUNCT
ap-5050	196	14	relative	relative	ADJ
ap-5050	196	15	velocity	velocity	NOUN
ap-5050	196	16	curve	curve	NOUN
ap-5050	196	17	;	;	PUNCT
ap-5050	196	18	(	(	PUNCT
ap-5050	196	19	b	b	X
ap-5050	196	20	)	)	PUNCT
ap-5050	196	21	the	the	DET
ap-5050	196	22	height	height	NOUN
ap-5050	196	23	of	of	ADP
ap-5050	196	24	particle	particle	NOUN
ap-5050	196	25	fall	fall	NOUN
ap-5050	196	26	movement	movement	PROPN
ap-5050	196	27	curve	curve	NOUN
ap-5050	196	28	.	.	PUNCT
ap-5050	197	1	figure	figure	NOUN
ap-5050	197	2	6	6	NUM
ap-5050	197	3	.	.	PUNCT
ap-5050	197	4	kinematic	kinematic	ADJ
ap-5050	197	5	parameter	parameter	NOUN
ap-5050	197	6	curves	curve	NOUN
ap-5050	197	7	for	for	ADP
ap-5050	197	8	particle	particle	NOUN
ap-5050	197	9	sliding	slide	VERB
ap-5050	197	10	in	in	ADP
ap-5050	197	11	an	an	DET
ap-5050	197	12	ellipse	ellipse	NOUN
ap-5050	197	13	,	,	PUNCT
ap-5050	197	14	which	which	PRON
ap-5050	197	15	rotates	rotate	VERB
ap-5050	197	16	with	with	ADP
ap-5050	197	17	angular	angular	ADJ
ap-5050	197	18	velocity	velocity	NOUN
ap-5050	197	19	ω	ω	NOUN
ap-5050	197	20	=	=	NOUN
ap-5050	197	21	20	20	NUM
ap-5050	197	22	s−1	s−1	PROPN
ap-5050	197	23	,	,	PUNCT
ap-5050	197	24	at	at	ADP
ap-5050	197	25	β	β	X
ap-5050	197	26	=	=	SYM
ap-5050	197	27	30	30	NUM
ap-5050	197	28	°	°	NUM
ap-5050	197	29	,	,	PUNCT
ap-5050	197	30	r	r	NOUN
ap-5050	197	31	=	=	SYM
ap-5050	197	32	0.1	0.1	NUM
ap-5050	197	33	m	m	NOUN
ap-5050	197	34	,	,	PUNCT
ap-5050	197	35	f	f	PROPN
ap-5050	198	1	=	=	NOUN
ap-5050	198	2	fr	fr	NOUN
ap-5050	198	3	=	=	NOUN
ap-5050	198	4	0.3	0.3	NUM
ap-5050	198	5	:	:	PUNCT
ap-5050	198	6	(	(	PUNCT
ap-5050	198	7	a	a	X
ap-5050	198	8	)	)	PUNCT
ap-5050	198	9	relative	relative	ADJ
ap-5050	198	10	velocity	velocity	NOUN
ap-5050	198	11	curve	curve	NOUN
ap-5050	198	12	;	;	PUNCT
ap-5050	198	13	(	(	PUNCT
ap-5050	198	14	b	b	X
ap-5050	198	15	)	)	PUNCT
ap-5050	198	16	the	the	DET
ap-5050	198	17	height	height	NOUN
ap-5050	198	18	of	of	ADP
ap-5050	198	19	relative	relative	ADJ
ap-5050	198	20	motion	motion	NOUN
ap-5050	198	21	curve	curve	NOUN
ap-5050	198	22	.	.	PUNCT
ap-5050	199	1	72	72	NUM
ap-5050	199	2	vol	vol	NOUN
ap-5050	199	3	.	.	PUNCT
ap-5050	200	1	59	59	NUM
ap-5050	200	2	no	no	NOUN
ap-5050	200	3	.	.	PUNCT
ap-5050	201	1	1/2019	1/2019	NUM
ap-5050	201	2	particle	particle	NOUN
ap-5050	201	3	motion	motion	NOUN
ap-5050	201	4	over	over	ADP
ap-5050	201	5	the	the	DET
ap-5050	201	6	edge	edge	NOUN
ap-5050	201	7	of	of	ADP
ap-5050	201	8	an	an	DET
ap-5050	201	9	inclined	inclined	ADJ
ap-5050	201	10	plane	plane	NOUN
ap-5050	201	11	figure	figure	NOUN
ap-5050	201	12	7	7	NUM
ap-5050	201	13	.	.	PUNCT
ap-5050	201	14	kinematic	kinematic	ADJ
ap-5050	201	15	parameter	parameter	NOUN
ap-5050	201	16	curves	curve	NOUN
ap-5050	201	17	for	for	ADP
ap-5050	201	18	particle	particle	NOUN
ap-5050	201	19	sliding	slide	VERB
ap-5050	201	20	in	in	ADP
ap-5050	201	21	an	an	DET
ap-5050	201	22	ellipse	ellipse	NOUN
ap-5050	201	23	,	,	PUNCT
ap-5050	201	24	which	which	PRON
ap-5050	201	25	rotates	rotate	VERB
ap-5050	201	26	with	with	ADP
ap-5050	201	27	angular	angular	ADJ
ap-5050	201	28	velocity	velocity	NOUN
ap-5050	201	29	ω	ω	NOUN
ap-5050	201	30	=	=	NOUN
ap-5050	201	31	20	20	NUM
ap-5050	201	32	s−1	s−1	PROPN
ap-5050	201	33	,	,	PUNCT
ap-5050	201	34	at	at	ADP
ap-5050	201	35	β	β	X
ap-5050	201	36	=	=	SYM
ap-5050	201	37	35	35	NUM
ap-5050	201	38	°	°	NUM
ap-5050	201	39	,	,	PUNCT
ap-5050	201	40	r	r	NOUN
ap-5050	201	41	=	=	SYM
ap-5050	201	42	0.1	0.1	NUM
ap-5050	201	43	m	m	NOUN
ap-5050	201	44	,	,	PUNCT
ap-5050	201	45	f	f	PROPN
ap-5050	202	1	=	=	NOUN
ap-5050	202	2	fr	fr	NOUN
ap-5050	202	3	=	=	NOUN
ap-5050	202	4	0.3	0.3	NUM
ap-5050	202	5	:	:	PUNCT
ap-5050	202	6	(	(	PUNCT
ap-5050	202	7	a	a	X
ap-5050	202	8	)	)	PUNCT
ap-5050	202	9	the	the	DET
ap-5050	202	10	height	height	NOUN
ap-5050	202	11	of	of	ADP
ap-5050	202	12	relative	relative	ADJ
ap-5050	202	13	motion	motion	NOUN
ap-5050	202	14	curve	curve	NOUN
ap-5050	202	15	;	;	PUNCT
ap-5050	202	16	(	(	PUNCT
ap-5050	202	17	b	b	X
ap-5050	202	18	)	)	PUNCT
ap-5050	202	19	the	the	DET
ap-5050	202	20	trajectory	trajectory	NOUN
ap-5050	202	21	of	of	ADP
ap-5050	202	22	absolute	absolute	ADJ
ap-5050	202	23	particle	particle	NOUN
ap-5050	202	24	motion	motion	NOUN
ap-5050	202	25	.	.	PUNCT
ap-5050	203	1	figure	figure	NOUN
ap-5050	203	2	8	8	NUM
ap-5050	203	3	.	.	PUNCT
ap-5050	204	1	the	the	DET
ap-5050	204	2	height	height	NOUN
ap-5050	204	3	z	z	NOUN
ap-5050	204	4	curve	curve	NOUN
ap-5050	204	5	(	(	PUNCT
ap-5050	204	6	at	at	ADP
ap-5050	204	7	the	the	DET
ap-5050	204	8	top	top	NOUN
ap-5050	204	9	)	)	PUNCT
ap-5050	204	10	and	and	CCONJ
ap-5050	204	11	the	the	DET
ap-5050	204	12	surface	surface	NOUN
ap-5050	204	13	reaction	reaction	NOUN
ap-5050	204	14	n	n	PRON
ap-5050	204	15	curve	curve	NOUN
ap-5050	204	16	(	(	PUNCT
ap-5050	204	17	at	at	ADP
ap-5050	204	18	the	the	DET
ap-5050	204	19	bottom	bottom	NOUN
ap-5050	204	20	)	)	PUNCT
ap-5050	204	21	at	at	ADP
ap-5050	204	22	ω	ω	PROPN
ap-5050	204	23	=	=	SYM
ap-5050	204	24	24	24	NUM
ap-5050	204	25	s−1	s−1	PROPN
ap-5050	204	26	,	,	PUNCT
ap-5050	204	27	β	β	X
ap-5050	204	28	=	=	NOUN
ap-5050	204	29	35	35	NUM
ap-5050	204	30	°	°	NUM
ap-5050	204	31	,	,	PUNCT
ap-5050	204	32	r	r	NOUN
ap-5050	204	33	=	=	SYM
ap-5050	204	34	0.1	0.1	NUM
ap-5050	204	35	m	m	NOUN
ap-5050	204	36	,	,	PUNCT
ap-5050	204	37	f	f	PROPN
ap-5050	205	1	=	=	NOUN
ap-5050	205	2	fr	fr	PROPN
ap-5050	205	3	=	=	PUNCT
ap-5050	205	4	0.3	0.3	NUM
ap-5050	205	5	.	.	PUNCT
ap-5050	206	1	figure	figure	NOUN
ap-5050	206	2	9	9	NUM
ap-5050	206	3	.	.	PUNCT
ap-5050	207	1	the	the	DET
ap-5050	207	2	height	height	NOUN
ap-5050	207	3	z	z	NOUN
ap-5050	207	4	curve	curve	NOUN
ap-5050	207	5	(	(	PUNCT
ap-5050	207	6	at	at	ADP
ap-5050	207	7	the	the	DET
ap-5050	207	8	top	top	NOUN
ap-5050	207	9	)	)	PUNCT
ap-5050	207	10	and	and	CCONJ
ap-5050	207	11	the	the	DET
ap-5050	207	12	surface	surface	NOUN
ap-5050	207	13	reaction	reaction	NOUN
ap-5050	207	14	n	n	PRON
ap-5050	207	15	curve	curve	NOUN
ap-5050	207	16	(	(	PUNCT
ap-5050	207	17	at	at	ADP
ap-5050	207	18	the	the	DET
ap-5050	207	19	bottom	bottom	NOUN
ap-5050	207	20	)	)	PUNCT
ap-5050	207	21	at	at	ADP
ap-5050	207	22	ω	ω	PROPN
ap-5050	207	23	=	=	SYM
ap-5050	207	24	24	24	NUM
ap-5050	207	25	s−1	s−1	PROPN
ap-5050	207	26	,	,	PUNCT
ap-5050	207	27	β	β	X
ap-5050	207	28	=	=	NOUN
ap-5050	207	29	35	35	NUM
ap-5050	207	30	°	°	NUM
ap-5050	207	31	,	,	PUNCT
ap-5050	207	32	r	r	NOUN
ap-5050	207	33	=	=	PUNCT
ap-5050	207	34	0.25	0.25	NUM
ap-5050	207	35	m	m	NOUN
ap-5050	207	36	,	,	PUNCT
ap-5050	207	37	f	f	PROPN
ap-5050	207	38	=	=	NOUN
ap-5050	207	39	fr	fr	PROPN
ap-5050	207	40	=	=	PUNCT
ap-5050	207	41	0.3	0.3	NUM
ap-5050	207	42	.	.	PUNCT
ap-5050	208	1	73	73	NUM
ap-5050	208	2	s.	s.	PROPN
ap-5050	208	3	f.	f.	PROPN
ap-5050	208	4	pylypaka	pylypaka	PROPN
ap-5050	208	5	,	,	PUNCT
ap-5050	208	6	m.	m.	PROPN
ap-5050	208	7	b.	b.	PROPN
ap-5050	208	8	klendii	klendii	PROPN
ap-5050	208	9	,	,	PUNCT
ap-5050	208	10	v.	v.	PROPN
ap-5050	208	11	m.	m.	PROPN
ap-5050	208	12	nesvidomin	nesvidomin	PROPN
ap-5050	208	13	,	,	PUNCT
ap-5050	208	14	v.	v.	PROPN
ap-5050	208	15	i.	i.	PROPN
ap-5050	208	16	trokhaniak	trokhaniak	PROPN
ap-5050	208	17	acta	acta	PROPN
ap-5050	208	18	polytechnica	polytechnica	PROPN
ap-5050	208	19	figure	figure	NOUN
ap-5050	208	20	10	10	NUM
ap-5050	208	21	.	.	PUNCT
ap-5050	209	1	the	the	DET
ap-5050	209	2	height	height	NOUN
ap-5050	209	3	z	z	NOUN
ap-5050	209	4	curve	curve	NOUN
ap-5050	209	5	(	(	PUNCT
ap-5050	209	6	at	at	ADP
ap-5050	209	7	the	the	DET
ap-5050	209	8	top	top	NOUN
ap-5050	209	9	)	)	PUNCT
ap-5050	209	10	and	and	CCONJ
ap-5050	209	11	the	the	DET
ap-5050	209	12	surface	surface	NOUN
ap-5050	209	13	reaction	reaction	NOUN
ap-5050	209	14	n	n	PRON
ap-5050	209	15	curve	curve	NOUN
ap-5050	209	16	(	(	PUNCT
ap-5050	209	17	at	at	ADP
ap-5050	209	18	the	the	DET
ap-5050	209	19	bottom)at	bottom)at	NOUN
ap-5050	209	20	ω	ω	PROPN
ap-5050	209	21	=	=	SYM
ap-5050	209	22	20	20	NUM
ap-5050	209	23	s−1	s−1	PROPN
ap-5050	209	24	,	,	PUNCT
ap-5050	209	25	β	β	X
ap-5050	209	26	=	=	SYM
ap-5050	209	27	30	30	NUM
ap-5050	209	28	°	°	NUM
ap-5050	209	29	,	,	PUNCT
ap-5050	209	30	r	r	NOUN
ap-5050	209	31	=	=	SYM
ap-5050	209	32	0.1	0.1	NUM
ap-5050	209	33	m	m	NOUN
ap-5050	209	34	,	,	PUNCT
ap-5050	209	35	f	f	PROPN
ap-5050	209	36	=	=	PUNCT
ap-5050	209	37	0.2	0.2	NUM
ap-5050	209	38	,	,	PUNCT
ap-5050	209	39	fr	fr	NOUN
ap-5050	209	40	=	=	NOUN
ap-5050	209	41	0.3	0.3	NUM
ap-5050	209	42	.	.	PUNCT
ap-5050	210	1	figure	figure	VERB
ap-5050	210	2	11	11	NUM
ap-5050	210	3	.	.	PUNCT
ap-5050	211	1	trajectories	trajectory	NOUN
ap-5050	211	2	of	of	ADP
ap-5050	211	3	absolute	absolute	ADJ
ap-5050	211	4	motion	motion	NOUN
ap-5050	211	5	over	over	ADP
ap-5050	211	6	the	the	DET
ap-5050	211	7	inner	inner	ADJ
ap-5050	211	8	surface	surface	NOUN
ap-5050	211	9	of	of	ADP
ap-5050	211	10	a	a	DET
ap-5050	211	11	limiting	limit	VERB
ap-5050	211	12	cylinder	cylinder	NOUN
ap-5050	211	13	of	of	ADP
ap-5050	211	14	radius	radius	NOUN
ap-5050	211	15	r	r	NOUN
ap-5050	211	16	=	=	NOUN
ap-5050	211	17	0.1	0.1	NUM
ap-5050	211	18	:	:	PUNCT
ap-5050	211	19	(	(	PUNCT
ap-5050	211	20	a	a	X
ap-5050	211	21	)	)	PUNCT
ap-5050	211	22	ω	ω	NOUN
ap-5050	211	23	=	=	SYM
ap-5050	211	24	20	20	NUM
ap-5050	211	25	s−1	s−1	PROPN
ap-5050	211	26	,	,	PUNCT
ap-5050	211	27	β	β	X
ap-5050	211	28	=	=	SYM
ap-5050	211	29	30	30	NUM
ap-5050	211	30	°	°	NUM
ap-5050	211	31	,	,	PUNCT
ap-5050	211	32	f	f	PROPN
ap-5050	211	33	=	=	PUNCT
ap-5050	211	34	0.2	0.2	NUM
ap-5050	211	35	,	,	PUNCT
ap-5050	211	36	fr	fr	NOUN
ap-5050	211	37	=	=	NOUN
ap-5050	211	38	0.3	0.3	NUM
ap-5050	211	39	;	;	PUNCT
ap-5050	211	40	(	(	PUNCT
ap-5050	211	41	b	b	X
ap-5050	211	42	)	)	PUNCT
ap-5050	211	43	ω	ω	NOUN
ap-5050	211	44	=	=	NOUN
ap-5050	211	45	18	18	NUM
ap-5050	211	46	s−1	s−1	PROPN
ap-5050	211	47	,	,	PUNCT
ap-5050	211	48	β	β	X
ap-5050	211	49	=	=	NOUN
ap-5050	211	50	45	45	NUM
ap-5050	211	51	°	°	NUM
ap-5050	211	52	,	,	PUNCT
ap-5050	211	53	f	f	PROPN
ap-5050	211	54	=	=	SYM
ap-5050	211	55	0.1	0.1	NUM
ap-5050	211	56	,	,	PUNCT
ap-5050	211	57	fr	fr	NOUN
ap-5050	211	58	=	=	NUM
ap-5050	211	59	0.5	0.5	NUM
ap-5050	211	60	.	.	PUNCT
ap-5050	212	1	having	having	AUX
ap-5050	212	2	compared	compare	VERB
ap-5050	212	3	the	the	DET
ap-5050	212	4	curves	curve	NOUN
ap-5050	212	5	in	in	ADP
ap-5050	212	6	figure	figure	NOUN
ap-5050	212	7	6b	6b	NOUN
ap-5050	212	8	and	and	CCONJ
ap-5050	212	9	the	the	DET
ap-5050	212	10	ones	one	NOUN
ap-5050	212	11	in	in	ADP
ap-5050	212	12	figure	figure	NOUN
ap-5050	212	13	10	10	NUM
ap-5050	212	14	,	,	PUNCT
ap-5050	212	15	at	at	ADP
ap-5050	212	16	the	the	DET
ap-5050	212	17	top	top	NOUN
ap-5050	212	18	,	,	PUNCT
ap-5050	212	19	it	it	PRON
ap-5050	212	20	can	can	AUX
ap-5050	212	21	be	be	AUX
ap-5050	212	22	deduced	deduce	VERB
ap-5050	212	23	that	that	SCONJ
ap-5050	212	24	the	the	DET
ap-5050	212	25	number	number	NOUN
ap-5050	212	26	of	of	ADP
ap-5050	212	27	upward	upward	ADJ
ap-5050	212	28	movements	movement	NOUN
ap-5050	212	29	and	and	CCONJ
ap-5050	212	30	the	the	DET
ap-5050	212	31	number	number	NOUN
ap-5050	212	32	of	of	ADP
ap-5050	212	33	particle	particle	NOUN
ap-5050	212	34	fall	fall	NOUN
ap-5050	212	35	movements	movement	NOUN
ap-5050	212	36	increased	increase	VERB
ap-5050	212	37	in	in	ADP
ap-5050	212	38	the	the	DET
ap-5050	212	39	latter	latter	ADJ
ap-5050	212	40	case	case	NOUN
ap-5050	212	41	,	,	PUNCT
ap-5050	212	42	that	that	PRON
ap-5050	212	43	is	be	AUX
ap-5050	212	44	to	to	PART
ap-5050	212	45	say	say	VERB
ap-5050	212	46	,	,	PUNCT
ap-5050	212	47	the	the	DET
ap-5050	212	48	decrease	decrease	NOUN
ap-5050	212	49	of	of	ADP
ap-5050	212	50	the	the	DET
ap-5050	212	51	friction	friction	NOUN
ap-5050	212	52	coefficient	coefficient	NOUN
ap-5050	212	53	f	f	PROPN
ap-5050	212	54	resulted	result	VERB
ap-5050	212	55	in	in	ADP
ap-5050	212	56	the	the	DET
ap-5050	212	57	increase	increase	NOUN
ap-5050	212	58	of	of	ADP
ap-5050	212	59	the	the	DET
ap-5050	212	60	particle	particle	NOUN
ap-5050	212	61	absolute	absolute	ADJ
ap-5050	212	62	velocity	velocity	NOUN
ap-5050	212	63	.	.	PUNCT
ap-5050	213	1	this	this	DET
ap-5050	213	2	result	result	NOUN
ap-5050	213	3	is	be	AUX
ap-5050	213	4	inconsistent	inconsistent	ADJ
ap-5050	213	5	with	with	ADP
ap-5050	213	6	a	a	DET
ap-5050	213	7	plane	plane	NOUN
ap-5050	213	8	problem	problem	NOUN
ap-5050	213	9	at	at	ADP
ap-5050	213	10	β	β	X
ap-5050	213	11	=	=	SYM
ap-5050	213	12	0	0	X
ap-5050	213	13	.	.	PUNCT
ap-5050	214	1	for	for	ADP
ap-5050	214	2	a	a	DET
ap-5050	214	3	plane	plane	NOUN
ap-5050	214	4	problem	problem	NOUN
ap-5050	214	5	,	,	PUNCT
ap-5050	214	6	the	the	DET
ap-5050	214	7	friction	friction	NOUN
ap-5050	214	8	force	force	NOUN
ap-5050	214	9	f	f	PROPN
ap-5050	214	10	between	between	ADP
ap-5050	214	11	a	a	DET
ap-5050	214	12	particle	particle	NOUN
ap-5050	214	13	and	and	CCONJ
ap-5050	214	14	a	a	DET
ap-5050	214	15	round	round	ADJ
ap-5050	214	16	disk	disk	NOUN
ap-5050	214	17	is	be	AUX
ap-5050	214	18	a	a	DET
ap-5050	214	19	driving	drive	VERB
ap-5050	214	20	force	force	NOUN
ap-5050	214	21	,	,	PUNCT
ap-5050	214	22	which	which	PRON
ap-5050	214	23	pulls	pull	VERB
ap-5050	214	24	it	it	PRON
ap-5050	214	25	in	in	ADP
ap-5050	214	26	a	a	DET
ap-5050	214	27	motion	motion	NOUN
ap-5050	214	28	in	in	ADP
ap-5050	214	29	a	a	DET
ap-5050	214	30	circle	circle	NOUN
ap-5050	214	31	in	in	ADP
ap-5050	214	32	the	the	DET
ap-5050	214	33	direction	direction	NOUN
ap-5050	214	34	of	of	ADP
ap-5050	214	35	the	the	DET
ap-5050	214	36	disk	disk	NOUN
ap-5050	214	37	rotation	rotation	NOUN
ap-5050	214	38	.	.	PUNCT
ap-5050	215	1	the	the	DET
ap-5050	215	2	increase	increase	NOUN
ap-5050	215	3	of	of	ADP
ap-5050	215	4	the	the	DET
ap-5050	215	5	friction	friction	NOUN
ap-5050	215	6	f	f	PROPN
ap-5050	215	7	results	result	VERB
ap-5050	215	8	in	in	ADP
ap-5050	215	9	the	the	DET
ap-5050	215	10	increase	increase	NOUN
ap-5050	215	11	of	of	ADP
ap-5050	215	12	the	the	DET
ap-5050	215	13	force	force	NOUN
ap-5050	215	14	f	f	PROPN
ap-5050	215	15	and	and	CCONJ
ap-5050	215	16	,	,	PUNCT
ap-5050	215	17	thus	thus	ADV
ap-5050	215	18	,	,	PUNCT
ap-5050	215	19	the	the	DET
ap-5050	215	20	absolute	absolute	ADJ
ap-5050	215	21	velocity	velocity	NOUN
ap-5050	215	22	of	of	ADP
ap-5050	215	23	the	the	DET
ap-5050	215	24	particle	particle	NOUN
ap-5050	215	25	motion	motion	NOUN
ap-5050	215	26	in	in	ADP
ap-5050	215	27	a	a	DET
ap-5050	215	28	circle	circle	NOUN
ap-5050	215	29	increases	increase	NOUN
ap-5050	215	30	as	as	ADV
ap-5050	215	31	well	well	ADV
ap-5050	215	32	(	(	PUNCT
ap-5050	215	33	figure	figure	NOUN
ap-5050	215	34	2	2	NUM
ap-5050	215	35	)	)	PUNCT
ap-5050	215	36	.	.	PUNCT
ap-5050	216	1	by	by	ADP
ap-5050	216	2	contrast	contrast	NOUN
ap-5050	216	3	,	,	PUNCT
ap-5050	216	4	the	the	DET
ap-5050	216	5	increase	increase	NOUN
ap-5050	216	6	of	of	ADP
ap-5050	216	7	the	the	DET
ap-5050	216	8	friction	friction	NOUN
ap-5050	216	9	coefficient	coefficient	NOUN
ap-5050	216	10	fr	fr	PROPN
ap-5050	216	11	results	result	VERB
ap-5050	216	12	in	in	ADP
ap-5050	216	13	the	the	DET
ap-5050	216	14	decrease	decrease	NOUN
ap-5050	216	15	of	of	ADP
ap-5050	216	16	the	the	DET
ap-5050	216	17	absolute	absolute	ADJ
ap-5050	216	18	velocity	velocity	NOUN
ap-5050	216	19	of	of	ADP
ap-5050	216	20	the	the	DET
ap-5050	216	21	particle	particle	NOUN
ap-5050	216	22	motion	motion	NOUN
ap-5050	216	23	in	in	ADP
ap-5050	216	24	a	a	DET
ap-5050	216	25	circle	circle	NOUN
ap-5050	216	26	,	,	PUNCT
ap-5050	216	27	since	since	SCONJ
ap-5050	216	28	the	the	DET
ap-5050	216	29	friction	friction	NOUN
ap-5050	216	30	force	force	NOUN
ap-5050	217	1	fr	fr	PROPN
ap-5050	217	2	is	be	AUX
ap-5050	217	3	a	a	DET
ap-5050	217	4	decelerating	decelerate	VERB
ap-5050	217	5	force	force	NOUN
ap-5050	217	6	,	,	PUNCT
ap-5050	217	7	which	which	PRON
ap-5050	217	8	is	be	AUX
ap-5050	217	9	directed	direct	VERB
ap-5050	217	10	opposite	opposite	ADV
ap-5050	217	11	to	to	ADP
ap-5050	217	12	its	its	PRON
ap-5050	217	13	direction	direction	NOUN
ap-5050	217	14	.	.	PUNCT
ap-5050	218	1	in	in	ADP
ap-5050	218	2	the	the	DET
ap-5050	218	3	case	case	NOUN
ap-5050	218	4	of	of	ADP
ap-5050	218	5	the	the	DET
ap-5050	218	6	particle	particle	NOUN
ap-5050	218	7	relative	relative	ADJ
ap-5050	218	8	motion	motion	NOUN
ap-5050	218	9	in	in	ADP
ap-5050	218	10	an	an	DET
ap-5050	218	11	ellipse	ellipse	NOUN
ap-5050	218	12	(	(	PUNCT
ap-5050	218	13	at	at	ADP
ap-5050	218	14	β	β	X
ap-5050	218	15	6=	6=	ADP
ap-5050	218	16	0	0	NUM
ap-5050	218	17	)	)	PUNCT
ap-5050	218	18	,	,	PUNCT
ap-5050	218	19	it	it	PRON
ap-5050	218	20	will	will	AUX
ap-5050	218	21	be	be	AUX
ap-5050	218	22	vice	vice	ADV
ap-5050	218	23	versa	versa	ADV
ap-5050	218	24	as	as	ADV
ap-5050	218	25	well	well	ADV
ap-5050	218	26	:	:	PUNCT
ap-5050	218	27	the	the	DET
ap-5050	218	28	increase	increase	NOUN
ap-5050	218	29	of	of	ADP
ap-5050	218	30	the	the	DET
ap-5050	218	31	friction	friction	NOUN
ap-5050	218	32	coefficient	coefficient	NOUN
ap-5050	218	33	fr	fr	PROPN
ap-5050	218	34	will	will	AUX
ap-5050	218	35	increase	increase	VERB
ap-5050	218	36	the	the	DET
ap-5050	218	37	absolute	absolute	ADJ
ap-5050	218	38	velocity	velocity	NOUN
ap-5050	218	39	of	of	ADP
ap-5050	218	40	the	the	DET
ap-5050	218	41	particle	particle	NOUN
ap-5050	218	42	motion	motion	NOUN
ap-5050	218	43	.	.	PUNCT
ap-5050	219	1	at	at	ADP
ap-5050	219	2	first	first	ADJ
ap-5050	219	3	glance	glance	NOUN
ap-5050	219	4	,	,	PUNCT
ap-5050	219	5	it	it	PRON
ap-5050	219	6	is	be	AUX
ap-5050	219	7	paradoxical	paradoxical	ADJ
ap-5050	219	8	,	,	PUNCT
ap-5050	219	9	but	but	CCONJ
ap-5050	219	10	it	it	PRON
ap-5050	219	11	has	have	VERB
ap-5050	219	12	its	its	PRON
ap-5050	219	13	explanation	explanation	NOUN
ap-5050	219	14	.	.	PUNCT
ap-5050	220	1	for	for	ADP
ap-5050	220	2	a	a	DET
ap-5050	220	3	plane	plane	NOUN
ap-5050	220	4	problem	problem	NOUN
ap-5050	220	5	,	,	PUNCT
ap-5050	220	6	the	the	DET
ap-5050	220	7	only	only	ADJ
ap-5050	220	8	driving	drive	VERB
ap-5050	220	9	force	force	NOUN
ap-5050	220	10	is	be	AUX
ap-5050	220	11	the	the	DET
ap-5050	220	12	force	force	NOUN
ap-5050	220	13	f	f	NOUN
ap-5050	220	14	=	=	NOUN
ap-5050	220	15	fn	fn	PROPN
ap-5050	220	16	.	.	PUNCT
ap-5050	221	1	the	the	DET
ap-5050	221	2	reaction	reaction	NOUN
ap-5050	221	3	force	force	NOUN
ap-5050	221	4	n	n	PRON
ap-5050	221	5	is	be	AUX
ap-5050	221	6	constant	constant	ADJ
ap-5050	221	7	and	and	CCONJ
ap-5050	221	8	it	it	PRON
ap-5050	221	9	is	be	AUX
ap-5050	221	10	balanced	balance	VERB
ap-5050	221	11	by	by	ADP
ap-5050	221	12	the	the	DET
ap-5050	221	13	particle	particle	NOUN
ap-5050	221	14	weight	weight	NOUN
ap-5050	221	15	force	force	NOUN
ap-5050	221	16	mg	mg	PROPN
ap-5050	221	17	.	.	PUNCT
ap-5050	222	1	if	if	SCONJ
ap-5050	222	2	β	β	PROPN
ap-5050	222	3	6=	6=	ADP
ap-5050	222	4	0	0	NUM
ap-5050	222	5	,	,	PUNCT
ap-5050	222	6	the	the	DET
ap-5050	222	7	reaction	reaction	NOUN
ap-5050	222	8	force	force	NOUN
ap-5050	222	9	component	component	PROPN
ap-5050	222	10	n	n	PROPN
ap-5050	222	11	,	,	PUNCT
ap-5050	222	12	which	which	PRON
ap-5050	222	13	is	be	AUX
ap-5050	222	14	directed	direct	VERB
ap-5050	222	15	upwards	upwards	ADV
ap-5050	222	16	,	,	PUNCT
ap-5050	222	17	has	have	VERB
ap-5050	222	18	the	the	DET
ap-5050	222	19	following	follow	VERB
ap-5050	222	20	expression	expression	NOUN
ap-5050	222	21	n	n	ADP
ap-5050	222	22	cosβ	cosβ	NOUN
ap-5050	222	23	according	accord	VERB
ap-5050	222	24	to	to	ADP
ap-5050	222	25	the	the	DET
ap-5050	222	26	last	last	ADJ
ap-5050	222	27	equation	equation	NOUN
ap-5050	222	28	in	in	ADP
ap-5050	222	29	(	(	PUNCT
ap-5050	222	30	26	26	NUM
ap-5050	222	31	)	)	PUNCT
ap-5050	222	32	.	.	PUNCT
ap-5050	223	1	the	the	DET
ap-5050	223	2	angle	angle	NOUN
ap-5050	223	3	cosine	cosine	NOUN
ap-5050	223	4	β	β	PROPN
ap-5050	223	5	is	be	AUX
ap-5050	223	6	a	a	DET
ap-5050	223	7	constant	constant	ADJ
ap-5050	223	8	value	value	NOUN
ap-5050	223	9	,	,	PUNCT
ap-5050	223	10	thus	thus	ADV
ap-5050	223	11	,	,	PUNCT
ap-5050	223	12	this	this	DET
ap-5050	223	13	force	force	NOUN
ap-5050	223	14	is	be	AUX
ap-5050	223	15	in	in	ADP
ap-5050	223	16	a	a	DET
ap-5050	223	17	direct	direct	ADJ
ap-5050	223	18	proportion	proportion	NOUN
ap-5050	223	19	to	to	ADP
ap-5050	223	20	the	the	DET
ap-5050	223	21	reaction	reaction	NOUN
ap-5050	223	22	n	n	ADV
ap-5050	223	23	.	.	PUNCT
ap-5050	224	1	at	at	ADP
ap-5050	224	2	the	the	DET
ap-5050	224	3	bottom	bottom	NOUN
ap-5050	224	4	of	of	ADP
ap-5050	224	5	figure	figure	NOUN
ap-5050	224	6	10	10	NUM
ap-5050	224	7	,	,	PUNCT
ap-5050	224	8	it	it	PRON
ap-5050	224	9	can	can	AUX
ap-5050	224	10	be	be	AUX
ap-5050	224	11	seen	see	VERB
ap-5050	224	12	that	that	SCONJ
ap-5050	224	13	the	the	DET
ap-5050	224	14	force	force	NOUN
ap-5050	224	15	n	n	PRON
ap-5050	224	16	ranges	range	VERB
ap-5050	224	17	widely	widely	ADV
ap-5050	224	18	,	,	PUNCT
ap-5050	224	19	here	here	ADV
ap-5050	224	20	,	,	PUNCT
ap-5050	224	21	it	it	PRON
ap-5050	224	22	has	have	VERB
ap-5050	224	23	the	the	DET
ap-5050	224	24	highest	high	ADJ
ap-5050	224	25	value	value	NOUN
ap-5050	224	26	when	when	SCONJ
ap-5050	224	27	a	a	DET
ap-5050	224	28	particle	particle	NOUN
ap-5050	224	29	is	be	AUX
ap-5050	224	30	located	locate	VERB
ap-5050	224	31	in	in	ADP
ap-5050	224	32	the	the	DET
ap-5050	224	33	low	low	ADJ
ap-5050	224	34	point	point	NOUN
ap-5050	224	35	of	of	ADP
ap-5050	224	36	an	an	DET
ap-5050	224	37	ellipse	ellipse	NOUN
ap-5050	224	38	.	.	PUNCT
ap-5050	225	1	it	it	PRON
ap-5050	225	2	makes	make	VERB
ap-5050	225	3	a	a	DET
ap-5050	225	4	particle	particle	NOUN
ap-5050	225	5	move	move	NOUN
ap-5050	225	6	upwards	upwards	ADV
ap-5050	225	7	and	and	CCONJ
ap-5050	225	8	the	the	DET
ap-5050	225	9	decrease	decrease	NOUN
ap-5050	225	10	of	of	ADP
ap-5050	225	11	the	the	DET
ap-5050	225	12	friction	friction	NOUN
ap-5050	225	13	force	force	NOUN
ap-5050	225	14	,	,	PUNCT
ap-5050	225	15	that	that	PRON
ap-5050	225	16	is	be	AUX
ap-5050	225	17	to	to	PART
ap-5050	225	18	say	say	VERB
ap-5050	225	19	,	,	PUNCT
ap-5050	225	20	the	the	DET
ap-5050	225	21	decrease	decrease	NOUN
ap-5050	225	22	of	of	ADP
ap-5050	225	23	the	the	DET
ap-5050	225	24	coefficient	coefficient	NOUN
ap-5050	225	25	f	f	PROPN
ap-5050	225	26	will	will	AUX
ap-5050	225	27	facilitate	facilitate	VERB
ap-5050	225	28	its	its	PRON
ap-5050	225	29	motion	motion	NOUN
ap-5050	225	30	.	.	PUNCT
ap-5050	226	1	this	this	PRON
ap-5050	226	2	explains	explain	VERB
ap-5050	226	3	the	the	DET
ap-5050	226	4	fact	fact	NOUN
ap-5050	226	5	that	that	SCONJ
ap-5050	226	6	the	the	DET
ap-5050	226	7	velocity	velocity	NOUN
ap-5050	226	8	of	of	ADP
ap-5050	226	9	the	the	DET
ap-5050	226	10	particle	particle	NOUN
ap-5050	226	11	sliding	slide	VERB
ap-5050	226	12	in	in	ADP
ap-5050	226	13	an	an	DET
ap-5050	226	14	ellipse	ellipse	NOUN
ap-5050	226	15	is	be	AUX
ap-5050	226	16	the	the	DET
ap-5050	226	17	greatest	great	ADJ
ap-5050	226	18	near	near	ADP
ap-5050	226	19	its	its	PRON
ap-5050	226	20	low	low	ADJ
ap-5050	226	21	point	point	NOUN
ap-5050	226	22	,	,	PUNCT
ap-5050	226	23	which	which	PRON
ap-5050	226	24	has	have	AUX
ap-5050	226	25	been	be	AUX
ap-5050	226	26	determined	determine	VERB
ap-5050	226	27	as	as	ADP
ap-5050	226	28	a	a	DET
ap-5050	226	29	result	result	NOUN
ap-5050	226	30	of	of	ADP
ap-5050	226	31	the	the	DET
ap-5050	226	32	analysis	analysis	NOUN
ap-5050	226	33	of	of	ADP
ap-5050	226	34	the	the	DET
ap-5050	226	35	curves	curve	NOUN
ap-5050	226	36	presented	present	VERB
ap-5050	226	37	in	in	ADP
ap-5050	226	38	figure	figure	NOUN
ap-5050	226	39	6	6	NUM
ap-5050	226	40	.	.	PUNCT
ap-5050	227	1	figure	figure	NOUN
ap-5050	227	2	11a	11a	NOUN
ap-5050	227	3	presents	present	VERB
ap-5050	227	4	the	the	DET
ap-5050	227	5	absolute	absolute	ADJ
ap-5050	227	6	trajectory	trajectory	NOUN
ap-5050	227	7	74	74	NUM
ap-5050	227	8	vol	vol	NOUN
ap-5050	227	9	.	.	PUNCT
ap-5050	228	1	59	59	NUM
ap-5050	228	2	no	no	NOUN
ap-5050	228	3	.	.	PUNCT
ap-5050	229	1	1/2019	1/2019	NUM
ap-5050	229	2	particle	particle	NOUN
ap-5050	229	3	motion	motion	NOUN
ap-5050	229	4	over	over	ADP
ap-5050	229	5	the	the	DET
ap-5050	229	6	edge	edge	NOUN
ap-5050	229	7	of	of	ADP
ap-5050	229	8	an	an	DET
ap-5050	229	9	inclined	inclined	ADJ
ap-5050	229	10	plane	plane	NOUN
ap-5050	229	11	figure	figure	NOUN
ap-5050	229	12	12	12	NUM
ap-5050	229	13	.	.	PUNCT
ap-5050	230	1	a	a	DET
ap-5050	230	2	cascade	cascade	NOUN
ap-5050	230	3	operating	operating	NOUN
ap-5050	230	4	element	element	NOUN
ap-5050	230	5	.	.	PUNCT
ap-5050	231	1	of	of	ADP
ap-5050	231	2	a	a	DET
ap-5050	231	3	particle	particle	NOUN
ap-5050	231	4	motion	motion	NOUN
ap-5050	231	5	.	.	PUNCT
ap-5050	232	1	it	it	PRON
ap-5050	232	2	is	be	AUX
ap-5050	232	3	characterized	characterize	VERB
ap-5050	232	4	by	by	ADP
ap-5050	232	5	the	the	DET
ap-5050	232	6	abrupt	abrupt	ADJ
ap-5050	232	7	change	change	NOUN
ap-5050	232	8	in	in	ADP
ap-5050	232	9	the	the	DET
ap-5050	232	10	direction	direction	NOUN
ap-5050	232	11	of	of	ADP
ap-5050	232	12	the	the	DET
ap-5050	232	13	motion	motion	NOUN
ap-5050	232	14	in	in	ADP
ap-5050	232	15	the	the	DET
ap-5050	232	16	bottom	bottom	ADJ
ap-5050	232	17	part	part	NOUN
ap-5050	232	18	and	and	CCONJ
ap-5050	232	19	a	a	DET
ap-5050	232	20	more	more	ADV
ap-5050	232	21	long	long	ADJ
ap-5050	232	22	-	-	PUNCT
ap-5050	232	23	term	term	NOUN
ap-5050	232	24	stay	stay	NOUN
ap-5050	232	25	at	at	ADP
ap-5050	232	26	the	the	DET
ap-5050	232	27	top	top	ADJ
ap-5050	232	28	part	part	NOUN
ap-5050	232	29	of	of	ADP
ap-5050	232	30	an	an	DET
ap-5050	232	31	ellipse	ellipse	NOUN
ap-5050	232	32	.	.	PUNCT
ap-5050	233	1	in	in	ADP
ap-5050	233	2	addition	addition	NOUN
ap-5050	233	3	,	,	PUNCT
ap-5050	233	4	it	it	PRON
ap-5050	233	5	proves	prove	VERB
ap-5050	233	6	that	that	SCONJ
ap-5050	233	7	the	the	DET
ap-5050	233	8	velocity	velocity	NOUN
ap-5050	233	9	of	of	ADP
ap-5050	233	10	the	the	DET
ap-5050	233	11	particle	particle	NOUN
ap-5050	233	12	sliding	slide	VERB
ap-5050	233	13	along	along	ADP
ap-5050	233	14	an	an	DET
ap-5050	233	15	ellipse	ellipse	NOUN
ap-5050	233	16	is	be	AUX
ap-5050	233	17	greater	great	ADJ
ap-5050	233	18	in	in	ADP
ap-5050	233	19	the	the	DET
ap-5050	233	20	bottom	bottom	ADJ
ap-5050	233	21	part	part	NOUN
ap-5050	233	22	than	than	SCONJ
ap-5050	233	23	it	it	PRON
ap-5050	233	24	is	be	AUX
ap-5050	233	25	in	in	ADP
ap-5050	233	26	the	the	DET
ap-5050	233	27	top	top	ADJ
ap-5050	233	28	part	part	NOUN
ap-5050	233	29	.	.	PUNCT
ap-5050	234	1	the	the	DET
ap-5050	234	2	investigations	investigation	NOUN
ap-5050	234	3	show	show	VERB
ap-5050	234	4	that	that	SCONJ
ap-5050	234	5	the	the	DET
ap-5050	234	6	increase	increase	NOUN
ap-5050	234	7	of	of	ADP
ap-5050	234	8	the	the	DET
ap-5050	234	9	friction	friction	NOUN
ap-5050	234	10	coefficient	coefficient	NOUN
ap-5050	234	11	fr	fr	NOUN
ap-5050	234	12	for	for	ADP
ap-5050	234	13	0.1	0.1	NUM
ap-5050	234	14	results	result	NOUN
ap-5050	234	15	in	in	ADP
ap-5050	234	16	almost	almost	ADV
ap-5050	234	17	the	the	DET
ap-5050	234	18	same	same	ADJ
ap-5050	234	19	effect	effect	NOUN
ap-5050	234	20	as	as	ADP
ap-5050	234	21	the	the	DET
ap-5050	234	22	decrease	decrease	NOUN
ap-5050	234	23	of	of	ADP
ap-5050	234	24	the	the	DET
ap-5050	234	25	coefficient	coefficient	NOUN
ap-5050	234	26	f	f	PROPN
ap-5050	234	27	for	for	ADP
ap-5050	234	28	the	the	DET
ap-5050	234	29	same	same	ADJ
ap-5050	234	30	value	value	NOUN
ap-5050	234	31	.	.	PUNCT
ap-5050	235	1	if	if	SCONJ
ap-5050	235	2	there	there	PRON
ap-5050	235	3	is	be	VERB
ap-5050	235	4	an	an	DET
ap-5050	235	5	increase	increase	NOUN
ap-5050	235	6	in	in	ADP
ap-5050	235	7	the	the	DET
ap-5050	235	8	coefficient	coefficient	NOUN
ap-5050	235	9	fr	fr	PROPN
ap-5050	235	10	,	,	PUNCT
ap-5050	235	11	the	the	DET
ap-5050	235	12	absolute	absolute	ADJ
ap-5050	235	13	angular	angular	ADJ
ap-5050	235	14	velocity	velocity	NOUN
ap-5050	235	15	of	of	ADP
ap-5050	235	16	rotation	rotation	NOUN
ap-5050	235	17	ω	ω	PROPN
ap-5050	235	18	−	−	PROPN
ap-5050	235	19	α′	α′	NUM
ap-5050	235	20	decreases	decrease	VERB
ap-5050	235	21	,	,	PUNCT
ap-5050	235	22	that	that	PRON
ap-5050	235	23	is	be	AUX
ap-5050	235	24	to	to	PART
ap-5050	235	25	say	say	VERB
ap-5050	235	26	,	,	PUNCT
ap-5050	235	27	the	the	DET
ap-5050	235	28	value	value	NOUN
ap-5050	235	29	of	of	ADP
ap-5050	235	30	the	the	DET
ap-5050	235	31	reaction	reaction	NOUN
ap-5050	235	32	nr	nr	PROPN
ap-5050	235	33	depends	depend	VERB
ap-5050	235	34	on	on	ADP
ap-5050	235	35	this	this	DET
ap-5050	235	36	squared	square	VERB
ap-5050	235	37	value	value	NOUN
ap-5050	235	38	.	.	PUNCT
ap-5050	236	1	it	it	PRON
ap-5050	236	2	can	can	AUX
ap-5050	236	3	be	be	AUX
ap-5050	236	4	assumed	assume	VERB
ap-5050	236	5	that	that	SCONJ
ap-5050	236	6	the	the	DET
ap-5050	236	7	increase	increase	NOUN
ap-5050	236	8	of	of	ADP
ap-5050	236	9	the	the	DET
ap-5050	236	10	coefficient	coefficient	NOUN
ap-5050	236	11	fr	fr	PROPN
ap-5050	236	12	results	result	VERB
ap-5050	236	13	in	in	ADP
ap-5050	236	14	the	the	DET
ap-5050	236	15	decrease	decrease	NOUN
ap-5050	236	16	of	of	ADP
ap-5050	236	17	the	the	DET
ap-5050	236	18	absolute	absolute	ADJ
ap-5050	236	19	angular	angular	ADJ
ap-5050	236	20	velocity	velocity	NOUN
ap-5050	236	21	ω	ω	NOUN
ap-5050	236	22	−	−	PROPN
ap-5050	236	23	α′	α′	NUM
ap-5050	236	24	,	,	PUNCT
ap-5050	236	25	which	which	PRON
ap-5050	236	26	square	square	NOUN
ap-5050	236	27	significantly	significantly	ADV
ap-5050	236	28	influences	influence	VERB
ap-5050	236	29	the	the	DET
ap-5050	236	30	decrease	decrease	NOUN
ap-5050	236	31	of	of	ADP
ap-5050	236	32	the	the	DET
ap-5050	236	33	decelerating	decelerate	VERB
ap-5050	236	34	force	force	NOUN
ap-5050	237	1	fr	fr	NOUN
ap-5050	237	2	=	=	PUNCT
ap-5050	237	3	frnr	frnr	ADJ
ap-5050	237	4	=	=	SYM
ap-5050	237	5	frmr(ω	frmr(ω	PROPN
ap-5050	237	6	−	−	PROPN
ap-5050	237	7	α′)2	α′)2	NOUN
ap-5050	237	8	,	,	PUNCT
ap-5050	237	9	whereas	whereas	SCONJ
ap-5050	237	10	the	the	DET
ap-5050	237	11	coefficient	coefficient	NOUN
ap-5050	237	12	fr	fr	NOUN
ap-5050	237	13	increases	increase	NOUN
ap-5050	237	14	.	.	PUNCT
ap-5050	238	1	thus	thus	ADV
ap-5050	238	2	,	,	PUNCT
ap-5050	238	3	if	if	SCONJ
ap-5050	238	4	there	there	PRON
ap-5050	238	5	is	be	VERB
ap-5050	238	6	a	a	DET
ap-5050	238	7	decrease	decrease	NOUN
ap-5050	238	8	in	in	ADP
ap-5050	238	9	the	the	DET
ap-5050	238	10	friction	friction	NOUN
ap-5050	238	11	coefficient	coefficient	NOUN
ap-5050	238	12	f	f	PROPN
ap-5050	238	13	and	and	CCONJ
ap-5050	238	14	there	there	PRON
ap-5050	238	15	is	be	VERB
ap-5050	238	16	an	an	DET
ap-5050	238	17	increase	increase	NOUN
ap-5050	238	18	in	in	ADP
ap-5050	238	19	the	the	DET
ap-5050	238	20	friction	friction	NOUN
ap-5050	238	21	coefficient	coefficient	NOUN
ap-5050	238	22	fr	fr	PROPN
ap-5050	238	23	,	,	PUNCT
ap-5050	238	24	the	the	DET
ap-5050	238	25	number	number	NOUN
ap-5050	238	26	of	of	ADP
ap-5050	238	27	upward	upward	ADJ
ap-5050	238	28	and	and	CCONJ
ap-5050	238	29	downward	downward	ADJ
ap-5050	238	30	movements	movement	NOUN
ap-5050	238	31	of	of	ADP
ap-5050	238	32	a	a	DET
ap-5050	238	33	particle	particle	NOUN
ap-5050	238	34	in	in	ADP
ap-5050	238	35	an	an	DET
ap-5050	238	36	ellipse	ellipse	NOUN
ap-5050	238	37	is	be	AUX
ap-5050	238	38	expected	expect	VERB
ap-5050	238	39	to	to	PART
ap-5050	238	40	be	be	AUX
ap-5050	238	41	increased	increase	VERB
ap-5050	238	42	or	or	CCONJ
ap-5050	238	43	there	there	PRON
ap-5050	238	44	can	can	AUX
ap-5050	238	45	be	be	AUX
ap-5050	238	46	an	an	DET
ap-5050	238	47	increase	increase	NOUN
ap-5050	238	48	of	of	ADP
ap-5050	238	49	the	the	DET
ap-5050	238	50	angle	angle	NOUN
ap-5050	238	51	of	of	ADP
ap-5050	238	52	the	the	DET
ap-5050	238	53	plane	plane	NOUN
ap-5050	238	54	inclination	inclination	NOUN
ap-5050	238	55	to	to	ADP
ap-5050	238	56	the	the	DET
ap-5050	238	57	limits	limit	NOUN
ap-5050	238	58	,	,	PUNCT
ap-5050	238	59	when	when	SCONJ
ap-5050	238	60	such	such	ADJ
ap-5050	238	61	motion	motion	NOUN
ap-5050	238	62	is	be	AUX
ap-5050	238	63	possible	possible	ADJ
ap-5050	238	64	.	.	PUNCT
ap-5050	239	1	figure	figure	NOUN
ap-5050	239	2	11b	11b	NOUN
ap-5050	239	3	presents	present	VERB
ap-5050	239	4	the	the	DET
ap-5050	239	5	trajectory	trajectory	NOUN
ap-5050	239	6	of	of	ADP
ap-5050	239	7	an	an	DET
ap-5050	239	8	absolute	absolute	ADJ
ap-5050	239	9	particle	particle	NOUN
ap-5050	239	10	motion	motion	NOUN
ap-5050	239	11	for	for	ADP
ap-5050	239	12	β	β	X
ap-5050	239	13	=	=	SYM
ap-5050	239	14	45	45	NUM
ap-5050	239	15	°	°	NOUN
ap-5050	239	16	at	at	ADP
ap-5050	239	17	f	f	PROPN
ap-5050	239	18	=	=	SYM
ap-5050	239	19	0.1	0.1	NUM
ap-5050	239	20	and	and	CCONJ
ap-5050	239	21	fr	fr	NOUN
ap-5050	239	22	=	=	NOUN
ap-5050	239	23	0.5	0.5	NUM
ap-5050	239	24	.	.	PUNCT
ap-5050	240	1	here	here	ADV
ap-5050	240	2	,	,	PUNCT
ap-5050	240	3	the	the	DET
ap-5050	240	4	angular	angular	ADJ
ap-5050	240	5	velocity	velocity	NOUN
ap-5050	240	6	was	be	AUX
ap-5050	240	7	decreased	decrease	VERB
ap-5050	240	8	to	to	ADP
ap-5050	240	9	ω	ω	PROPN
ap-5050	240	10	=	=	SYM
ap-5050	240	11	18	18	NUM
ap-5050	240	12	s−1	s−1	PROPN
ap-5050	240	13	in	in	ADP
ap-5050	240	14	order	order	NOUN
ap-5050	240	15	to	to	PART
ap-5050	240	16	avoid	avoid	VERB
ap-5050	240	17	a	a	DET
ap-5050	240	18	particle	particle	NOUN
ap-5050	240	19	detachment	detachment	NOUN
ap-5050	240	20	from	from	ADP
ap-5050	240	21	the	the	DET
ap-5050	240	22	plane	plane	NOUN
ap-5050	240	23	segment	segment	NOUN
ap-5050	240	24	.	.	PUNCT
ap-5050	241	1	figure	figure	NOUN
ap-5050	241	2	11b	11b	NOUN
ap-5050	241	3	shows	show	VERB
ap-5050	241	4	that	that	SCONJ
ap-5050	241	5	the	the	DET
ap-5050	241	6	difference	difference	NOUN
ap-5050	241	7	between	between	ADP
ap-5050	241	8	the	the	DET
ap-5050	241	9	particle	particle	NOUN
ap-5050	241	10	movement	movement	NOUN
ap-5050	241	11	in	in	ADP
ap-5050	241	12	the	the	DET
ap-5050	241	13	bottom	bottom	NOUN
ap-5050	241	14	and	and	CCONJ
ap-5050	241	15	the	the	DET
ap-5050	241	16	top	top	ADJ
ap-5050	241	17	parts	part	NOUN
ap-5050	241	18	of	of	ADP
ap-5050	241	19	an	an	DET
ap-5050	241	20	ellipse	ellipse	NOUN
ap-5050	241	21	is	be	AUX
ap-5050	241	22	increased	increase	VERB
ap-5050	241	23	even	even	ADV
ap-5050	241	24	more	more	ADV
ap-5050	241	25	.	.	PUNCT
ap-5050	242	1	particle	particle	NOUN
ap-5050	242	2	motion	motion	NOUN
ap-5050	242	3	is	be	AUX
ap-5050	242	4	similar	similar	ADJ
ap-5050	242	5	to	to	ADP
ap-5050	242	6	its	its	PRON
ap-5050	242	7	bottomupward	bottomupward	NOUN
ap-5050	242	8	throwing	throwing	NOUN
ap-5050	242	9	with	with	ADP
ap-5050	242	10	a	a	DET
ap-5050	242	11	long	long	ADJ
ap-5050	242	12	-	-	PUNCT
ap-5050	242	13	term	term	NOUN
ap-5050	242	14	stay	stay	NOUN
ap-5050	242	15	at	at	ADP
ap-5050	242	16	the	the	DET
ap-5050	242	17	top	top	ADJ
ap-5050	242	18	part	part	NOUN
ap-5050	242	19	of	of	ADP
ap-5050	242	20	an	an	DET
ap-5050	242	21	ellipse	ellipse	NOUN
ap-5050	242	22	before	before	SCONJ
ap-5050	242	23	it	it	PRON
ap-5050	242	24	moves	move	VERB
ap-5050	242	25	downwards	downward	NOUN
ap-5050	242	26	.	.	PUNCT
ap-5050	243	1	taking	take	VERB
ap-5050	243	2	into	into	ADP
ap-5050	243	3	consideration	consideration	NOUN
ap-5050	243	4	such	such	ADJ
ap-5050	243	5	particle	particle	NOUN
ap-5050	243	6	motion	motion	NOUN
ap-5050	243	7	,	,	PUNCT
ap-5050	243	8	several	several	ADJ
ap-5050	243	9	recommendations	recommendation	NOUN
ap-5050	243	10	can	can	AUX
ap-5050	243	11	be	be	AUX
ap-5050	243	12	formulated	formulate	VERB
ap-5050	243	13	for	for	ADP
ap-5050	243	14	designing	design	VERB
ap-5050	243	15	a	a	DET
ap-5050	243	16	device	device	NOUN
ap-5050	243	17	for	for	ADP
ap-5050	243	18	lifting	lift	VERB
ap-5050	243	19	a	a	DET
ap-5050	243	20	technological	technological	ADJ
ap-5050	243	21	material	material	NOUN
ap-5050	243	22	in	in	ADP
ap-5050	243	23	a	a	DET
ap-5050	243	24	vertical	vertical	ADJ
ap-5050	243	25	pipe	pipe	NOUN
ap-5050	243	26	.	.	PUNCT
ap-5050	244	1	in	in	ADP
ap-5050	244	2	order	order	NOUN
ap-5050	244	3	to	to	PART
ap-5050	244	4	provide	provide	VERB
ap-5050	244	5	a	a	DET
ap-5050	244	6	sufficient	sufficient	ADJ
ap-5050	244	7	material	material	NOUN
ap-5050	244	8	elevation	elevation	NOUN
ap-5050	244	9	,	,	PUNCT
ap-5050	244	10	it	it	PRON
ap-5050	244	11	is	be	AUX
ap-5050	244	12	necessary	necessary	ADJ
ap-5050	244	13	to	to	PART
ap-5050	244	14	decrease	decrease	VERB
ap-5050	244	15	the	the	DET
ap-5050	244	16	friction	friction	NOUN
ap-5050	244	17	coefficient	coefficient	NOUN
ap-5050	244	18	f	f	PROPN
ap-5050	244	19	and	and	CCONJ
ap-5050	244	20	to	to	PART
ap-5050	244	21	increase	increase	VERB
ap-5050	244	22	the	the	DET
ap-5050	244	23	friction	friction	NOUN
ap-5050	244	24	coefficient	coefficient	NOUN
ap-5050	244	25	fr	fr	INTJ
ap-5050	244	26	.	.	PUNCT
ap-5050	245	1	in	in	ADP
ap-5050	245	2	order	order	NOUN
ap-5050	245	3	to	to	PART
ap-5050	245	4	provide	provide	VERB
ap-5050	245	5	a	a	DET
ap-5050	245	6	continuous	continuous	ADJ
ap-5050	245	7	material	material	NOUN
ap-5050	245	8	feed	feed	NOUN
ap-5050	245	9	to	to	ADP
ap-5050	245	10	the	the	DET
ap-5050	245	11	specified	specified	ADJ
ap-5050	245	12	height	height	NOUN
ap-5050	245	13	,	,	PUNCT
ap-5050	245	14	a	a	DET
ap-5050	245	15	cascade	cascade	NOUN
ap-5050	245	16	operating	operating	NOUN
ap-5050	245	17	element	element	NOUN
ap-5050	245	18	can	can	AUX
ap-5050	245	19	be	be	AUX
ap-5050	245	20	designed	design	VERB
ap-5050	245	21	,	,	PUNCT
ap-5050	245	22	as	as	SCONJ
ap-5050	245	23	it	it	PRON
ap-5050	245	24	is	be	AUX
ap-5050	245	25	shown	show	VERB
ap-5050	245	26	in	in	ADP
ap-5050	245	27	figure	figure	NOUN
ap-5050	245	28	12	12	NUM
ap-5050	245	29	.	.	PUNCT
ap-5050	246	1	plane	plane	NOUN
ap-5050	246	2	segments	segment	NOUN
ap-5050	246	3	,	,	PUNCT
ap-5050	246	4	which	which	PRON
ap-5050	246	5	are	be	AUX
ap-5050	246	6	limited	limit	VERB
ap-5050	246	7	by	by	ADP
ap-5050	246	8	semi	semi	NOUN
ap-5050	246	9	-	-	NOUN
ap-5050	246	10	ellipses	ellipsis	NOUN
ap-5050	246	11	,	,	PUNCT
ap-5050	246	12	alternate	alternate	VERB
ap-5050	246	13	each	each	DET
ap-5050	246	14	other	other	ADJ
ap-5050	246	15	,	,	PUNCT
ap-5050	246	16	here	here	ADV
ap-5050	246	17	,	,	PUNCT
ap-5050	246	18	their	their	PRON
ap-5050	246	19	inclination	inclination	NOUN
ap-5050	246	20	angles	angle	VERB
ap-5050	246	21	alternate	alternate	VERB
ap-5050	246	22	in	in	ADP
ap-5050	246	23	sign	sign	NOUN
ap-5050	246	24	.	.	PUNCT
ap-5050	247	1	the	the	DET
ap-5050	247	2	top	top	ADJ
ap-5050	247	3	part	part	NOUN
ap-5050	247	4	of	of	ADP
ap-5050	247	5	the	the	DET
ap-5050	247	6	segment	segment	NOUN
ap-5050	247	7	is	be	AUX
ap-5050	247	8	cut	cut	VERB
ap-5050	247	9	,	,	PUNCT
ap-5050	247	10	since	since	SCONJ
ap-5050	247	11	there	there	PRON
ap-5050	247	12	is	be	VERB
ap-5050	247	13	a	a	DET
ap-5050	247	14	deceleration	deceleration	NOUN
ap-5050	247	15	of	of	ADP
ap-5050	247	16	the	the	DET
ap-5050	247	17	material	material	NOUN
ap-5050	247	18	movement	movement	NOUN
ap-5050	247	19	.	.	PUNCT
ap-5050	248	1	in	in	ADP
ap-5050	248	2	order	order	NOUN
ap-5050	248	3	to	to	PART
ap-5050	248	4	conduct	conduct	VERB
ap-5050	248	5	the	the	DET
ap-5050	248	6	experiments	experiment	NOUN
ap-5050	248	7	,	,	PUNCT
ap-5050	248	8	a	a	DET
ap-5050	248	9	cascade	cascade	NOUN
ap-5050	248	10	operating	operating	NOUN
ap-5050	248	11	element	element	NOUN
ap-5050	248	12	for	for	ADP
ap-5050	248	13	transporting	transport	VERB
ap-5050	248	14	loose	loose	ADJ
ap-5050	248	15	materials	material	NOUN
ap-5050	248	16	by	by	ADP
ap-5050	248	17	a	a	DET
ap-5050	248	18	vertical	vertical	ADJ
ap-5050	248	19	conveyer	conveyer	NOUN
ap-5050	248	20	was	be	AUX
ap-5050	248	21	made	make	VERB
ap-5050	248	22	.	.	PUNCT
ap-5050	249	1	the	the	DET
ap-5050	249	2	efficiency	efficiency	NOUN
ap-5050	249	3	of	of	ADP
ap-5050	249	4	a	a	DET
ap-5050	249	5	vertical	vertical	ADJ
ap-5050	249	6	conveyer	conveyer	NOUN
ap-5050	249	7	with	with	ADP
ap-5050	249	8	a	a	DET
ap-5050	249	9	screw	screw	ADJ
ap-5050	249	10	operating	operating	NOUN
ap-5050	249	11	element	element	NOUN
ap-5050	249	12	and	and	CCONJ
ap-5050	249	13	the	the	DET
ap-5050	249	14	efficiency	efficiency	NOUN
ap-5050	249	15	of	of	ADP
ap-5050	249	16	a	a	DET
ap-5050	249	17	conveyer	conveyer	NOUN
ap-5050	249	18	with	with	ADP
ap-5050	249	19	a	a	DET
ap-5050	249	20	cascade	cascade	NOUN
ap-5050	249	21	operating	operating	NOUN
ap-5050	249	22	element	element	NOUN
ap-5050	249	23	figure	figure	NOUN
ap-5050	249	24	13	13	NUM
ap-5050	249	25	.	.	PUNCT
ap-5050	250	1	the	the	DET
ap-5050	250	2	efficiency	efficiency	NOUN
ap-5050	250	3	of	of	ADP
ap-5050	250	4	a	a	DET
ap-5050	250	5	vertical	vertical	ADJ
ap-5050	250	6	conveyer	conveyer	NOUN
ap-5050	250	7	depending	depend	VERB
ap-5050	250	8	on	on	ADP
ap-5050	250	9	the	the	DET
ap-5050	250	10	angular	angular	ADJ
ap-5050	250	11	velocity	velocity	NOUN
ap-5050	250	12	of	of	ADP
ap-5050	250	13	its	its	PRON
ap-5050	250	14	operating	operating	NOUN
ap-5050	250	15	element	element	NOUN
ap-5050	250	16	:	:	PUNCT
ap-5050	250	17	1	1	NUM
ap-5050	250	18	–	–	PUNCT
ap-5050	250	19	a	a	DET
ap-5050	250	20	conveyer	conveyer	NOUN
ap-5050	250	21	with	with	ADP
ap-5050	250	22	a	a	DET
ap-5050	250	23	screw	screw	ADJ
ap-5050	250	24	operating	operating	NOUN
ap-5050	250	25	element	element	NOUN
ap-5050	250	26	;	;	PUNCT
ap-5050	250	27	2	2	NUM
ap-5050	250	28	–	–	PUNCT
ap-5050	250	29	a	a	DET
ap-5050	250	30	conveyer	conveyer	NOUN
ap-5050	250	31	with	with	ADP
ap-5050	250	32	a	a	DET
ap-5050	250	33	cascade	cascade	NOUN
ap-5050	250	34	operating	operating	NOUN
ap-5050	250	35	element	element	NOUN
ap-5050	250	36	.	.	PUNCT
ap-5050	251	1	was	be	AUX
ap-5050	251	2	determined	determine	VERB
ap-5050	251	3	depending	depend	VERB
ap-5050	251	4	on	on	ADP
ap-5050	251	5	the	the	DET
ap-5050	251	6	frequency	frequency	NOUN
ap-5050	251	7	of	of	ADP
ap-5050	251	8	the	the	DET
ap-5050	251	9	rotation	rotation	NOUN
ap-5050	251	10	of	of	ADP
ap-5050	251	11	an	an	DET
ap-5050	251	12	operating	operating	NOUN
ap-5050	251	13	unit	unit	NOUN
ap-5050	251	14	when	when	SCONJ
ap-5050	251	15	conveying	convey	VERB
ap-5050	251	16	wheat	wheat	NOUN
ap-5050	251	17	(	(	PUNCT
ap-5050	251	18	f	f	X
ap-5050	251	19	=	=	SYM
ap-5050	251	20	0.3	0.3	NUM
ap-5050	251	21	;	;	PUNCT
ap-5050	251	22	fr	fr	PROPN
ap-5050	251	23	=	=	NOUN
ap-5050	251	24	0.3	0.3	NUM
ap-5050	251	25	)	)	PUNCT
ap-5050	251	26	.	.	PUNCT
ap-5050	252	1	the	the	DET
ap-5050	252	2	results	result	NOUN
ap-5050	252	3	of	of	ADP
ap-5050	252	4	the	the	DET
ap-5050	252	5	experimental	experimental	ADJ
ap-5050	252	6	investigation	investigation	NOUN
ap-5050	252	7	are	be	AUX
ap-5050	252	8	presented	present	VERB
ap-5050	252	9	in	in	ADP
ap-5050	252	10	figure	figure	NOUN
ap-5050	252	11	13	13	NUM
ap-5050	252	12	.	.	PUNCT
ap-5050	253	1	it	it	PRON
ap-5050	253	2	has	have	AUX
ap-5050	253	3	been	be	AUX
ap-5050	253	4	determined	determine	VERB
ap-5050	253	5	that	that	SCONJ
ap-5050	253	6	the	the	DET
ap-5050	253	7	efficiency	efficiency	NOUN
ap-5050	253	8	of	of	ADP
ap-5050	253	9	a	a	DET
ap-5050	253	10	conveyer	conveyer	NOUN
ap-5050	253	11	is	be	AUX
ap-5050	253	12	at	at	ADP
ap-5050	253	13	maximum	maximum	ADJ
ap-5050	253	14	and	and	CCONJ
ap-5050	253	15	,	,	PUNCT
ap-5050	253	16	further	far	ADV
ap-5050	253	17	,	,	PUNCT
ap-5050	253	18	it	it	PRON
ap-5050	253	19	remains	remain	VERB
ap-5050	253	20	practically	practically	ADV
ap-5050	253	21	unchanged	unchanged	ADJ
ap-5050	253	22	,	,	PUNCT
ap-5050	253	23	if	if	SCONJ
ap-5050	253	24	the	the	DET
ap-5050	253	25	angular	angular	ADJ
ap-5050	253	26	velocity	velocity	NOUN
ap-5050	253	27	of	of	ADP
ap-5050	253	28	the	the	DET
ap-5050	253	29	operating	operate	VERB
ap-5050	253	30	unit	unit	NOUN
ap-5050	253	31	increases	increase	VERB
ap-5050	253	32	as	as	ADP
ap-5050	253	33	a	a	DET
ap-5050	253	34	result	result	NOUN
ap-5050	253	35	of	of	ADP
ap-5050	253	36	the	the	DET
ap-5050	253	37	spillage	spillage	NOUN
ap-5050	253	38	of	of	ADP
ap-5050	253	39	grain	grain	NOUN
ap-5050	253	40	through	through	ADP
ap-5050	253	41	holes	hole	NOUN
ap-5050	253	42	and	and	CCONJ
ap-5050	253	43	gaps	gap	NOUN
ap-5050	253	44	.	.	PUNCT
ap-5050	254	1	the	the	DET
ap-5050	254	2	efficiency	efficiency	NOUN
ap-5050	254	3	of	of	ADP
ap-5050	254	4	a	a	DET
ap-5050	254	5	conveyer	conveyer	NOUN
ap-5050	254	6	with	with	ADP
ap-5050	254	7	a	a	DET
ap-5050	254	8	cascade	cascade	NOUN
ap-5050	254	9	operating	operating	NOUN
ap-5050	254	10	element	element	NOUN
ap-5050	254	11	is	be	AUX
ap-5050	254	12	practically	practically	ADV
ap-5050	254	13	the	the	DET
ap-5050	254	14	same	same	ADJ
ap-5050	254	15	as	as	ADP
ap-5050	254	16	the	the	DET
ap-5050	254	17	efficiency	efficiency	NOUN
ap-5050	254	18	of	of	ADP
ap-5050	254	19	a	a	DET
ap-5050	254	20	conveyer	conveyer	NOUN
ap-5050	254	21	with	with	ADP
ap-5050	254	22	a	a	DET
ap-5050	254	23	screw	screw	ADJ
ap-5050	254	24	operating	operating	NOUN
ap-5050	254	25	element	element	NOUN
ap-5050	254	26	(	(	PUNCT
ap-5050	254	27	error	error	NOUN
ap-5050	254	28	is	be	AUX
ap-5050	254	29	not	not	PART
ap-5050	254	30	more	more	ADJ
ap-5050	254	31	than	than	ADP
ap-5050	254	32	5	5	NUM
ap-5050	254	33	%	%	NOUN
ap-5050	254	34	)	)	PUNCT
ap-5050	254	35	and	and	CCONJ
ap-5050	254	36	,	,	PUNCT
ap-5050	254	37	that	that	PRON
ap-5050	254	38	is	be	AUX
ap-5050	254	39	why	why	SCONJ
ap-5050	254	40	a	a	DET
ap-5050	254	41	cascade	cascade	NOUN
ap-5050	254	42	operating	operating	NOUN
ap-5050	254	43	element	element	NOUN
ap-5050	254	44	is	be	AUX
ap-5050	254	45	more	more	ADV
ap-5050	254	46	appropriate	appropriate	ADJ
ap-5050	254	47	to	to	PART
ap-5050	254	48	be	be	AUX
ap-5050	254	49	applied	apply	VERB
ap-5050	254	50	in	in	ADP
ap-5050	254	51	conveyers	conveyer	NOUN
ap-5050	254	52	,	,	PUNCT
ap-5050	254	53	since	since	SCONJ
ap-5050	254	54	one	one	NUM
ap-5050	254	55	of	of	ADP
ap-5050	254	56	the	the	DET
ap-5050	254	57	promising	promising	ADJ
ap-5050	254	58	directions	direction	NOUN
ap-5050	254	59	in	in	ADP
ap-5050	254	60	determining	determine	VERB
ap-5050	254	61	the	the	DET
ap-5050	254	62	manufacturability	manufacturability	NOUN
ap-5050	254	63	of	of	ADP
ap-5050	254	64	screw	screw	ADJ
ap-5050	254	65	conveyer	conveyer	NOUN
ap-5050	254	66	operating	operate	VERB
ap-5050	254	67	elements	element	NOUN
ap-5050	254	68	is	be	AUX
ap-5050	254	69	the	the	DET
ap-5050	254	70	application	application	NOUN
ap-5050	254	71	of	of	ADP
ap-5050	254	72	flat	flat	ADJ
ap-5050	254	73	blades	blade	NOUN
ap-5050	254	74	,	,	PUNCT
ap-5050	254	75	which	which	PRON
ap-5050	254	76	are	be	AUX
ap-5050	254	77	inclined	incline	VERB
ap-5050	254	78	to	to	ADP
ap-5050	254	79	the	the	DET
ap-5050	254	80	axis	axis	NOUN
ap-5050	254	81	of	of	ADP
ap-5050	254	82	the	the	DET
ap-5050	254	83	rotation	rotation	NOUN
ap-5050	254	84	and	and	CCONJ
ap-5050	254	85	are	be	AUX
ap-5050	254	86	attached	attach	VERB
ap-5050	254	87	to	to	ADP
ap-5050	254	88	the	the	DET
ap-5050	254	89	cylindrical	cylindrical	ADJ
ap-5050	254	90	shaft	shaft	NOUN
ap-5050	254	91	of	of	ADP
ap-5050	254	92	a	a	DET
ap-5050	254	93	frame	frame	NOUN
ap-5050	254	94	,	,	PUNCT
ap-5050	254	95	instead	instead	ADV
ap-5050	254	96	of	of	ADP
ap-5050	254	97	helical	helical	ADJ
ap-5050	254	98	spirals	spiral	NOUN
ap-5050	254	99	.	.	PUNCT
ap-5050	255	1	the	the	DET
ap-5050	255	2	intention	intention	NOUN
ap-5050	255	3	is	be	AUX
ap-5050	255	4	to	to	PART
ap-5050	255	5	make	make	VERB
ap-5050	255	6	such	such	ADJ
ap-5050	255	7	blades	blade	NOUN
ap-5050	255	8	using	use	VERB
ap-5050	255	9	a	a	DET
ap-5050	255	10	sheet	sheet	NOUN
ap-5050	255	11	metal	metal	NOUN
ap-5050	255	12	forming	form	VERB
ap-5050	255	13	method	method	NOUN
ap-5050	255	14	and	and	CCONJ
ap-5050	255	15	further	far	ADV
ap-5050	255	16	welding	weld	VERB
ap-5050	255	17	them	they	PRON
ap-5050	255	18	to	to	ADP
ap-5050	255	19	a	a	DET
ap-5050	255	20	cylindrical	cylindrical	ADJ
ap-5050	255	21	shaft	shaft	NOUN
ap-5050	255	22	,	,	PUNCT
ap-5050	255	23	since	since	SCONJ
ap-5050	255	24	it	it	PRON
ap-5050	255	25	is	be	AUX
ap-5050	255	26	cheaper	cheap	ADJ
ap-5050	255	27	.	.	PUNCT
ap-5050	256	1	4	4	X
ap-5050	256	2	.	.	X
ap-5050	256	3	conclusions	conclusion	NOUN
ap-5050	256	4	a	a	DET
ap-5050	256	5	particle	particle	NOUN
ap-5050	256	6	motion	motion	NOUN
ap-5050	256	7	on	on	ADP
ap-5050	256	8	an	an	DET
ap-5050	256	9	inclined	inclined	ADJ
ap-5050	256	10	plane	plane	NOUN
ap-5050	256	11	that	that	PRON
ap-5050	256	12	rotates	rotate	VERB
ap-5050	256	13	around	around	ADP
ap-5050	256	14	the	the	DET
ap-5050	256	15	axis	axis	NOUN
ap-5050	256	16	of	of	ADP
ap-5050	256	17	a	a	DET
ap-5050	256	18	vertical	vertical	ADJ
ap-5050	256	19	limiting	limit	VERB
ap-5050	256	20	cylinder	cylinder	NOUN
ap-5050	256	21	differs	differ	VERB
ap-5050	256	22	from	from	ADP
ap-5050	256	23	a	a	DET
ap-5050	256	24	particle	particle	NOUN
ap-5050	256	25	motion	motion	NOUN
ap-5050	256	26	on	on	ADP
ap-5050	256	27	a	a	DET
ap-5050	256	28	screw	screw	NOUN
ap-5050	256	29	surface	surface	NOUN
ap-5050	256	30	,	,	PUNCT
ap-5050	256	31	which	which	PRON
ap-5050	256	32	rotates	rotate	VERB
ap-5050	256	33	in	in	ADP
ap-5050	256	34	a	a	DET
ap-5050	256	35	vertical	vertical	ADJ
ap-5050	256	36	cylinder	cylinder	NOUN
ap-5050	256	37	.	.	PUNCT
ap-5050	257	1	the	the	DET
ap-5050	257	2	difference	difference	NOUN
ap-5050	257	3	is	be	AUX
ap-5050	257	4	in	in	ADP
ap-5050	257	5	variable	variable	ADJ
ap-5050	257	6	kinematic	kinematic	ADJ
ap-5050	257	7	and	and	CCONJ
ap-5050	257	8	dynamic	dynamic	ADJ
ap-5050	257	9	motion	motion	NOUN
ap-5050	257	10	patterns	pattern	NOUN
ap-5050	257	11	.	.	PUNCT
ap-5050	258	1	in	in	ADP
ap-5050	258	2	order	order	NOUN
ap-5050	258	3	to	to	PART
ap-5050	258	4	provide	provide	VERB
ap-5050	258	5	particle	particle	NOUN
ap-5050	258	6	sliding	slide	VERB
ap-5050	258	7	on	on	ADP
ap-5050	258	8	a	a	DET
ap-5050	258	9	plane	plane	NOUN
ap-5050	258	10	and	and	CCONJ
ap-5050	258	11	in	in	ADP
ap-5050	258	12	an	an	DET
ap-5050	258	13	ellipse	ellipse	NOUN
ap-5050	258	14	at	at	ADP
ap-5050	258	15	the	the	DET
ap-5050	258	16	same	same	ADJ
ap-5050	258	17	time	time	NOUN
ap-5050	258	18	,	,	PUNCT
ap-5050	258	19	it	it	PRON
ap-5050	258	20	is	be	AUX
ap-5050	258	21	necessary	necessary	ADJ
ap-5050	258	22	to	to	PART
ap-5050	258	23	provide	provide	VERB
ap-5050	258	24	the	the	DET
ap-5050	258	25	required	require	VERB
ap-5050	258	26	angular	angular	ADJ
ap-5050	258	27	velocity	velocity	NOUN
ap-5050	258	28	of	of	ADP
ap-5050	258	29	the	the	DET
ap-5050	258	30	flat	flat	ADJ
ap-5050	258	31	segment	segment	NOUN
ap-5050	258	32	rotation	rotation	NOUN
ap-5050	258	33	.	.	PUNCT
ap-5050	259	1	75	75	NUM
ap-5050	259	2	s.	s.	PROPN
ap-5050	259	3	f.	f.	PROPN
ap-5050	259	4	pylypaka	pylypaka	PROPN
ap-5050	259	5	,	,	PUNCT
ap-5050	259	6	m.	m.	PROPN
ap-5050	259	7	b.	b.	PROPN
ap-5050	259	8	klendii	klendii	PROPN
ap-5050	259	9	,	,	PUNCT
ap-5050	259	10	v.	v.	PROPN
ap-5050	259	11	m.	m.	PROPN
ap-5050	259	12	nesvidomin	nesvidomin	PROPN
ap-5050	259	13	,	,	PUNCT
ap-5050	259	14	v.	v.	PROPN
ap-5050	259	15	i.	i.	PROPN
ap-5050	259	16	trokhaniak	trokhaniak	PROPN
ap-5050	259	17	acta	acta	PROPN
ap-5050	259	18	polytechnica	polytechnica	PROPN
ap-5050	259	19	its	its	PRON
ap-5050	259	20	motion	motion	NOUN
ap-5050	259	21	pattern	pattern	NOUN
ap-5050	259	22	is	be	AUX
ap-5050	259	23	influenced	influence	VERB
ap-5050	259	24	by	by	ADP
ap-5050	259	25	the	the	DET
ap-5050	259	26	coefficients	coefficient	NOUN
ap-5050	259	27	of	of	ADP
ap-5050	259	28	the	the	DET
ap-5050	259	29	particle	particle	NOUN
ap-5050	259	30	friction	friction	NOUN
ap-5050	259	31	on	on	ADP
ap-5050	259	32	the	the	DET
ap-5050	259	33	surfaces	surface	NOUN
ap-5050	259	34	of	of	ADP
ap-5050	259	35	a	a	DET
ap-5050	259	36	plane	plane	NOUN
ap-5050	259	37	and	and	CCONJ
ap-5050	259	38	a	a	DET
ap-5050	259	39	cylindrical	cylindrical	ADJ
ap-5050	259	40	cover	cover	NOUN
ap-5050	259	41	,	,	PUNCT
ap-5050	259	42	the	the	DET
ap-5050	259	43	radius	radius	NOUN
ap-5050	259	44	of	of	ADP
ap-5050	259	45	a	a	DET
ap-5050	259	46	cylinder	cylinder	NOUN
ap-5050	259	47	,	,	PUNCT
ap-5050	259	48	the	the	DET
ap-5050	259	49	angular	angular	ADJ
ap-5050	259	50	velocity	velocity	NOUN
ap-5050	259	51	of	of	ADP
ap-5050	259	52	segment	segment	NOUN
ap-5050	259	53	rotation	rotation	NOUN
ap-5050	259	54	and	and	CCONJ
ap-5050	259	55	the	the	DET
ap-5050	259	56	inclination	inclination	NOUN
ap-5050	259	57	angle	angle	NOUN
ap-5050	259	58	of	of	ADP
ap-5050	259	59	a	a	DET
ap-5050	259	60	plane	plane	NOUN
ap-5050	259	61	.	.	PUNCT
ap-5050	260	1	at	at	ADP
ap-5050	260	2	a	a	DET
ap-5050	260	3	certain	certain	ADJ
ap-5050	260	4	combination	combination	NOUN
ap-5050	260	5	of	of	ADP
ap-5050	260	6	these	these	DET
ap-5050	260	7	parameters	parameter	NOUN
ap-5050	260	8	,	,	PUNCT
ap-5050	260	9	a	a	DET
ap-5050	260	10	particle	particle	NOUN
ap-5050	260	11	may	may	AUX
ap-5050	260	12	“	"	PUNCT
ap-5050	260	13	stick	stick	VERB
ap-5050	260	14	”	"	PUNCT
ap-5050	260	15	in	in	ADP
ap-5050	260	16	an	an	DET
ap-5050	260	17	ellipse	ellipse	NOUN
ap-5050	260	18	or	or	CCONJ
ap-5050	260	19	detach	detach	VERB
ap-5050	260	20	from	from	ADP
ap-5050	260	21	a	a	DET
ap-5050	260	22	plane	plane	NOUN
ap-5050	260	23	in	in	ADP
ap-5050	260	24	the	the	DET
ap-5050	260	25	top	top	ADJ
ap-5050	260	26	position	position	NOUN
ap-5050	260	27	.	.	PUNCT
ap-5050	261	1	it	it	PRON
ap-5050	261	2	is	be	AUX
ap-5050	261	3	possible	possible	ADJ
ap-5050	261	4	to	to	PART
ap-5050	261	5	increase	increase	VERB
ap-5050	261	6	the	the	DET
ap-5050	261	7	number	number	NOUN
ap-5050	261	8	of	of	ADP
ap-5050	261	9	particle	particle	NOUN
ap-5050	261	10	passings	passing	NOUN
ap-5050	261	11	along	along	ADP
ap-5050	261	12	an	an	DET
ap-5050	261	13	ellipse	ellipse	NOUN
ap-5050	261	14	per	per	ADP
ap-5050	261	15	unit	unit	NOUN
ap-5050	261	16	time	time	NOUN
ap-5050	261	17	due	due	ADP
ap-5050	261	18	to	to	ADP
ap-5050	261	19	the	the	DET
ap-5050	261	20	decrease	decrease	NOUN
ap-5050	261	21	of	of	ADP
ap-5050	261	22	the	the	DET
ap-5050	261	23	coefficient	coefficient	NOUN
ap-5050	261	24	of	of	ADP
ap-5050	261	25	its	its	PRON
ap-5050	261	26	friction	friction	NOUN
ap-5050	261	27	on	on	ADP
ap-5050	261	28	an	an	DET
ap-5050	261	29	inclined	inclined	ADJ
ap-5050	261	30	plane	plane	NOUN
ap-5050	261	31	and	and	CCONJ
ap-5050	261	32	due	due	ADP
ap-5050	261	33	to	to	ADP
ap-5050	261	34	the	the	DET
ap-5050	261	35	increase	increase	NOUN
ap-5050	261	36	of	of	ADP
ap-5050	261	37	the	the	DET
ap-5050	261	38	coefficient	coefficient	NOUN
ap-5050	261	39	of	of	ADP
ap-5050	261	40	its	its	PRON
ap-5050	261	41	friction	friction	NOUN
ap-5050	261	42	on	on	ADP
ap-5050	261	43	the	the	DET
ap-5050	261	44	inner	inner	ADJ
ap-5050	261	45	surface	surface	NOUN
ap-5050	261	46	of	of	ADP
ap-5050	261	47	a	a	DET
ap-5050	261	48	limiting	limit	VERB
ap-5050	261	49	cylinder	cylinder	NOUN
ap-5050	261	50	.	.	PUNCT
ap-5050	262	1	a	a	DET
ap-5050	262	2	cascade	cascade	NOUN
ap-5050	262	3	operating	operating	NOUN
ap-5050	262	4	element	element	NOUN
ap-5050	262	5	,	,	PUNCT
ap-5050	262	6	which	which	PRON
ap-5050	262	7	can	can	AUX
ap-5050	262	8	compete	compete	VERB
ap-5050	262	9	with	with	ADP
ap-5050	262	10	a	a	DET
ap-5050	262	11	screw	screw	ADJ
ap-5050	262	12	operating	operating	NOUN
ap-5050	262	13	element	element	NOUN
ap-5050	262	14	in	in	ADP
ap-5050	262	15	reclaim	reclaim	NOUN
ap-5050	262	16	conveyers	conveyer	NOUN
ap-5050	262	17	due	due	ADP
ap-5050	262	18	to	to	ADP
ap-5050	262	19	the	the	DET
ap-5050	262	20	ease	ease	NOUN
ap-5050	262	21	of	of	ADP
ap-5050	262	22	its	its	PRON
ap-5050	262	23	manufacturing	manufacturing	NOUN
ap-5050	262	24	,	,	PUNCT
ap-5050	262	25	has	have	AUX
ap-5050	262	26	been	be	AUX
ap-5050	262	27	designed	design	VERB
ap-5050	262	28	.	.	PUNCT
ap-5050	263	1	references	reference	NOUN
ap-5050	263	2	[	[	X
ap-5050	263	3	1	1	NUM
ap-5050	263	4	]	]	X
ap-5050	263	5	p.	p.	NOUN
ap-5050	263	6	m.	m.	PROPN
ap-5050	263	7	vasylenko	vasylenko	PROPN
ap-5050	263	8	,	,	PUNCT
ap-5050	263	9	theory	theory	NOUN
ap-5050	263	10	of	of	ADP
ap-5050	263	11	particle	particle	NOUN
ap-5050	263	12	motion	motion	NOUN
ap-5050	263	13	over	over	ADP
ap-5050	263	14	rough	rough	ADJ
ap-5050	263	15	surfaces	surface	NOUN
ap-5050	263	16	of	of	ADP
ap-5050	263	17	agricultural	agricultural	ADJ
ap-5050	263	18	machines	machine	NOUN
ap-5050	263	19	.	.	PUNCT
ap-5050	264	1	kyiv	kyiv	ADJ
ap-5050	264	2	,	,	PUNCT
ap-5050	264	3	ukraine	ukraine	NOUN
ap-5050	264	4	:	:	PUNCT
ap-5050	264	5	ukrainian	ukrainian	PROPN
ap-5050	264	6	academy	academy	PROPN
ap-5050	264	7	of	of	ADP
ap-5050	264	8	agricultural	agricultural	ADJ
ap-5050	264	9	sciences	science	NOUN
ap-5050	264	10	,	,	PUNCT
ap-5050	264	11	pp	pp	ADP
ap-5050	264	12	.	.	PROPN
ap-5050	265	1	283	283	NUM
ap-5050	265	2	,	,	PUNCT
ap-5050	265	3	1960	1960	NUM
ap-5050	265	4	.	.	PUNCT
ap-5050	266	1	[	[	X
ap-5050	266	2	2	2	NUM
ap-5050	266	3	]	]	X
ap-5050	266	4	p.	p.	NOUN
ap-5050	266	5	m.	m.	NOUN
ap-5050	266	6	zaika	zaika	PROPN
ap-5050	266	7	,	,	PUNCT
ap-5050	266	8	“	"	PUNCT
ap-5050	266	9	concerning	concern	VERB
ap-5050	266	10	one	one	NUM
ap-5050	266	11	family	family	NOUN
ap-5050	266	12	of	of	ADP
ap-5050	266	13	regular	regular	ADJ
ap-5050	266	14	particle	particle	NOUN
ap-5050	266	15	motion	motion	NOUN
ap-5050	266	16	over	over	ADP
ap-5050	266	17	an	an	DET
ap-5050	266	18	oscillating	oscillate	VERB
ap-5050	266	19	plane	plane	NOUN
ap-5050	266	20	of	of	ADP
ap-5050	266	21	vibratory	vibratory	ADJ
ap-5050	266	22	grain	grain	NOUN
ap-5050	266	23	-	-	PUNCT
ap-5050	266	24	cleaning	clean	VERB
ap-5050	266	25	machine	machine	NOUN
ap-5050	266	26	,	,	PUNCT
ap-5050	266	27	”	"	PUNCT
ap-5050	266	28	theory	theory	NOUN
ap-5050	266	29	of	of	ADP
ap-5050	266	30	mechanisms	mechanism	NOUN
ap-5050	266	31	and	and	CCONJ
ap-5050	266	32	machines	machine	NOUN
ap-5050	266	33	,	,	PUNCT
ap-5050	266	34	vol	vol	NOUN
ap-5050	266	35	.	.	PROPN
ap-5050	266	36	1	1	X
ap-5050	266	37	.	.	X
ap-5050	266	38	m.	m.	NOUN
ap-5050	266	39	gorkii	gorkii	PROPN
ap-5050	266	40	kharkiv	kharkiv	PROPN
ap-5050	266	41	state	state	PROPN
ap-5050	266	42	university	university	PROPN
ap-5050	266	43	,	,	PUNCT
ap-5050	266	44	pp	pp	ADJ
ap-5050	266	45	.	.	PUNCT
ap-5050	267	1	28	28	NUM
ap-5050	267	2	-	-	SYM
ap-5050	267	3	33	33	NUM
ap-5050	267	4	,	,	PUNCT
ap-5050	267	5	1966	1966	NUM
ap-5050	267	6	.	.	PUNCT
ap-5050	268	1	[	[	X
ap-5050	268	2	3	3	X
ap-5050	268	3	]	]	PUNCT
ap-5050	268	4	m.	m.	PROPN
ap-5050	268	5	b.	b.	PROPN
ap-5050	268	6	klendii	klendii	PROPN
ap-5050	268	7	,	,	PUNCT
ap-5050	268	8	o.	o.	PROPN
ap-5050	268	9	m.	m.	NOUN
ap-5050	268	10	klendii	klendii	PROPN
ap-5050	268	11	.	.	PUNCT
ap-5050	269	1	inverrelation	inverrelation	NOUN
ap-5050	269	2	between	between	ADP
ap-5050	269	3	incidence	incidence	ADJ
ap-5050	269	4	ange	ange	NOUN
ap-5050	269	5	and	and	CCONJ
ap-5050	269	6	roll	roll	NOUN
ap-5050	269	7	ange	ange	NOUN
ap-5050	269	8	of	of	ADP
ap-5050	269	9	concave	concave	VERB
ap-5050	269	10	disks	disk	NOUN
ap-5050	269	11	of	of	ADP
ap-5050	269	12	soil	soil	NOUN
ap-5050	269	13	tillage	tillage	NOUN
ap-5050	269	14	implements	implement	NOUN
ap-5050	269	15	,	,	PUNCT
ap-5050	269	16	inmateh	inmateh	NOUN
ap-5050	269	17	:	:	PUNCT
ap-5050	269	18	agricultural	agricultural	ADJ
ap-5050	269	19	engineering	engineering	NOUN
ap-5050	269	20	,	,	PUNCT
ap-5050	269	21	vol.49	vol.49	PROPN
ap-5050	269	22	,	,	PUNCT
ap-5050	269	23	no.2	no.2	PROPN
ap-5050	269	24	,	,	PUNCT
ap-5050	269	25	pp.13	pp.13	NOUN
ap-5050	269	26	-	-	PUNCT
ap-5050	269	27	20	20	NUM
ap-5050	269	28	,	,	PUNCT
ap-5050	269	29	2016	2016	NUM
ap-5050	269	30	;	;	PUNCT
ap-5050	269	31	[	[	X
ap-5050	269	32	4	4	X
ap-5050	269	33	]	]	X
ap-5050	269	34	hevko	hevko	PROPN
ap-5050	269	35	r.b	r.b	PROPN
ap-5050	269	36	.	.	PROPN
ap-5050	269	37	,	,	PUNCT
ap-5050	269	38	dzyura	dzyura	NOUN
ap-5050	269	39	v.o	v.o	PROPN
ap-5050	269	40	.	.	PROPN
ap-5050	269	41	,	,	PUNCT
ap-5050	269	42	romanovsky	romanovsky	PROPN
ap-5050	269	43	r.m	r.m	PROPN
ap-5050	269	44	.	.	PROPN
ap-5050	269	45	mathematical	mathematical	ADJ
ap-5050	269	46	model	model	NOUN
ap-5050	269	47	of	of	ADP
ap-5050	269	48	the	the	DET
ap-5050	269	49	pneumatic	pneumatic	ADJ
ap-5050	269	50	-	-	PUNCT
ap-5050	269	51	screw	screw	ADJ
ap-5050	269	52	conveyor	conveyor	NOUN
ap-5050	269	53	screw	screw	NOUN
ap-5050	269	54	mechanism	mechanism	NOUN
ap-5050	269	55	operation	operation	NOUN
ap-5050	269	56	,	,	PUNCT
ap-5050	269	57	inmateh	inmateh	NOUN
ap-5050	269	58	:	:	PUNCT
ap-5050	269	59	agricultural	agricultural	ADJ
ap-5050	269	60	engineering	engineering	NOUN
ap-5050	269	61	,	,	PUNCT
ap-5050	269	62	vol.44	vol.44	NOUN
ap-5050	269	63	,	,	PUNCT
ap-5050	269	64	no.3	no.3	PROPN
ap-5050	269	65	,	,	PUNCT
ap-5050	269	66	pp.103	pp.103	NOUN
ap-5050	269	67	-	-	X
ap-5050	269	68	110	110	NUM
ap-5050	269	69	,	,	PUNCT
ap-5050	269	70	2014	2014	NUM
ap-5050	269	71	.	.	PUNCT
ap-5050	270	1	[	[	X
ap-5050	270	2	5	5	X
ap-5050	270	3	]	]	PUNCT
ap-5050	270	4	pylypaka	pylypaka	PROPN
ap-5050	270	5	s.	s.	PROPN
ap-5050	270	6	,	,	PUNCT
ap-5050	270	7	klendii	klendii	PROPN
ap-5050	270	8	m.	m.	NOUN
ap-5050	270	9	,	,	PUNCT
ap-5050	270	10	klendii	klendii	PROPN
ap-5050	270	11	o.	o.	PROPN
ap-5050	270	12	particle	particle	NOUN
ap-5050	270	13	motion	motion	NOUN
ap-5050	270	14	on	on	ADP
ap-5050	270	15	the	the	DET
ap-5050	270	16	surface	surface	NOUN
ap-5050	270	17	of	of	ADP
ap-5050	270	18	a	a	DET
ap-5050	270	19	concave	concave	ADJ
ap-5050	270	20	soil	soil	NOUN
ap-5050	270	21	-	-	PUNCT
ap-5050	270	22	tilling	till	VERB
ap-5050	270	23	disk	disk	NOUN
ap-5050	270	24	,	,	PUNCT
ap-5050	270	25	acta	acta	PROPN
ap-5050	270	26	polytechnica	polytechnica	PROPN
ap-5050	270	27	,	,	PUNCT
ap-5050	270	28	journal	journal	NOUN
ap-5050	270	29	of	of	ADP
ap-5050	270	30	advanced	advanced	ADJ
ap-5050	270	31	engineering	engineering	NOUN
ap-5050	270	32	,	,	PUNCT
ap-5050	270	33	vol.58	vol.58	PROPN
ap-5050	270	34	,	,	PUNCT
ap-5050	270	35	no.3	no.3	NOUN
ap-5050	270	36	,	,	PUNCT
ap-5050	270	37	pp.201	pp.201	NOUN
ap-5050	270	38	-	-	PUNCT
ap-5050	270	39	208	208	NUM
ap-5050	270	40	,	,	PUNCT
ap-5050	270	41	2018	2018	NUM
ap-5050	270	42	.	.	PUNCT
ap-5050	271	1	[	[	X
ap-5050	271	2	6	6	NUM
ap-5050	271	3	]	]	PUNCT
ap-5050	271	4	p.	p.	NOUN
ap-5050	271	5	ratanavararaksa	ratanavararaksa	NOUN
ap-5050	271	6	and	and	CCONJ
ap-5050	271	7	m.	m.	NOUN
ap-5050	271	8	dejnakarintra	dejnakarintra	PROPN
ap-5050	271	9	,	,	PUNCT
ap-5050	271	10	“	"	PUNCT
ap-5050	271	11	series	series	NOUN
ap-5050	271	12	solutions	solution	NOUN
ap-5050	271	13	of	of	ADP
ap-5050	271	14	the	the	DET
ap-5050	271	15	anharmonic	anharmonic	ADJ
ap-5050	271	16	motion	motion	NOUN
ap-5050	271	17	equation	equation	NOUN
ap-5050	271	18	y′′+y2	y′′+y2	NOUN
ap-5050	271	19	=	=	PUNCT
ap-5050	271	20	c	c	X
ap-5050	271	21	,	,	PUNCT
ap-5050	271	22	”	"	PUNCT
ap-5050	271	23	engineering	engineering	NOUN
ap-5050	271	24	journal	journal	NOUN
ap-5050	271	25	,	,	PUNCT
ap-5050	271	26	vol	vol	NOUN
ap-5050	271	27	.	.	PROPN
ap-5050	271	28	20	20	NUM
ap-5050	271	29	,	,	PUNCT
ap-5050	271	30	no	no	INTJ
ap-5050	271	31	.	.	NOUN
ap-5050	271	32	5	5	NUM
ap-5050	271	33	,	,	PUNCT
ap-5050	271	34	pp	pp	ADJ
ap-5050	271	35	.	.	PUNCT
ap-5050	271	36	203	203	NUM
ap-5050	271	37	-	-	SYM
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ap-5050	271	40	2016	2016	NUM
ap-5050	271	41	.	.	PUNCT
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ap-5050	272	9	i.	i.	PROPN
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ap-5050	272	25	processes	process	NOUN
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ap-5050	273	2	,	,	PUNCT
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ap-5050	273	7	pp	pp	ADJ
ap-5050	273	8	.	.	PUNCT
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ap-5050	273	10	-	-	SYM
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ap-5050	275	10	,	,	PUNCT
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ap-5050	275	12	,	,	PUNCT
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ap-5050	275	14	-	-	SYM
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ap-5050	275	16	,	,	PUNCT
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ap-5050	275	18	.	.	PUNCT
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ap-5050	276	10	.	.	PUNCT
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ap-5050	277	5	,	,	PUNCT
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ap-5050	277	7	,	,	PUNCT
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ap-5050	277	12	.	.	PUNCT
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ap-5050	278	5	i.	i.	PROPN
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ap-5050	278	7	.	.	PUNCT
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ap-5050	279	2	basis	basis	NOUN
ap-5050	279	3	and	and	CCONJ
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ap-5050	279	5	for	for	ADP
ap-5050	279	6	a	a	DET
ap-5050	279	7	sorting	sort	VERB
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ap-5050	279	9	‘	'	PUNCT
ap-5050	279	10	zmeika	zmeika	X
ap-5050	279	11	’	'	PUNCT
ap-5050	279	12	,	,	PUNCT
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ap-5050	279	15	,	,	PUNCT
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ap-5050	279	17	.	.	PROPN
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ap-5050	280	2	-	-	SYM
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ap-5050	280	6	.	.	PUNCT
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ap-5050	281	5	,	,	PUNCT
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ap-5050	281	7	1	1	NUM
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ap-5050	281	9	2	2	NUM
ap-5050	281	10	material	material	NOUN
ap-5050	281	11	and	and	CCONJ
ap-5050	281	12	methods	method	NOUN
ap-5050	281	13	3	3	NUM
ap-5050	281	14	results	result	VERB
ap-5050	281	15	4	4	NUM
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ap-5050	281	17	references	reference	NOUN