id	sid	tid	token	lemma	pos
asir-2864	1	1	applied	apply	VERB
asir-2864	1	2	science	science	NOUN
asir-2864	1	3	and	and	CCONJ
asir-2864	1	4	innovative	innovative	ADJ
asir-2864	1	5	research	research	NOUN
asir-2864	1	6	issn	issn	VERB
asir-2864	1	7	2474	2474	NUM
asir-2864	1	8	-	-	SYM
asir-2864	1	9	4972	4972	NUM
asir-2864	1	10	(	(	PUNCT
asir-2864	1	11	print	print	NOUN
asir-2864	1	12	)	)	PUNCT
asir-2864	1	13	issn	issn	VERB
asir-2864	1	14	2474	2474	NUM
asir-2864	1	15	-	-	SYM
asir-2864	1	16	4980	4980	NUM
asir-2864	1	17	(	(	PUNCT
asir-2864	1	18	online	online	ADJ
asir-2864	1	19	)	)	PUNCT
asir-2864	1	20	vol	vol	NOUN
asir-2864	1	21	.	.	PROPN
asir-2864	2	1	4	4	NUM
asir-2864	2	2	,	,	PUNCT
asir-2864	2	3	no	no	INTJ
asir-2864	2	4	.	.	NOUN
asir-2864	2	5	2	2	NUM
asir-2864	2	6	,	,	PUNCT
asir-2864	2	7	2020	2020	NUM
asir-2864	2	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	VERB
asir-2864	2	9	41	41	NUM
asir-2864	2	10	original	original	ADJ
asir-2864	2	11	paper	paper	NOUN
asir-2864	2	12	excel	excel	VERB
asir-2864	2	13	files	file	NOUN
asir-2864	2	14	for	for	ADP
asir-2864	2	15	newton	newton	PROPN
asir-2864	2	16	’s	’s	PART
asir-2864	2	17	proposition	proposition	NOUN
asir-2864	2	18	v	v	ADP
asir-2864	2	19	pavlos	pavlo	NOUN
asir-2864	2	20	mihas1	mihas1	PROPN
asir-2864	2	21	*	*	ADJ
asir-2864	2	22	1	1	NUM
asir-2864	2	23	retired	retired	ADJ
asir-2864	2	24	professor	professor	NOUN
asir-2864	2	25	of	of	ADP
asir-2864	2	26	didactics	didactics	NOUN
asir-2864	2	27	of	of	ADP
asir-2864	2	28	physics	physics	PROPN
asir-2864	2	29	,	,	PUNCT
asir-2864	2	30	department	department	PROPN
asir-2864	2	31	of	of	ADP
asir-2864	2	32	elementary	elementary	ADJ
asir-2864	2	33	education	education	PROPN
asir-2864	2	34	,	,	PUNCT
asir-2864	2	35	democritus	democritus	PROPN
asir-2864	2	36	university	university	PROPN
asir-2864	2	37	,	,	PUNCT
asir-2864	2	38	nea	nea	PROPN
asir-2864	2	39	chili	chili	PROPN
asir-2864	2	40	,	,	PUNCT
asir-2864	2	41	alexandroupolis	alexandroupolis	PROPN
asir-2864	2	42	,	,	PUNCT
asir-2864	2	43	gr68100	gr68100	PROPN
asir-2864	2	44	,	,	PUNCT
asir-2864	2	45	greece	greece	PROPN
asir-2864	2	46	received	receive	VERB
asir-2864	2	47	:	:	PUNCT
asir-2864	2	48	may	may	AUX
asir-2864	2	49	3	3	NUM
asir-2864	2	50	,	,	PUNCT
asir-2864	2	51	2020	2020	NUM
asir-2864	2	52	accepted	accept	VERB
asir-2864	2	53	:	:	PUNCT
asir-2864	2	54	may	may	AUX
asir-2864	2	55	11	11	NUM
asir-2864	2	56	,	,	PUNCT
asir-2864	2	57	2020	2020	NUM
asir-2864	2	58	online	online	ADV
asir-2864	2	59	published	publish	VERB
asir-2864	2	60	:	:	PUNCT
asir-2864	2	61	may	may	AUX
asir-2864	2	62	19	19	NUM
asir-2864	2	63	,	,	PUNCT
asir-2864	2	64	2020	2020	NUM
asir-2864	2	65	doi:10.22158	doi:10.22158	NOUN
asir-2864	2	66	/	/	SYM
asir-2864	2	67	asir.v4n2p41	asir.v4n2p41	PROPN
asir-2864	2	68	url	url	PROPN
asir-2864	2	69	:	:	PUNCT
asir-2864	2	70	http://dx.doi.org/10.22158/asir.v4n2p41	http://dx.doi.org/10.22158/asir.v4n2p41	PROPN
asir-2864	2	71	abstract	abstract	ADJ
asir-2864	2	72	newton	newton	PROPN
asir-2864	2	73	in	in	ADP
asir-2864	2	74	principia	principia	PROPN
asir-2864	2	75	gives	give	VERB
asir-2864	2	76	us	we	PRON
asir-2864	2	77	a	a	DET
asir-2864	2	78	mathematical	mathematical	ADJ
asir-2864	2	79	method	method	NOUN
asir-2864	2	80	of	of	ADP
asir-2864	2	81	finding	find	VERB
asir-2864	2	82	the	the	DET
asir-2864	2	83	center	center	NOUN
asir-2864	2	84	of	of	ADP
asir-2864	2	85	force	force	NOUN
asir-2864	2	86	for	for	ADP
asir-2864	2	87	a	a	DET
asir-2864	2	88	body	body	NOUN
asir-2864	2	89	moving	move	VERB
asir-2864	2	90	on	on	ADP
asir-2864	2	91	an	an	DET
asir-2864	2	92	ellipse	ellipse	NOUN
asir-2864	2	93	in	in	ADP
asir-2864	2	94	proposition	proposition	NOUN
asir-2864	2	95	v	v	ADP
asir-2864	2	96	,	,	PUNCT
asir-2864	2	97	problem	problem	NOUN
asir-2864	2	98	i.	i.	PROPN
asir-2864	2	99	the	the	DET
asir-2864	2	100	same	same	ADJ
asir-2864	2	101	thinking	thinking	NOUN
asir-2864	2	102	can	can	AUX
asir-2864	2	103	be	be	AUX
asir-2864	2	104	applied	apply	VERB
asir-2864	2	105	also	also	ADV
asir-2864	2	106	to	to	ADP
asir-2864	2	107	the	the	DET
asir-2864	2	108	case	case	NOUN
asir-2864	2	109	of	of	ADP
asir-2864	2	110	a	a	DET
asir-2864	2	111	hyperbola	hyperbola	PROPN
asir-2864	2	112	and	and	CCONJ
asir-2864	2	113	also	also	ADV
asir-2864	2	114	a	a	DET
asir-2864	2	115	parabola	parabola	NOUN
asir-2864	2	116	,	,	PUNCT
asir-2864	2	117	only	only	ADV
asir-2864	2	118	that	that	SCONJ
asir-2864	2	119	in	in	ADP
asir-2864	2	120	the	the	DET
asir-2864	2	121	last	last	ADJ
asir-2864	2	122	case	case	NOUN
asir-2864	2	123	the	the	DET
asir-2864	2	124	center	center	NOUN
asir-2864	2	125	of	of	ADP
asir-2864	2	126	force	force	NOUN
asir-2864	2	127	is	be	AUX
asir-2864	2	128	at	at	ADP
asir-2864	2	129	infinite	infinite	ADJ
asir-2864	2	130	distance	distance	NOUN
asir-2864	2	131	.	.	PUNCT
asir-2864	3	1	for	for	ADP
asir-2864	3	2	the	the	DET
asir-2864	3	3	first	first	ADJ
asir-2864	3	4	two	two	NUM
asir-2864	3	5	cases	case	NOUN
asir-2864	3	6	there	there	PRON
asir-2864	3	7	are	be	VERB
asir-2864	3	8	3	3	NUM
asir-2864	3	9	cases	case	NOUN
asir-2864	3	10	of	of	ADP
asir-2864	3	11	possible	possible	ADJ
asir-2864	3	12	forces	force	NOUN
asir-2864	3	13	:	:	PUNCT
asir-2864	3	14	a	a	X
asir-2864	3	15	)	)	PUNCT
asir-2864	3	16	an	an	DET
asir-2864	3	17	force	force	NOUN
asir-2864	3	18	proportional	proportional	ADJ
asir-2864	3	19	to	to	ADP
asir-2864	3	20	the	the	DET
asir-2864	3	21	distance	distance	NOUN
asir-2864	3	22	from	from	ADP
asir-2864	3	23	the	the	DET
asir-2864	3	24	center	center	NOUN
asir-2864	3	25	.	.	PUNCT
asir-2864	4	1	for	for	ADP
asir-2864	4	2	ellipse	ellipse	NOUN
asir-2864	4	3	an	an	DET
asir-2864	4	4	attractive	attractive	ADJ
asir-2864	4	5	force	force	NOUN
asir-2864	4	6	for	for	ADP
asir-2864	4	7	hyperbola	hyperbola	PROPN
asir-2864	4	8	a	a	DET
asir-2864	4	9	repulsive	repulsive	ADJ
asir-2864	4	10	,	,	PUNCT
asir-2864	4	11	b	b	NOUN
asir-2864	4	12	)	)	PUNCT
asir-2864	4	13	a	a	DET
asir-2864	4	14	force	force	NOUN
asir-2864	4	15	proportional	proportional	NOUN
asir-2864	4	16	to	to	ADP
asir-2864	4	17	the	the	DET
asir-2864	4	18	inverse	inverse	NOUN
asir-2864	4	19	of	of	ADP
asir-2864	4	20	the	the	DET
asir-2864	4	21	square	square	NOUN
asir-2864	4	22	of	of	ADP
asir-2864	4	23	the	the	DET
asir-2864	4	24	distance	distance	NOUN
asir-2864	4	25	from	from	ADP
asir-2864	4	26	the	the	DET
asir-2864	4	27	left	left	ADJ
asir-2864	4	28	focus	focus	NOUN
asir-2864	4	29	,	,	PUNCT
asir-2864	4	30	for	for	ADP
asir-2864	4	31	ellipse	ellipse	NOUN
asir-2864	4	32	an	an	DET
asir-2864	4	33	attractive	attractive	ADJ
asir-2864	4	34	and	and	CCONJ
asir-2864	4	35	for	for	ADP
asir-2864	4	36	hyperbola	hyperbola	PROPN
asir-2864	4	37	a	a	DET
asir-2864	4	38	repulsive	repulsive	ADJ
asir-2864	4	39	force	force	NOUN
asir-2864	4	40	,	,	PUNCT
asir-2864	4	41	c	c	X
asir-2864	4	42	)	)	PUNCT
asir-2864	4	43	an	an	DET
asir-2864	4	44	attractive	attractive	ADJ
asir-2864	4	45	force	force	NOUN
asir-2864	4	46	inversely	inversely	ADV
asir-2864	4	47	proportional	proportional	ADJ
asir-2864	4	48	to	to	ADP
asir-2864	4	49	the	the	DET
asir-2864	4	50	square	square	NOUN
asir-2864	4	51	of	of	ADP
asir-2864	4	52	the	the	DET
asir-2864	4	53	distance	distance	NOUN
asir-2864	4	54	,	,	PUNCT
asir-2864	4	55	inversely	inversely	ADV
asir-2864	4	56	proportional	proportional	ADJ
asir-2864	4	57	to	to	ADP
asir-2864	4	58	the	the	DET
asir-2864	4	59	square	square	NOUN
asir-2864	4	60	of	of	ADP
asir-2864	4	61	the	the	DET
asir-2864	4	62	distance	distance	NOUN
asir-2864	4	63	for	for	ADP
asir-2864	4	64	both	both	CCONJ
asir-2864	4	65	the	the	DET
asir-2864	4	66	ellipse	ellipse	NOUN
asir-2864	4	67	and	and	CCONJ
asir-2864	4	68	the	the	DET
asir-2864	4	69	hyperbola	hyperbola	PROPN
asir-2864	4	70	.	.	PUNCT
asir-2864	5	1	this	this	DET
asir-2864	5	2	method	method	NOUN
asir-2864	5	3	when	when	SCONJ
asir-2864	5	4	applied	apply	VERB
asir-2864	5	5	to	to	ADP
asir-2864	5	6	the	the	DET
asir-2864	5	7	case	case	NOUN
asir-2864	5	8	of	of	ADP
asir-2864	5	9	circular	circular	ADJ
asir-2864	5	10	orbits	orbit	NOUN
asir-2864	5	11	for	for	ADP
asir-2864	5	12	which	which	PRON
asir-2864	5	13	we	we	PRON
asir-2864	5	14	can	can	AUX
asir-2864	5	15	find	find	VERB
asir-2864	5	16	the	the	DET
asir-2864	5	17	center	center	NOUN
asir-2864	5	18	of	of	ADP
asir-2864	5	19	force	force	NOUN
asir-2864	5	20	with	with	ADP
asir-2864	5	21	the	the	DET
asir-2864	5	22	same	same	ADJ
asir-2864	5	23	method	method	NOUN
asir-2864	5	24	:	:	PUNCT
asir-2864	5	25	newton	newton	PROPN
asir-2864	5	26	studied	study	VERB
asir-2864	5	27	a	a	DET
asir-2864	5	28	semicircular	semicircular	ADJ
asir-2864	5	29	orbit	orbit	NOUN
asir-2864	5	30	with	with	ADP
asir-2864	5	31	center	center	NOUN
asir-2864	5	32	of	of	ADP
asir-2864	5	33	force	force	NOUN
asir-2864	5	34	at	at	ADP
asir-2864	5	35	infinite	infinite	ADJ
asir-2864	5	36	distance	distance	NOUN
asir-2864	5	37	,	,	PUNCT
asir-2864	5	38	and	and	CCONJ
asir-2864	5	39	the	the	DET
asir-2864	5	40	case	case	NOUN
asir-2864	5	41	of	of	ADP
asir-2864	5	42	a	a	DET
asir-2864	5	43	central	central	ADJ
asir-2864	5	44	force	force	NOUN
asir-2864	5	45	whose	whose	DET
asir-2864	5	46	center	center	NOUN
asir-2864	5	47	is	be	AUX
asir-2864	5	48	located	locate	VERB
asir-2864	5	49	on	on	ADP
asir-2864	5	50	the	the	DET
asir-2864	5	51	circular	circular	ADJ
asir-2864	5	52	orbit	orbit	NOUN
asir-2864	5	53	or	or	CCONJ
asir-2864	5	54	inside	inside	ADP
asir-2864	5	55	the	the	DET
asir-2864	5	56	circle	circle	NOUN
asir-2864	5	57	studied	study	VERB
asir-2864	5	58	the	the	DET
asir-2864	5	59	case	case	NOUN
asir-2864	5	60	of	of	ADP
asir-2864	5	61	a	a	DET
asir-2864	5	62	spiral	spiral	ADJ
asir-2864	5	63	orbit	orbit	NOUN
asir-2864	5	64	.	.	PUNCT
asir-2864	6	1	in	in	ADP
asir-2864	6	2	each	each	DET
asir-2864	6	3	the	the	DET
asir-2864	6	4	law	law	NOUN
asir-2864	6	5	of	of	ADP
asir-2864	6	6	the	the	DET
asir-2864	6	7	force	force	NOUN
asir-2864	6	8	was	be	AUX
asir-2864	6	9	derived	derive	VERB
asir-2864	6	10	by	by	ADP
asir-2864	6	11	using	use	VERB
asir-2864	6	12	the	the	DET
asir-2864	6	13	law	law	NOUN
asir-2864	6	14	of	of	ADP
asir-2864	6	15	areas	area	NOUN
asir-2864	6	16	.	.	PUNCT
asir-2864	7	1	keywords	keyword	VERB
asir-2864	7	2	conservation	conservation	NOUN
asir-2864	7	3	of	of	ADP
asir-2864	7	4	angular	angular	ADJ
asir-2864	7	5	momentum	momentum	NOUN
asir-2864	7	6	,	,	PUNCT
asir-2864	7	7	law	law	NOUN
asir-2864	7	8	of	of	ADP
asir-2864	7	9	areas	area	NOUN
asir-2864	7	10	,	,	PUNCT
asir-2864	7	11	central	central	ADJ
asir-2864	7	12	forces	force	NOUN
asir-2864	7	13	,	,	PUNCT
asir-2864	7	14	law	law	NOUN
asir-2864	7	15	of	of	ADP
asir-2864	7	16	force	force	NOUN
asir-2864	7	17	1	1	NUM
asir-2864	7	18	.	.	PUNCT
asir-2864	8	1	introduction	introduction	NOUN
asir-2864	8	2	in	in	ADP
asir-2864	8	3	newton	newton	PROPN
asir-2864	8	4	’s	’s	PART
asir-2864	8	5	words	word	NOUN
asir-2864	8	6	:	:	PUNCT
asir-2864	8	7	there	there	PRON
asir-2864	8	8	being	be	AUX
asir-2864	8	9	given	give	VERB
asir-2864	8	10	,	,	PUNCT
asir-2864	8	11	in	in	ADP
asir-2864	8	12	any	any	DET
asir-2864	8	13	places	place	NOUN
asir-2864	8	14	,	,	PUNCT
asir-2864	8	15	the	the	DET
asir-2864	8	16	velocity	velocity	NOUN
asir-2864	8	17	with	with	ADP
asir-2864	8	18	which	which	PRON
asir-2864	8	19	a	a	DET
asir-2864	8	20	body	body	NOUN
asir-2864	8	21	describes	describe	VERB
asir-2864	8	22	a	a	DET
asir-2864	8	23	given	give	VERB
asir-2864	8	24	figure	figure	NOUN
asir-2864	8	25	,	,	PUNCT
asir-2864	8	26	by	by	ADP
asir-2864	8	27	means	mean	NOUN
asir-2864	8	28	of	of	ADP
asir-2864	8	29	forces	force	NOUN
asir-2864	8	30	directed	direct	VERB
asir-2864	8	31	to	to	ADP
asir-2864	8	32	some	some	DET
asir-2864	8	33	common	common	ADJ
asir-2864	8	34	center	center	NOUN
asir-2864	8	35	:	:	PUNCT
asir-2864	8	36	to	to	PART
asir-2864	8	37	find	find	VERB
asir-2864	8	38	that	that	DET
asir-2864	8	39	center	center	NOUN
asir-2864	8	40	(	(	PUNCT
asir-2864	8	41	newton	newton	PROPN
asir-2864	8	42	,	,	PUNCT
asir-2864	8	43	n.d	n.d	PROPN
asir-2864	8	44	.	.	PROPN
asir-2864	8	45	)	)	PUNCT
asir-2864	8	46	.	.	PUNCT
asir-2864	9	1	his	his	PRON
asir-2864	9	2	proof	proof	NOUN
asir-2864	9	3	is	be	AUX
asir-2864	9	4	simple	simple	ADJ
asir-2864	9	5	but	but	CCONJ
asir-2864	9	6	also	also	ADV
asir-2864	9	7	needs	need	VERB
asir-2864	9	8	some	some	DET
asir-2864	9	9	explanation	explanation	NOUN
asir-2864	9	10	:	:	PUNCT
asir-2864	9	11	newton	newton	PROPN
asir-2864	9	12	uses	use	VERB
asir-2864	9	13	the	the	DET
asir-2864	9	14	constancy	constancy	NOUN
asir-2864	9	15	of	of	ADP
asir-2864	9	16	angular	angular	ADJ
asir-2864	9	17	momentum	momentum	NOUN
asir-2864	9	18	which	which	PRON
asir-2864	9	19	he	he	PRON
asir-2864	9	20	explained	explain	VERB
asir-2864	9	21	in	in	ADP
asir-2864	9	22	by	by	ADP
asir-2864	9	23	proposition	proposition	NOUN
asir-2864	9	24	i	i	PRON
asir-2864	9	25	,	,	PUNCT
asir-2864	9	26	theorem	theorem	VERB
asir-2864	9	27	.	.	PUNCT
asir-2864	10	1	the	the	DET
asir-2864	10	2	areas	area	NOUN
asir-2864	10	3	,	,	PUNCT
asir-2864	10	4	which	which	DET
asir-2864	10	5	bodies	body	NOUN
asir-2864	10	6	made	make	VERB
asir-2864	10	7	to	to	PART
asir-2864	10	8	move	move	VERB
asir-2864	10	9	describe	describe	NOUN
asir-2864	10	10	by	by	ADP
asir-2864	10	11	radii	radius	NOUN
asir-2864	10	12	drawn	draw	VERB
asir-2864	10	13	to	to	ADP
asir-2864	10	14	an	an	DET
asir-2864	10	15	immovable	immovable	ADJ
asir-2864	10	16	center	center	NOUN
asir-2864	10	17	of	of	ADP
asir-2864	10	18	force	force	NOUN
asir-2864	10	19	lie	lie	VERB
asir-2864	10	20	unmoving	unmoving	ADJ
asir-2864	10	21	planes	plane	NOUN
asir-2864	10	22	,	,	PUNCT
asir-2864	10	23	and	and	CCONJ
asir-2864	10	24	are	be	AUX
asir-2864	10	25	proportional	proportional	ADJ
asir-2864	10	26	to	to	ADP
asir-2864	10	27	the	the	DET
asir-2864	10	28	times	time	NOUN
asir-2864	10	29	in	in	ADP
asir-2864	10	30	which	which	PRON
asir-2864	10	31	they	they	PRON
asir-2864	10	32	are	be	AUX
asir-2864	10	33	described	describe	VERB
asir-2864	10	34	(	(	PUNCT
asir-2864	10	35	newton	newton	PROPN
asir-2864	10	36	,	,	PUNCT
asir-2864	10	37	1999	1999	NUM
asir-2864	10	38	)	)	PUNCT
asir-2864	10	39	.	.	PUNCT
asir-2864	11	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-2864	11	2	applied	apply	VERB
asir-2864	11	3	science	science	NOUN
asir-2864	11	4	and	and	CCONJ
asir-2864	11	5	innovative	innovative	ADJ
asir-2864	11	6	research	research	NOUN
asir-2864	11	7	vol	vol	NOUN
asir-2864	11	8	.	.	PROPN
asir-2864	12	1	4	4	NUM
asir-2864	12	2	,	,	PUNCT
asir-2864	12	3	no	no	INTJ
asir-2864	12	4	.	.	NOUN
asir-2864	12	5	2	2	NUM
asir-2864	12	6	,	,	PUNCT
asir-2864	12	7	2020	2020	NUM
asir-2864	12	8	42	42	NUM
asir-2864	12	9	published	publish	VERB
asir-2864	12	10	by	by	ADP
asir-2864	12	11	scholink	scholink	PROPN
asir-2864	12	12	inc	inc	PROPN
asir-2864	12	13	.	.	PROPN
asir-2864	12	14	figure	figure	NOUN
asir-2864	12	15	1	1	NUM
asir-2864	12	16	.	.	PUNCT
asir-2864	13	1	law	law	NOUN
asir-2864	13	2	of	of	ADP
asir-2864	13	3	areas	area	NOUN
asir-2864	13	4	actually	actually	ADV
asir-2864	13	5	this	this	DET
asir-2864	13	6	proposition	proposition	NOUN
asir-2864	13	7	is	be	AUX
asir-2864	13	8	very	very	ADV
asir-2864	13	9	useful	useful	ADJ
asir-2864	13	10	for	for	ADP
asir-2864	13	11	teaching	teaching	NOUN
asir-2864	13	12	purposes	purpose	NOUN
asir-2864	13	13	.	.	PUNCT
asir-2864	14	1	the	the	DET
asir-2864	14	2	length	length	NOUN
asir-2864	14	3	of	of	ADP
asir-2864	14	4	the	the	DET
asir-2864	14	5	movement	movement	NOUN
asir-2864	14	6	in	in	ADP
asir-2864	14	7	the	the	DET
asir-2864	14	8	unit	unit	NOUN
asir-2864	14	9	of	of	ADP
asir-2864	14	10	time	time	NOUN
asir-2864	14	11	is	be	AUX
asir-2864	14	12	equal	equal	ADJ
asir-2864	14	13	to	to	ADP
asir-2864	14	14	the	the	DET
asir-2864	14	15	velocity	velocity	NOUN
asir-2864	14	16	.	.	PUNCT
asir-2864	15	1	if	if	SCONJ
asir-2864	15	2	from	from	ADP
asir-2864	15	3	the	the	DET
asir-2864	15	4	center	center	NOUN
asir-2864	16	1	k	k	NOUN
asir-2864	16	2	we	we	PRON
asir-2864	16	3	draw	draw	VERB
asir-2864	16	4	the	the	DET
asir-2864	16	5	radii	radius	NOUN
asir-2864	16	6	ka	ka	PROPN
asir-2864	16	7	,	,	PUNCT
asir-2864	16	8	kb	kb	PROPN
asir-2864	16	9	,	,	PUNCT
asir-2864	16	10	kc	kc	PROPN
asir-2864	16	11	,	,	PUNCT
asir-2864	16	12	then	then	ADV
asir-2864	16	13	the	the	DET
asir-2864	16	14	areas	area	NOUN
asir-2864	16	15	kab	kab	PROPN
asir-2864	16	16	,	,	PUNCT
asir-2864	16	17	kbc	kbc	PROPN
asir-2864	16	18	,	,	PUNCT
asir-2864	16	19	are	be	AUX
asir-2864	16	20	equal	equal	ADJ
asir-2864	16	21	,	,	PUNCT
asir-2864	16	22	since	since	SCONJ
asir-2864	16	23	the	the	DET
asir-2864	16	24	triangles	triangle	NOUN
asir-2864	16	25	kab	kab	PROPN
asir-2864	16	26	,	,	PUNCT
asir-2864	16	27	kmn	kmn	PROPN
asir-2864	16	28	have	have	VERB
asir-2864	16	29	equal	equal	ADJ
asir-2864	16	30	bases	basis	NOUN
asir-2864	16	31	and	and	CCONJ
asir-2864	16	32	equal	equal	ADJ
asir-2864	16	33	heights	height	NOUN
asir-2864	16	34	,	,	PUNCT
asir-2864	16	35	but	but	CCONJ
asir-2864	16	36	also	also	ADV
asir-2864	16	37	the	the	DET
asir-2864	16	38	triangles	triangle	NOUN
asir-2864	16	39	kbc	kbc	PROPN
asir-2864	16	40	and	and	CCONJ
asir-2864	16	41	kbm	kbm	PROPN
asir-2864	16	42	have	have	VERB
asir-2864	16	43	the	the	DET
asir-2864	16	44	same	same	ADJ
asir-2864	16	45	base	base	NOUN
asir-2864	16	46	(	(	PUNCT
asir-2864	16	47	kb	kb	PROPN
asir-2864	16	48	)	)	PUNCT
asir-2864	16	49	and	and	CCONJ
asir-2864	16	50	heights	height	VERB
asir-2864	16	51	dc	dc	NOUN
asir-2864	16	52	=	=	NOUN
asir-2864	16	53	nm	nm	NOUN
asir-2864	16	54	as	as	SCONJ
asir-2864	16	55	we	we	PRON
asir-2864	16	56	can	can	AUX
asir-2864	16	57	see	see	VERB
asir-2864	16	58	in	in	ADP
asir-2864	16	59	figure	figure	NOUN
asir-2864	16	60	1	1	NUM
asir-2864	16	61	,	,	PUNCT
asir-2864	16	62	the	the	DET
asir-2864	16	63	constancy	constancy	NOUN
asir-2864	16	64	of	of	ADP
asir-2864	16	65	the	the	DET
asir-2864	16	66	areas	area	NOUN
asir-2864	16	67	is	be	AUX
asir-2864	16	68	valid	valid	ADJ
asir-2864	16	69	for	for	ADP
asir-2864	16	70	central	central	ADJ
asir-2864	16	71	force	force	NOUN
asir-2864	16	72	which	which	PRON
asir-2864	16	73	for	for	ADP
asir-2864	16	74	newton	newton	PROPN
asir-2864	16	75	’s	’s	PART
asir-2864	16	76	model	model	NOUN
asir-2864	16	77	is	be	AUX
asir-2864	16	78	given	give	VERB
asir-2864	16	79	by	by	ADP
asir-2864	16	80	impulses	impulse	NOUN
asir-2864	16	81	along	along	ADP
asir-2864	16	82	the	the	DET
asir-2864	16	83	lines	line	NOUN
asir-2864	16	84	which	which	PRON
asir-2864	16	85	join	join	VERB
asir-2864	16	86	the	the	DET
asir-2864	16	87	end	end	NOUN
asir-2864	16	88	of	of	ADP
asir-2864	16	89	the	the	DET
asir-2864	16	90	velocity	velocity	NOUN
asir-2864	16	91	vector	vector	NOUN
asir-2864	16	92	to	to	ADP
asir-2864	16	93	the	the	DET
asir-2864	16	94	center	center	NOUN
asir-2864	16	95	of	of	ADP
asir-2864	16	96	force	force	NOUN
asir-2864	16	97	.	.	PUNCT
asir-2864	17	1	as	as	SCONJ
asir-2864	17	2	is	be	AUX
asir-2864	17	3	seen	see	VERB
asir-2864	17	4	in	in	ADP
asir-2864	17	5	the	the	DET
asir-2864	17	6	figure	figure	NOUN
asir-2864	17	7	1	1	NUM
asir-2864	17	8	the	the	DET
asir-2864	17	9	law	law	NOUN
asir-2864	17	10	is	be	AUX
asir-2864	17	11	valid	valid	ADJ
asir-2864	17	12	in	in	ADP
asir-2864	17	13	the	the	DET
asir-2864	17	14	case	case	NOUN
asir-2864	17	15	of	of	ADP
asir-2864	17	16	a	a	DET
asir-2864	17	17	central	central	ADJ
asir-2864	17	18	force	force	NOUN
asir-2864	17	19	.	.	PUNCT
asir-2864	18	1	2	2	X
asir-2864	18	2	.	.	X
asir-2864	18	3	proposition	proposition	NOUN
asir-2864	18	4	v	v	ADP
asir-2864	18	5	,	,	PUNCT
asir-2864	18	6	problem	problem	NOUN
asir-2864	18	7	i	i	PRON
asir-2864	18	8	for	for	ADP
asir-2864	18	9	ellipse	ellipse	NOUN
asir-2864	18	10	in	in	ADP
asir-2864	18	11	the	the	DET
asir-2864	18	12	case	case	NOUN
asir-2864	18	13	of	of	ADP
asir-2864	18	14	the	the	DET
asir-2864	18	15	ellipse	ellipse	NOUN
asir-2864	18	16	we	we	PRON
asir-2864	18	17	consider	consider	VERB
asir-2864	18	18	as	as	ADP
asir-2864	18	19	newton	newton	PROPN
asir-2864	18	20	(	(	PUNCT
asir-2864	18	21	1981	1981	NUM
asir-2864	18	22	)	)	PUNCT
asir-2864	18	23	points	point	VERB
asir-2864	18	24	p	p	X
asir-2864	18	25	,	,	PUNCT
asir-2864	18	26	q	q	ADJ
asir-2864	18	27	,	,	PUNCT
asir-2864	18	28	r	r	NOUN
asir-2864	18	29	where	where	SCONJ
asir-2864	18	30	we	we	PRON
asir-2864	18	31	draw	draw	VERB
asir-2864	18	32	the	the	DET
asir-2864	18	33	velocity	velocity	NOUN
asir-2864	18	34	vectors	vector	NOUN
asir-2864	18	35	vp	vp	PROPN
asir-2864	18	36	,	,	PUNCT
asir-2864	18	37	vq	vq	PROPN
asir-2864	18	38	,	,	PUNCT
asir-2864	18	39	vr	vr	PROPN
asir-2864	18	40	.	.	PROPN
asir-2864	18	41	one	one	NUM
asir-2864	18	42	question	question	NOUN
asir-2864	18	43	that	that	PRON
asir-2864	18	44	can	can	AUX
asir-2864	18	45	be	be	AUX
asir-2864	18	46	asked	ask	VERB
asir-2864	18	47	is	be	AUX
asir-2864	18	48	what	what	PRON
asir-2864	18	49	kind	kind	NOUN
asir-2864	18	50	of	of	ADP
asir-2864	18	51	force	force	NOUN
asir-2864	18	52	caused	cause	VERB
asir-2864	18	53	this	this	DET
asir-2864	18	54	movement	movement	NOUN
asir-2864	18	55	(	(	PUNCT
asir-2864	18	56	figure	figure	NOUN
asir-2864	18	57	2	2	NUM
asir-2864	18	58	)	)	PUNCT
asir-2864	18	59	?	?	PUNCT
asir-2864	19	1	the	the	DET
asir-2864	19	2	students	student	NOUN
asir-2864	19	3	can	can	AUX
asir-2864	19	4	check	check	VERB
asir-2864	19	5	the	the	DET
asir-2864	19	6	figure	figure	NOUN
asir-2864	19	7	and	and	CCONJ
asir-2864	19	8	guess	guess	VERB
asir-2864	19	9	the	the	DET
asir-2864	19	10	force	force	NOUN
asir-2864	19	11	.	.	PUNCT
asir-2864	20	1	they	they	PRON
asir-2864	20	2	can	can	AUX
asir-2864	20	3	think	think	VERB
asir-2864	20	4	from	from	ADP
asir-2864	20	5	the	the	DET
asir-2864	20	6	size	size	NOUN
asir-2864	20	7	of	of	ADP
asir-2864	20	8	the	the	DET
asir-2864	20	9	3	3	NUM
asir-2864	20	10	velocities	velocity	NOUN
asir-2864	20	11	.	.	PUNCT
asir-2864	21	1	the	the	DET
asir-2864	21	2	teacher	teacher	NOUN
asir-2864	21	3	can	can	AUX
asir-2864	21	4	move	move	VERB
asir-2864	21	5	a	a	DET
asir-2864	21	6	little	little	ADJ
asir-2864	21	7	bit	bit	NOUN
asir-2864	21	8	the	the	DET
asir-2864	21	9	points	point	NOUN
asir-2864	21	10	and	and	CCONJ
asir-2864	21	11	the	the	DET
asir-2864	21	12	students	student	NOUN
asir-2864	21	13	can	can	AUX
asir-2864	21	14	try	try	VERB
asir-2864	21	15	to	to	PART
asir-2864	21	16	think	think	VERB
asir-2864	21	17	of	of	ADP
asir-2864	21	18	where	where	SCONJ
asir-2864	21	19	is	be	AUX
asir-2864	21	20	the	the	DET
asir-2864	21	21	center	center	NOUN
asir-2864	21	22	of	of	ADP
asir-2864	21	23	force	force	NOUN
asir-2864	21	24	.	.	PUNCT
asir-2864	22	1	this	this	DET
asir-2864	22	2	problem	problem	NOUN
asir-2864	22	3	was	be	AUX
asir-2864	22	4	used	use	VERB
asir-2864	22	5	in	in	ADP
asir-2864	22	6	attempts	attempt	NOUN
asir-2864	22	7	to	to	PART
asir-2864	22	8	teach	teach	VERB
asir-2864	22	9	principia	principia	PROPN
asir-2864	22	10	(	(	PUNCT
asir-2864	22	11	alfred	alfred	PROPN
asir-2864	22	12	,	,	PUNCT
asir-2864	22	13	1964	1964	NUM
asir-2864	22	14	)	)	PUNCT
asir-2864	22	15	.	.	PUNCT
asir-2864	23	1	figure	figure	NOUN
asir-2864	23	2	2	2	NUM
asir-2864	23	3	.	.	PUNCT
asir-2864	23	4	where	where	SCONJ
asir-2864	23	5	is	be	AUX
asir-2864	23	6	the	the	DET
asir-2864	23	7	center	center	NOUN
asir-2864	23	8	of	of	ADP
asir-2864	23	9	force	force	NOUN
asir-2864	23	10	that	that	PRON
asir-2864	23	11	produces	produce	VERB
asir-2864	23	12	the	the	DET
asir-2864	23	13	velocities	velocity	NOUN
asir-2864	23	14	?	?	PUNCT
asir-2864	24	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2864	24	2	applied	apply	VERB
asir-2864	24	3	science	science	NOUN
asir-2864	24	4	and	and	CCONJ
asir-2864	24	5	innovative	innovative	ADJ
asir-2864	24	6	research	research	NOUN
asir-2864	24	7	vol	vol	NOUN
asir-2864	24	8	.	.	PROPN
asir-2864	25	1	4	4	NUM
asir-2864	25	2	,	,	PUNCT
asir-2864	25	3	no	no	INTJ
asir-2864	25	4	.	.	NOUN
asir-2864	25	5	2	2	NUM
asir-2864	25	6	,	,	PUNCT
asir-2864	25	7	2020	2020	NUM
asir-2864	25	8	43	43	NUM
asir-2864	25	9	published	publish	VERB
asir-2864	25	10	by	by	ADP
asir-2864	25	11	scholink	scholink	PROPN
asir-2864	25	12	inc	inc	PROPN
asir-2864	25	13	.	.	PUNCT
asir-2864	26	1	it	it	PRON
asir-2864	26	2	is	be	AUX
asir-2864	26	3	known	know	VERB
asir-2864	26	4	from	from	ADP
asir-2864	26	5	history	history	NOUN
asir-2864	26	6	that	that	PRON
asir-2864	26	7	newton	newton	PROPN
asir-2864	26	8	was	be	AUX
asir-2864	26	9	asked	ask	VERB
asir-2864	26	10	by	by	ADP
asir-2864	26	11	halley	halley	PROPN
asir-2864	26	12	,	,	PUNCT
asir-2864	26	13	what	what	PRON
asir-2864	26	14	he	he	PRON
asir-2864	26	15	thought	think	VERB
asir-2864	26	16	the	the	DET
asir-2864	26	17	curve	curve	NOUN
asir-2864	26	18	would	would	AUX
asir-2864	26	19	be	be	AUX
asir-2864	26	20	that	that	PRON
asir-2864	26	21	would	would	AUX
asir-2864	26	22	be	be	AUX
asir-2864	26	23	described	describe	VERB
asir-2864	26	24	by	by	ADP
asir-2864	26	25	the	the	DET
asir-2864	26	26	planets	planet	NOUN
asir-2864	26	27	supposing	suppose	VERB
asir-2864	26	28	the	the	DET
asir-2864	26	29	force	force	NOUN
asir-2864	26	30	of	of	ADP
asir-2864	26	31	attraction	attraction	NOUN
asir-2864	26	32	towards	towards	ADP
asir-2864	26	33	the	the	DET
asir-2864	26	34	sun	sun	NOUN
asir-2864	26	35	to	to	PART
asir-2864	26	36	be	be	AUX
asir-2864	26	37	reciprocal	reciprocal	ADJ
asir-2864	26	38	to	to	ADP
asir-2864	26	39	the	the	DET
asir-2864	26	40	square	square	NOUN
asir-2864	26	41	of	of	ADP
asir-2864	26	42	their	their	PRON
asir-2864	26	43	distance	distance	NOUN
asir-2864	26	44	from	from	ADP
asir-2864	26	45	it	it	PRON
asir-2864	26	46	(	(	PUNCT
asir-2864	26	47	newton	newton	PROPN
asir-2864	26	48	and	and	CCONJ
asir-2864	26	49	kepler	kepler	PROPN
asir-2864	26	50	ex	ex	PROPN
asir-2864	26	51	libris	libris	PROPN
asir-2864	26	52	,	,	PUNCT
asir-2864	26	53	n.d	n.d	PROPN
asir-2864	26	54	.	.	PROPN
asir-2864	26	55	)	)	PUNCT
asir-2864	26	56	.	.	PUNCT
asir-2864	27	1	newton	newton	PROPN
asir-2864	27	2	answered	answer	VERB
asir-2864	27	3	that	that	SCONJ
asir-2864	27	4	this	this	DET
asir-2864	27	5	curve	curve	NOUN
asir-2864	27	6	is	be	AUX
asir-2864	27	7	an	an	DET
asir-2864	27	8	ellipse	ellipse	NOUN
asir-2864	27	9	.	.	PUNCT
asir-2864	28	1	in	in	ADP
asir-2864	28	2	the	the	DET
asir-2864	28	3	present	present	ADJ
asir-2864	28	4	problem	problem	NOUN
asir-2864	28	5	we	we	PRON
asir-2864	28	6	have	have	VERB
asir-2864	28	7	an	an	DET
asir-2864	28	8	ellipse	ellipse	NOUN
asir-2864	28	9	but	but	CCONJ
asir-2864	28	10	the	the	DET
asir-2864	28	11	answer	answer	NOUN
asir-2864	28	12	is	be	AUX
asir-2864	28	13	not	not	PART
asir-2864	28	14	always	always	ADV
asir-2864	28	15	a	a	DET
asir-2864	28	16	force	force	NOUN
asir-2864	28	17	reciprocal	reciprocal	ADJ
asir-2864	28	18	to	to	ADP
asir-2864	28	19	the	the	DET
asir-2864	28	20	square	square	NOUN
asir-2864	28	21	.	.	PUNCT
asir-2864	29	1	newton	newton	PROPN
asir-2864	29	2	gave	give	VERB
asir-2864	29	3	in	in	ADP
asir-2864	29	4	principia	principia	PROPN
asir-2864	29	5	the	the	DET
asir-2864	29	6	proposition	proposition	NOUN
asir-2864	29	7	which	which	PRON
asir-2864	29	8	can	can	AUX
asir-2864	29	9	be	be	AUX
asir-2864	29	10	answered	answer	VERB
asir-2864	29	11	by	by	ADP
asir-2864	29	12	either	either	CCONJ
asir-2864	29	13	gravitational	gravitational	ADJ
asir-2864	29	14	forces	force	NOUN
asir-2864	29	15	directed	direct	VERB
asir-2864	29	16	towards	towards	ADP
asir-2864	29	17	either	either	DET
asir-2864	29	18	one	one	NUM
asir-2864	29	19	of	of	ADP
asir-2864	29	20	the	the	DET
asir-2864	29	21	foci	focus	NOUN
asir-2864	29	22	or	or	CCONJ
asir-2864	29	23	by	by	ADP
asir-2864	29	24	a	a	DET
asir-2864	29	25	force	force	NOUN
asir-2864	29	26	proportional	proportional	NOUN
asir-2864	29	27	to	to	ADP
asir-2864	29	28	the	the	DET
asir-2864	29	29	distance	distance	NOUN
asir-2864	29	30	from	from	ADP
asir-2864	29	31	the	the	DET
asir-2864	29	32	center	center	NOUN
asir-2864	29	33	and	and	CCONJ
asir-2864	29	34	directed	direct	VERB
asir-2864	29	35	to	to	ADP
asir-2864	29	36	it	it	PRON
asir-2864	29	37	(	(	PUNCT
asir-2864	29	38	which	which	PRON
asir-2864	29	39	was	be	AUX
asir-2864	29	40	proposed	propose	VERB
asir-2864	29	41	by	by	ADP
asir-2864	29	42	hooke	hooke	PROPN
asir-2864	29	43	(	(	PUNCT
asir-2864	29	44	michael	michael	PROPN
asir-2864	29	45	,	,	PUNCT
asir-2864	29	46	1994	1994	NUM
asir-2864	29	47	)	)	PUNCT
asir-2864	29	48	)	)	PUNCT
asir-2864	29	49	.	.	PUNCT
asir-2864	30	1	the	the	DET
asir-2864	30	2	motion	motion	NOUN
asir-2864	30	3	around	around	ADP
asir-2864	30	4	the	the	DET
asir-2864	30	5	center	center	NOUN
asir-2864	30	6	will	will	AUX
asir-2864	30	7	have	have	VERB
asir-2864	30	8	a	a	DET
asir-2864	30	9	constant	constant	ADJ
asir-2864	30	10	angular	angular	ADJ
asir-2864	30	11	momentum	momentum	NOUN
asir-2864	30	12	,	,	PUNCT
asir-2864	30	13	or	or	CCONJ
asir-2864	30	14	the	the	DET
asir-2864	30	15	areas	area	NOUN
asir-2864	30	16	described	describe	VERB
asir-2864	30	17	by	by	ADP
asir-2864	30	18	the	the	DET
asir-2864	30	19	radius	radius	NOUN
asir-2864	30	20	drawn	draw	VERB
asir-2864	30	21	from	from	ADP
asir-2864	30	22	the	the	DET
asir-2864	30	23	center	center	NOUN
asir-2864	30	24	of	of	ADP
asir-2864	30	25	the	the	DET
asir-2864	30	26	force	force	NOUN
asir-2864	30	27	to	to	ADP
asir-2864	30	28	the	the	DET
asir-2864	30	29	particle	particle	NOUN
asir-2864	30	30	will	will	AUX
asir-2864	30	31	be	be	AUX
asir-2864	30	32	equal	equal	ADJ
asir-2864	30	33	in	in	ADP
asir-2864	30	34	equal	equal	ADJ
asir-2864	30	35	times	time	NOUN
asir-2864	30	36	.	.	PUNCT
asir-2864	31	1	to	to	PART
asir-2864	31	2	find	find	VERB
asir-2864	31	3	the	the	DET
asir-2864	31	4	center	center	NOUN
asir-2864	31	5	we	we	PRON
asir-2864	31	6	precede	precede	VERB
asir-2864	31	7	either	either	CCONJ
asir-2864	31	8	by	by	ADP
asir-2864	31	9	calculating	calculate	VERB
asir-2864	31	10	with	with	ADP
asir-2864	31	11	the	the	DET
asir-2864	31	12	use	use	NOUN
asir-2864	31	13	of	of	ADP
asir-2864	31	14	analytic	analytic	ADJ
asir-2864	31	15	geometry	geometry	NOUN
asir-2864	31	16	or	or	CCONJ
asir-2864	31	17	with	with	ADP
asir-2864	31	18	newton	newton	PROPN
asir-2864	31	19	’s	’s	PART
asir-2864	31	20	method	method	NOUN
asir-2864	31	21	(	(	PUNCT
asir-2864	31	22	the	the	DET
asir-2864	31	23	equations	equation	NOUN
asir-2864	31	24	from	from	ADP
asir-2864	31	25	which	which	PRON
asir-2864	31	26	we	we	PRON
asir-2864	31	27	derive	derive	VERB
asir-2864	31	28	the	the	DET
asir-2864	31	29	center	center	NOUN
asir-2864	31	30	of	of	ADP
asir-2864	31	31	force	force	NOUN
asir-2864	31	32	,	,	PUNCT
asir-2864	31	33	are	be	AUX
asir-2864	31	34	presented	present	VERB
asir-2864	31	35	in	in	ADP
asir-2864	31	36	the	the	DET
asir-2864	31	37	end	end	NOUN
asir-2864	31	38	of	of	ADP
asir-2864	31	39	the	the	DET
asir-2864	31	40	paper	paper	NOUN
asir-2864	31	41	)	)	PUNCT
asir-2864	31	42	.	.	PUNCT
asir-2864	32	1	we	we	PRON
asir-2864	32	2	draw	draw	VERB
asir-2864	32	3	the	the	DET
asir-2864	32	4	three	three	NUM
asir-2864	32	5	lines	line	NOUN
asir-2864	32	6	pt	pt	PROPN
asir-2864	32	7	,	,	PUNCT
asir-2864	32	8	tqz	tqz	PROPN
asir-2864	32	9	,	,	PUNCT
asir-2864	32	10	zr	zr	PRON
asir-2864	32	11	which	which	PRON
asir-2864	32	12	touch	touch	VERB
asir-2864	32	13	the	the	DET
asir-2864	32	14	curve	curve	NOUN
asir-2864	32	15	at	at	ADP
asir-2864	32	16	the	the	DET
asir-2864	32	17	points	point	NOUN
asir-2864	32	18	,	,	PUNCT
asir-2864	32	19	p	p	X
asir-2864	32	20	,	,	PUNCT
asir-2864	32	21	q	q	ADJ
asir-2864	32	22	,	,	PUNCT
asir-2864	32	23	r	r	NOUN
asir-2864	32	24	,	,	PUNCT
asir-2864	32	25	and	and	CCONJ
asir-2864	32	26	meet	meet	VERB
asir-2864	32	27	in	in	ADP
asir-2864	32	28	t	t	PROPN
asir-2864	32	29	and	and	CCONJ
asir-2864	32	30	z	z	PROPN
asir-2864	32	31	(	(	PUNCT
asir-2864	32	32	see	see	VERB
asir-2864	32	33	figure	figure	NOUN
asir-2864	32	34	3	3	NUM
asir-2864	32	35	)	)	PUNCT
asir-2864	32	36	on	on	ADP
asir-2864	32	37	the	the	DET
asir-2864	32	38	tangents	tangent	NOUN
asir-2864	32	39	erect	erect	VERB
asir-2864	32	40	the	the	DET
asir-2864	32	41	perpendiculars	perpendiculars	PROPN
asir-2864	32	42	pa	pa	PROPN
asir-2864	32	43	,	,	PUNCT
asir-2864	32	44	qb	qb	PROPN
asir-2864	32	45	,	,	PUNCT
asir-2864	32	46	rc	rc	PROPN
asir-2864	32	47	,	,	PUNCT
asir-2864	32	48	reciprocally	reciprocally	ADV
asir-2864	32	49	proportional	proportional	ADJ
asir-2864	32	50	to	to	ADP
asir-2864	32	51	the	the	DET
asir-2864	32	52	velocities	velocity	NOUN
asir-2864	32	53	of	of	ADP
asir-2864	32	54	the	the	DET
asir-2864	32	55	body	body	NOUN
asir-2864	32	56	in	in	ADP
asir-2864	32	57	the	the	DET
asir-2864	32	58	points	point	NOUN
asir-2864	32	59	p	p	X
asir-2864	32	60	,	,	PUNCT
asir-2864	32	61	q	q	ADJ
asir-2864	32	62	,	,	PUNCT
asir-2864	32	63	r	r	NOUN
asir-2864	32	64	,	,	PUNCT
asir-2864	32	65	from	from	ADP
asir-2864	32	66	which	which	PRON
asir-2864	32	67	the	the	DET
asir-2864	32	68	perpendiculars	perpendicular	NOUN
asir-2864	32	69	were	be	AUX
asir-2864	32	70	raised	raise	VERB
asir-2864	32	71	.	.	PUNCT
asir-2864	33	1	so	so	ADV
asir-2864	33	2	𝐴	𝐴	PROPN
asir-2864	33	3	=	=	PROPN
asir-2864	33	4	𝑘	𝑘	DET
asir-2864	33	5	𝑉𝑃	𝑉𝑃	PROPN
asir-2864	33	6	,	,	PUNCT
asir-2864	33	7	𝑄𝐵	𝑄𝐵	PROPN
asir-2864	33	8	=	=	PROPN
asir-2864	33	9	𝑘	𝑘	PROPN
asir-2864	33	10	𝑉𝑄	𝑉𝑄	NOUN
asir-2864	33	11	,	,	PUNCT
asir-2864	33	12	𝑅𝐶	𝑅𝐶	PROPN
asir-2864	33	13	=	=	SYM
asir-2864	33	14	𝑘	𝑘	DET
asir-2864	33	15	𝑉𝑅	𝑉𝑅	PROPN
asir-2864	33	16	.	.	PUNCT
asir-2864	34	1	from	from	ADP
asir-2864	34	2	a	a	DET
asir-2864	34	3	,	,	PUNCT
asir-2864	34	4	b	b	NOUN
asir-2864	34	5	,	,	PUNCT
asir-2864	34	6	we	we	PRON
asir-2864	34	7	draw	draw	VERB
asir-2864	34	8	perpendiculars	perpendicular	NOUN
asir-2864	34	9	to	to	ADP
asir-2864	34	10	pa	pa	PROPN
asir-2864	34	11	and	and	CCONJ
asir-2864	34	12	qb	qb	PROPN
asir-2864	34	13	correspondingly	correspondingly	ADV
asir-2864	34	14	.	.	PUNCT
asir-2864	35	1	these	these	DET
asir-2864	35	2	perpendiculars	perpendiculars	PROPN
asir-2864	35	3	meet	meet	VERB
asir-2864	35	4	at	at	ADP
asir-2864	35	5	d.	d.	PROPN
asir-2864	35	6	we	we	PRON
asir-2864	35	7	draw	draw	VERB
asir-2864	35	8	from	from	ADP
asir-2864	35	9	c	c	PROPN
asir-2864	35	10	a	a	DET
asir-2864	35	11	perpendicular	perpendicular	NOUN
asir-2864	35	12	to	to	ADP
asir-2864	35	13	rc	rc	PROPN
asir-2864	35	14	which	which	PRON
asir-2864	35	15	meets	meet	VERB
asir-2864	35	16	bd	bd	PROPN
asir-2864	35	17	at	at	ADP
asir-2864	35	18	e.	e.	PROPN
asir-2864	35	19	we	we	PRON
asir-2864	35	20	draw	draw	VERB
asir-2864	35	21	from	from	ADP
asir-2864	35	22	d	d	PROPN
asir-2864	35	23	the	the	DET
asir-2864	35	24	perpendicular	perpendicular	ADJ
asir-2864	35	25	dp	dp	NOUN
asir-2864	35	26	”	"	PUNCT
asir-2864	35	27	to	to	ADP
asir-2864	35	28	vp	vp	PROPN
asir-2864	35	29	,	,	PUNCT
asir-2864	35	30	from	from	ADP
asir-2864	35	31	d	d	PROPN
asir-2864	35	32	the	the	DET
asir-2864	35	33	perpendicular	perpendicular	ADJ
asir-2864	35	34	dt	dt	NOUN
asir-2864	35	35	”	"	PUNCT
asir-2864	35	36	to	to	ADP
asir-2864	35	37	vq	vq	NOUN
asir-2864	35	38	,	,	PUNCT
asir-2864	35	39	and	and	CCONJ
asir-2864	35	40	form	form	NOUN
asir-2864	35	41	e	e	NOUN
asir-2864	35	42	the	the	DET
asir-2864	35	43	perpendicular	perpendicular	ADJ
asir-2864	35	44	er	er	INTJ
asir-2864	35	45	”	"	PUNCT
asir-2864	35	46	to	to	ADP
asir-2864	35	47	vr	vr	PROPN
asir-2864	35	48	.	.	PUNCT
asir-2864	36	1	so	so	ADV
asir-2864	36	2	we	we	PRON
asir-2864	36	3	have	have	VERB
asir-2864	36	4	v	v	NUM
asir-2864	36	5	p	p	NOUN
asir-2864	36	6	·	·	PUNCT
asir-2864	37	1	p	p	X
asir-2864	37	2	a	a	PRON
asir-2864	37	3	=	=	SYM
asir-2864	37	4	v	v	PROPN
asir-2864	37	5	p	p	X
asir-2864	37	6	·	·	PUNCT
asir-2864	37	7	dp	dp	NOUN
asir-2864	37	8	”	"	PUNCT
asir-2864	37	9	=	=	NOUN
asir-2864	37	10	v	v	NOUN
asir-2864	37	11	q	q	NOUN
asir-2864	37	12	·	·	PUNCT
asir-2864	37	13	bq	bq	NOUN
asir-2864	37	14	=	=	SYM
asir-2864	37	15	v	v	PROPN
asir-2864	37	16	q	q	NOUN
asir-2864	37	17	·	·	PUNCT
asir-2864	37	18	dt	dt	NOUN
asir-2864	37	19	”	"	PUNCT
asir-2864	37	20	so	so	ADV
asir-2864	37	21	for	for	ADP
asir-2864	37	22	point	point	NOUN
asir-2864	37	23	d	d	X
asir-2864	37	24	we	we	PRON
asir-2864	37	25	have	have	VERB
asir-2864	37	26	dp	dp	NOUN
asir-2864	37	27	”	"	PUNCT
asir-2864	37	28	·	·	PUNCT
asir-2864	37	29	v	v	ADP
asir-2864	37	30	p	p	X
asir-2864	37	31	=	=	PUNCT
asir-2864	37	32	dt	dt	PROPN
asir-2864	37	33	”	"	PUNCT
asir-2864	37	34	·	·	PROPN
asir-2864	37	35	v	v	NOUN
asir-2864	37	36	q.	q.	NOUN
asir-2864	37	37	also	also	ADV
asir-2864	37	38	for	for	ADP
asir-2864	37	39	point	point	NOUN
asir-2864	37	40	e	e	X
asir-2864	37	41	we	we	PRON
asir-2864	37	42	have	have	VERB
asir-2864	37	43	v	v	NUM
asir-2864	37	44	q	q	X
asir-2864	37	45	·	·	PUNCT
asir-2864	37	46	ez	ez	PROPN
asir-2864	37	47	”	"	PUNCT
asir-2864	37	48	=	=	SYM
asir-2864	37	49	v	v	ADP
asir-2864	37	50	r	r	NOUN
asir-2864	37	51	·	·	PUNCT
asir-2864	37	52	er	er	INTJ
asir-2864	37	53	”	"	PUNCT
asir-2864	37	54	.	.	PUNCT
asir-2864	38	1	these	these	DET
asir-2864	38	2	relations	relation	NOUN
asir-2864	38	3	resemble	resemble	VERB
asir-2864	38	4	the	the	DET
asir-2864	38	5	law	law	NOUN
asir-2864	38	6	of	of	ADP
asir-2864	38	7	areas	area	NOUN
asir-2864	38	8	but	but	CCONJ
asir-2864	38	9	actually	actually	ADV
asir-2864	38	10	they	they	PRON
asir-2864	38	11	are	be	AUX
asir-2864	38	12	valid	valid	ADJ
asir-2864	38	13	only	only	ADV
asir-2864	38	14	on	on	ADP
asir-2864	38	15	pairs	pair	NOUN
asir-2864	38	16	of	of	ADP
asir-2864	38	17	velocities	velocity	NOUN
asir-2864	38	18	.	.	PUNCT
asir-2864	39	1	we	we	PRON
asir-2864	39	2	can	can	AUX
asir-2864	39	3	repeat	repeat	VERB
asir-2864	39	4	the	the	DET
asir-2864	39	5	procedure	procedure	NOUN
asir-2864	39	6	for	for	ADP
asir-2864	39	7	different	different	ADJ
asir-2864	39	8	values	value	NOUN
asir-2864	39	9	of	of	ADP
asir-2864	39	10	k.	k.	PROPN
asir-2864	39	11	for	for	ADP
asir-2864	39	12	k	k	PROPN
asir-2864	39	13	→	→	SYM
asir-2864	39	14	0	0	X
asir-2864	39	15	the	the	DET
asir-2864	39	16	limiting	limit	VERB
asir-2864	39	17	lines	line	NOUN
asir-2864	39	18	are	be	AUX
asir-2864	39	19	the	the	DET
asir-2864	39	20	tangents	tangent	NOUN
asir-2864	39	21	at	at	ADP
asir-2864	39	22	p	p	X
asir-2864	39	23	,	,	PUNCT
asir-2864	39	24	q	q	ADJ
asir-2864	39	25	,	,	PUNCT
asir-2864	39	26	r	r	NOUN
asir-2864	39	27	which	which	PRON
asir-2864	39	28	meet	meet	VERB
asir-2864	39	29	correspondingly	correspondingly	ADV
asir-2864	39	30	at	at	ADP
asir-2864	39	31	t	t	PROPN
asir-2864	39	32	and	and	CCONJ
asir-2864	39	33	z.	z.	PROPN
asir-2864	39	34	if	if	SCONJ
asir-2864	39	35	we	we	PRON
asir-2864	39	36	increase	increase	VERB
asir-2864	39	37	the	the	DET
asir-2864	39	38	value	value	NOUN
asir-2864	39	39	of	of	ADP
asir-2864	39	40	k	k	PROPN
asir-2864	39	41	we	we	PRON
asir-2864	39	42	get	get	VERB
asir-2864	39	43	a	a	DET
asir-2864	39	44	smaller	small	ADJ
asir-2864	39	45	distance	distance	NOUN
asir-2864	39	46	of	of	ADP
asir-2864	39	47	de	de	X
asir-2864	40	1	and	and	CCONJ
asir-2864	40	2	we	we	PRON
asir-2864	40	3	can	can	AUX
asir-2864	40	4	reach	reach	VERB
asir-2864	40	5	the	the	DET
asir-2864	40	6	point	point	NOUN
asir-2864	40	7	where	where	SCONJ
asir-2864	40	8	the	the	DET
asir-2864	40	9	two	two	NUM
asir-2864	40	10	lines	line	NOUN
asir-2864	40	11	ze	ze	NOUN
asir-2864	40	12	and	and	CCONJ
asir-2864	40	13	td	td	PROPN
asir-2864	40	14	meet	meet	VERB
asir-2864	40	15	.	.	PUNCT
asir-2864	41	1	at	at	ADP
asir-2864	41	2	this	this	DET
asir-2864	41	3	point	point	NOUN
asir-2864	41	4	s	s	VERB
asir-2864	41	5	we	we	PRON
asir-2864	41	6	have	have	VERB
asir-2864	41	7	sr	sr	NOUN
asir-2864	41	8	’	'	PUNCT
asir-2864	41	9	·	·	PUNCT
asir-2864	41	10	v	v	X
asir-2864	41	11	r	r	NOUN
asir-2864	41	12	=	=	SYM
asir-2864	41	13	st	st	PROPN
asir-2864	41	14	’	'	PUNCT
asir-2864	41	15	·	·	PUNCT
asir-2864	41	16	v	v	X
asir-2864	41	17	q	q	NOUN
asir-2864	41	18	=	=	PUNCT
asir-2864	41	19	sp	sp	NOUN
asir-2864	41	20	’	'	PUNCT
asir-2864	41	21	·	·	PUNCT
asir-2864	42	1	v	v	X
asir-2864	42	2	p.	p.	NOUN
asir-2864	43	1	so	so	ADV
asir-2864	43	2	we	we	PRON
asir-2864	43	3	find	find	VERB
asir-2864	43	4	the	the	DET
asir-2864	43	5	point	point	NOUN
asir-2864	43	6	s	s	X
asir-2864	43	7	which	which	PRON
asir-2864	43	8	is	be	AUX
asir-2864	43	9	the	the	DET
asir-2864	43	10	center	center	NOUN
asir-2864	43	11	of	of	ADP
asir-2864	43	12	force	force	NOUN
asir-2864	43	13	.	.	PUNCT
asir-2864	44	1	so	so	ADV
asir-2864	44	2	pa	pa	PROPN
asir-2864	44	3	/	/	SYM
asir-2864	44	4	qb	qb	PROPN
asir-2864	44	5	=	=	PROPN
asir-2864	44	6	v	v	PROPN
asir-2864	44	7	q	q	NOUN
asir-2864	44	8	/	/	SYM
asir-2864	44	9	v	v	NOUN
asir-2864	44	10	p	p	X
asir-2864	44	11	,	,	PUNCT
asir-2864	44	12	and	and	CCONJ
asir-2864	44	13	qb	qb	PROPN
asir-2864	44	14	/	/	SYM
asir-2864	44	15	rc	rc	PROPN
asir-2864	44	16	=	=	PROPN
asir-2864	44	17	vr	vr	PROPN
asir-2864	44	18	/	/	SYM
asir-2864	44	19	vq	vq	PROPN
asir-2864	44	20	.	.	PROPN
asir-2864	44	21	figure	figure	NOUN
asir-2864	44	22	3	3	NUM
asir-2864	44	23	.	.	PUNCT
asir-2864	44	24	newton	newton	PROPN
asir-2864	44	25	’s	’s	PART
asir-2864	44	26	method	method	NOUN
asir-2864	44	27	for	for	ADP
asir-2864	44	28	finding	find	VERB
asir-2864	44	29	the	the	DET
asir-2864	44	30	center	center	NOUN
asir-2864	44	31	of	of	ADP
asir-2864	44	32	force	force	NOUN
asir-2864	44	33	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2864	44	34	applied	apply	VERB
asir-2864	44	35	science	science	NOUN
asir-2864	44	36	and	and	CCONJ
asir-2864	44	37	innovative	innovative	ADJ
asir-2864	44	38	research	research	NOUN
asir-2864	44	39	vol	vol	NOUN
asir-2864	44	40	.	.	PROPN
asir-2864	45	1	4	4	NUM
asir-2864	45	2	,	,	PUNCT
asir-2864	45	3	no	no	INTJ
asir-2864	45	4	.	.	NOUN
asir-2864	45	5	2	2	NUM
asir-2864	45	6	,	,	PUNCT
asir-2864	45	7	2020	2020	NUM
asir-2864	45	8	44	44	NUM
asir-2864	45	9	published	publish	VERB
asir-2864	45	10	by	by	ADP
asir-2864	45	11	scholink	scholink	PROPN
asir-2864	45	12	inc	inc	PROPN
asir-2864	45	13	.	.	PROPN
asir-2864	45	14	2.1	2.1	NUM
asir-2864	45	15	newton	newton	PROPN
asir-2864	45	16	’s	’s	PART
asir-2864	45	17	proof	proof	NOUN
asir-2864	45	18	as	as	SCONJ
asir-2864	45	19	explained	explain	VERB
asir-2864	45	20	by	by	ADP
asir-2864	45	21	chandraseckar	chandraseckar	ADJ
asir-2864	45	22	chandraseckar	chandraseckar	NOUN
asir-2864	45	23	(	(	PUNCT
asir-2864	45	24	1995	1995	NUM
asir-2864	45	25	)	)	PUNCT
asir-2864	46	1	gave	give	VERB
asir-2864	46	2	a	a	DET
asir-2864	46	3	proof	proof	NOUN
asir-2864	46	4	based	base	VERB
asir-2864	46	5	on	on	ADP
asir-2864	46	6	principia	principia	PROPN
asir-2864	46	7	easier	easier	ADV
asir-2864	46	8	to	to	PART
asir-2864	46	9	understand	understand	VERB
asir-2864	46	10	.	.	PUNCT
asir-2864	47	1	for	for	ADP
asir-2864	47	2	the	the	DET
asir-2864	47	3	points	point	NOUN
asir-2864	47	4	a	a	DET
asir-2864	47	5	,	,	PUNCT
asir-2864	47	6	b	b	NOUN
asir-2864	47	7	,	,	PUNCT
asir-2864	47	8	c	c	VERB
asir-2864	47	9	we	we	PRON
asir-2864	47	10	note	note	VERB
asir-2864	47	11	that	that	SCONJ
asir-2864	47	12	p	p	PROPN
asir-2864	47	13	a	a	X
asir-2864	47	14	:	:	PUNCT
asir-2864	47	15	qb	qb	PROPN
asir-2864	47	16	:	:	PUNCT
asir-2864	47	17	rc	rc	PROPN
asir-2864	47	18	=	=	PROPN
asir-2864	47	19	v	v	PROPN
asir-2864	47	20	p(−1	p(−1	NOUN
asir-2864	47	21	)	)	PUNCT
asir-2864	47	22	:	:	PUNCT
asir-2864	47	23	v	v	ADP
asir-2864	47	24	q(−1	q(−1	PROPN
asir-2864	47	25	)	)	PUNCT
asir-2864	47	26	:	:	PUNCT
asir-2864	47	27	v	v	X
asir-2864	47	28	e(−1	e(−1	NOUN
asir-2864	47	29	)	)	PUNCT
asir-2864	47	30	if	if	SCONJ
asir-2864	47	31	s	s	NOUN
asir-2864	47	32	should	should	AUX
asir-2864	47	33	be	be	AUX
asir-2864	47	34	the	the	DET
asir-2864	47	35	(	(	PUNCT
asir-2864	47	36	yet	yet	ADV
asir-2864	47	37	unspecified	unspecified	ADJ
asir-2864	47	38	)	)	PUNCT
asir-2864	47	39	center	center	NOUN
asir-2864	47	40	of	of	ADP
asir-2864	47	41	attraction	attraction	NOUN
asir-2864	47	42	,	,	PUNCT
asir-2864	47	43	drop	drop	VERB
asir-2864	47	44	the	the	DET
asir-2864	47	45	perpendiculars	perpendiculars	PROPN
asir-2864	47	46	sp	sp	NOUN
asir-2864	47	47	’	'	PUNCT
asir-2864	47	48	and	and	CCONJ
asir-2864	47	49	st	st	PROPN
asir-2864	47	50	’	'	PUNCT
asir-2864	47	51	to	to	ADP
asir-2864	47	52	the	the	DET
asir-2864	47	53	tangents	tangent	NOUN
asir-2864	47	54	at	at	ADP
asir-2864	47	55	p	p	NOUN
asir-2864	47	56	and	and	CCONJ
asir-2864	47	57	q.	q.	NOUN
asir-2864	47	58	and	and	CCONJ
asir-2864	47	59	draw	draw	VERB
asir-2864	47	60	(	(	PUNCT
asir-2864	47	61	as	as	ADP
asir-2864	47	62	illustrated	illustrate	VERB
asir-2864	47	63	)	)	PUNCT
asir-2864	47	64	ce	ce	PROPN
asir-2864	47	65	,	,	PUNCT
asir-2864	47	66	ebd	ebd	PROPN
asir-2864	47	67	,	,	PUNCT
asir-2864	47	68	and	and	CCONJ
asir-2864	47	69	da	da	NOUN
asir-2864	47	70	parallels	parallel	VERB
asir-2864	47	71	to	to	ADP
asir-2864	47	72	the	the	DET
asir-2864	47	73	tangents	tangent	NOUN
asir-2864	47	74	at	at	ADP
asir-2864	47	75	r	r	NOUN
asir-2864	47	76	,	,	PUNCT
asir-2864	47	77	q	q	NOUN
asir-2864	47	78	,	,	PUNCT
asir-2864	47	79	and	and	CCONJ
asir-2864	47	80	p	p	NOUN
asir-2864	47	81	and	and	CCONJ
asir-2864	47	82	intersecting	intersect	VERB
asir-2864	47	83	at	at	ADP
asir-2864	47	84	the	the	DET
asir-2864	47	85	points	point	NOUN
asir-2864	47	86	e	e	NOUN
asir-2864	47	87	and	and	CCONJ
asir-2864	47	88	d.	d.	PROPN
asir-2864	47	89	now	now	ADV
asir-2864	47	90	drop	drop	VERB
asir-2864	47	91	the	the	DET
asir-2864	47	92	perpendiculars	perpendicular	NOUN
asir-2864	47	93	dp	dp	PROPN
asir-2864	47	94	”	"	PUNCT
asir-2864	47	95	and	and	CCONJ
asir-2864	47	96	dt	dt	X
asir-2864	47	97	”	"	PUNCT
asir-2864	47	98	to	to	ADP
asir-2864	47	99	the	the	DET
asir-2864	47	100	tangents	tangent	NOUN
asir-2864	47	101	at	at	ADP
asir-2864	47	102	p	p	NOUN
asir-2864	47	103	and	and	CCONJ
asir-2864	47	104	q.	q.	NOUN
asir-2864	47	105	then	then	ADV
asir-2864	47	106	by	by	ADP
asir-2864	47	107	the	the	DET
asir-2864	47	108	𝑆𝑃	𝑆𝑃	PROPN
asir-2864	47	109	’	'	PUNCT
asir-2864	47	110	𝑆𝑇	𝑆𝑇	PROPN
asir-2864	47	111	’	'	PUNCT
asir-2864	47	112	=	=	SYM
asir-2864	47	113	𝑉𝑄	𝑉𝑄	NOUN
asir-2864	47	114	𝑉𝑃	𝑉𝑃	NOUN
asir-2864	47	115	=	=	SYM
asir-2864	47	116	𝐴𝑃	𝐴𝑃	PROPN
asir-2864	47	117	𝐵𝑄	𝐵𝑄	PROPN
asir-2864	47	118	=	=	SYM
asir-2864	47	119	𝐷𝑃	𝐷𝑃	PROPN
asir-2864	47	120	’’	’'	PUNCT
asir-2864	47	121	𝐷𝑇	𝐷𝑇	PROPN
asir-2864	47	122	’’	’'	PUNCT
asir-2864	47	123	or	or	CCONJ
asir-2864	47	124	𝑆𝑃	𝑆𝑃	PROPN
asir-2864	47	125	’	'	PUNCT
asir-2864	47	126	𝐷𝑃	𝐷𝑃	PROPN
asir-2864	47	127	’’	’'	PUNCT
asir-2864	47	128	=	=	SYM
asir-2864	47	129	𝑆𝑇	𝑆𝑇	PROPN
asir-2864	47	130	’	'	PUNCT
asir-2864	47	131	𝐷𝑇	𝐷𝑇	NOUN
asir-2864	47	132	’’	’'	PUNCT
asir-2864	47	133	so	so	ADV
asir-2864	47	134	s	s	PROPN
asir-2864	47	135	,	,	PUNCT
asir-2864	47	136	d	d	NOUN
asir-2864	47	137	,	,	PUNCT
asir-2864	47	138	and	and	CCONJ
asir-2864	47	139	t	t	PROPN
asir-2864	47	140	lie	lie	VERB
asir-2864	47	141	on	on	ADP
asir-2864	47	142	the	the	DET
asir-2864	47	143	same	same	ADJ
asir-2864	47	144	line	line	NOUN
asir-2864	47	145	.	.	PUNCT
asir-2864	48	1	2.2	2.2	NUM
asir-2864	48	2	finding	find	VERB
asir-2864	48	3	the	the	DET
asir-2864	48	4	law	law	NOUN
asir-2864	48	5	of	of	ADP
asir-2864	48	6	the	the	DET
asir-2864	48	7	force	force	PROPN
asir-2864	48	8	newton	newton	PROPN
asir-2864	48	9	in	in	ADP
asir-2864	48	10	principia	principia	PROPN
asir-2864	48	11	gives	give	VERB
asir-2864	48	12	us	we	PRON
asir-2864	48	13	a	a	DET
asir-2864	48	14	mathematical	mathematical	ADJ
asir-2864	48	15	method	method	NOUN
asir-2864	48	16	of	of	ADP
asir-2864	48	17	finding	find	VERB
asir-2864	48	18	the	the	DET
asir-2864	48	19	center	center	NOUN
asir-2864	48	20	of	of	ADP
asir-2864	48	21	force	force	NOUN
asir-2864	48	22	for	for	ADP
asir-2864	48	23	a	a	DET
asir-2864	48	24	body	body	NOUN
asir-2864	48	25	moving	move	VERB
asir-2864	48	26	on	on	ADP
asir-2864	48	27	an	an	DET
asir-2864	48	28	ellipse	ellipse	NOUN
asir-2864	48	29	in	in	ADP
asir-2864	48	30	proposition	proposition	NOUN
asir-2864	48	31	v	v	ADP
asir-2864	48	32	,	,	PUNCT
asir-2864	48	33	problem	problem	NOUN
asir-2864	48	34	i.	i.	PROPN
asir-2864	48	35	the	the	DET
asir-2864	48	36	same	same	ADJ
asir-2864	48	37	thinking	thinking	NOUN
asir-2864	48	38	can	can	AUX
asir-2864	48	39	be	be	AUX
asir-2864	48	40	applied	apply	VERB
asir-2864	48	41	also	also	ADV
asir-2864	48	42	to	to	ADP
asir-2864	48	43	the	the	DET
asir-2864	48	44	case	case	NOUN
asir-2864	48	45	of	of	ADP
asir-2864	48	46	a	a	DET
asir-2864	48	47	hyperbola	hyperbola	PROPN
asir-2864	48	48	and	and	CCONJ
asir-2864	48	49	also	also	ADV
asir-2864	48	50	a	a	DET
asir-2864	48	51	parabola	parabola	NOUN
asir-2864	48	52	,	,	PUNCT
asir-2864	48	53	only	only	ADV
asir-2864	48	54	that	that	SCONJ
asir-2864	48	55	in	in	ADP
asir-2864	48	56	the	the	DET
asir-2864	48	57	last	last	ADJ
asir-2864	48	58	case	case	NOUN
asir-2864	48	59	the	the	DET
asir-2864	48	60	center	center	NOUN
asir-2864	48	61	of	of	ADP
asir-2864	48	62	force	force	NOUN
asir-2864	48	63	is	be	AUX
asir-2864	48	64	at	at	ADP
asir-2864	48	65	infinite	infinite	ADJ
asir-2864	48	66	distance	distance	NOUN
asir-2864	48	67	.	.	PUNCT
asir-2864	49	1	the	the	DET
asir-2864	49	2	forces	force	NOUN
asir-2864	49	3	that	that	PRON
asir-2864	49	4	studied	study	VERB
asir-2864	49	5	newton	newton	PROPN
asir-2864	49	6	in	in	ADP
asir-2864	49	7	the	the	DET
asir-2864	49	8	next	next	ADJ
asir-2864	49	9	pages	page	NOUN
asir-2864	49	10	of	of	ADP
asir-2864	49	11	principia	principia	PROPN
asir-2864	49	12	,	,	PUNCT
asir-2864	49	13	for	for	ADP
asir-2864	49	14	elliptical	elliptical	ADJ
asir-2864	49	15	motion	motion	NOUN
asir-2864	49	16	could	could	AUX
asir-2864	49	17	be	be	AUX
asir-2864	49	18	:	:	PUNCT
asir-2864	49	19	a	a	X
asir-2864	49	20	)	)	PUNCT
asir-2864	49	21	an	an	DET
asir-2864	49	22	elastic	elastic	ADJ
asir-2864	49	23	force	force	NOUN
asir-2864	49	24	with	with	ADP
asir-2864	49	25	center	center	NOUN
asir-2864	49	26	at	at	ADP
asir-2864	49	27	the	the	DET
asir-2864	49	28	origin	origin	NOUN
asir-2864	49	29	,	,	PUNCT
asir-2864	49	30	b	b	X
asir-2864	49	31	)	)	PUNCT
asir-2864	49	32	a	a	DET
asir-2864	49	33	gravitational	gravitational	ADJ
asir-2864	49	34	force	force	NOUN
asir-2864	49	35	with	with	ADP
asir-2864	49	36	center	center	NOUN
asir-2864	49	37	at	at	ADP
asir-2864	49	38	the	the	DET
asir-2864	49	39	left	left	ADJ
asir-2864	49	40	focus	focus	NOUN
asir-2864	49	41	or	or	CCONJ
asir-2864	49	42	c	c	X
asir-2864	49	43	)	)	PUNCT
asir-2864	49	44	a	a	DET
asir-2864	49	45	gravitational	gravitational	ADJ
asir-2864	49	46	force	force	NOUN
asir-2864	49	47	with	with	ADP
asir-2864	49	48	center	center	NOUN
asir-2864	49	49	at	at	ADP
asir-2864	49	50	the	the	DET
asir-2864	49	51	right	right	ADJ
asir-2864	49	52	focus	focus	NOUN
asir-2864	49	53	.	.	PUNCT
asir-2864	50	1	in	in	ADP
asir-2864	50	2	this	this	DET
asir-2864	50	3	article	article	NOUN
asir-2864	50	4	newton	newton	PROPN
asir-2864	50	5	’s	’s	PART
asir-2864	50	6	methods	method	NOUN
asir-2864	50	7	were	be	AUX
asir-2864	50	8	extended	extend	VERB
asir-2864	50	9	to	to	ADP
asir-2864	50	10	the	the	DET
asir-2864	50	11	case	case	NOUN
asir-2864	50	12	of	of	ADP
asir-2864	50	13	hyperbola	hyperbola	PROPN
asir-2864	50	14	,	,	PUNCT
asir-2864	50	15	where	where	SCONJ
asir-2864	50	16	the	the	DET
asir-2864	50	17	forces	force	NOUN
asir-2864	50	18	could	could	AUX
asir-2864	50	19	be	be	AUX
asir-2864	50	20	a	a	PRON
asir-2864	50	21	)	)	PUNCT
asir-2864	50	22	an	an	DET
asir-2864	50	23	attractive	attractive	ADJ
asir-2864	50	24	gravitational	gravitational	ADJ
asir-2864	50	25	force	force	NOUN
asir-2864	50	26	with	with	ADP
asir-2864	50	27	center	center	NOUN
asir-2864	50	28	one	one	NUM
asir-2864	50	29	pole	pole	NOUN
asir-2864	50	30	of	of	ADP
asir-2864	50	31	the	the	DET
asir-2864	50	32	hyperbola	hyperbola	PROPN
asir-2864	50	33	,	,	PUNCT
asir-2864	50	34	b	b	X
asir-2864	50	35	)	)	PUNCT
asir-2864	50	36	a	a	DET
asir-2864	50	37	repulsive	repulsive	ADJ
asir-2864	50	38	force	force	NOUN
asir-2864	50	39	with	with	ADP
asir-2864	50	40	center	center	NOUN
asir-2864	50	41	the	the	DET
asir-2864	50	42	other	other	ADJ
asir-2864	50	43	pole	pole	NOUN
asir-2864	50	44	of	of	ADP
asir-2864	50	45	the	the	DET
asir-2864	50	46	hyperbola	hyperbola	PROPN
asir-2864	50	47	,	,	PUNCT
asir-2864	50	48	c	c	X
asir-2864	50	49	)	)	PUNCT
asir-2864	50	50	an	an	DET
asir-2864	50	51	elastic	elastic	ADJ
asir-2864	50	52	force	force	NOUN
asir-2864	50	53	with	with	ADP
asir-2864	50	54	center	center	NOUN
asir-2864	50	55	at	at	ADP
asir-2864	50	56	the	the	DET
asir-2864	50	57	origin	origin	NOUN
asir-2864	50	58	.	.	PUNCT
asir-2864	51	1	it	it	PRON
asir-2864	51	2	is	be	AUX
asir-2864	51	3	possible	possible	ADJ
asir-2864	51	4	to	to	PART
asir-2864	51	5	prove	prove	VERB
asir-2864	51	6	using	use	VERB
asir-2864	51	7	the	the	DET
asir-2864	51	8	conservation	conservation	NOUN
asir-2864	51	9	of	of	ADP
asir-2864	51	10	the	the	DET
asir-2864	51	11	angular	angular	ADJ
asir-2864	51	12	momentum	momentum	NOUN
asir-2864	51	13	to	to	PART
asir-2864	51	14	prove	prove	VERB
asir-2864	51	15	that	that	SCONJ
asir-2864	51	16	the	the	DET
asir-2864	51	17	force	force	NOUN
asir-2864	51	18	is	be	AUX
asir-2864	51	19	proportional	proportional	ADJ
asir-2864	51	20	the	the	DET
asir-2864	51	21	inverse	inverse	NOUN
asir-2864	51	22	of	of	ADP
asir-2864	51	23	the	the	DET
asir-2864	51	24	square	square	NOUN
asir-2864	51	25	of	of	ADP
asir-2864	51	26	distance	distance	NOUN
asir-2864	51	27	r	r	NOUN
asir-2864	51	28	from	from	ADP
asir-2864	51	29	the	the	DET
asir-2864	51	30	focus	focus	NOUN
asir-2864	51	31	.	.	PUNCT
asir-2864	52	1	to	to	PART
asir-2864	52	2	find	find	VERB
asir-2864	52	3	the	the	DET
asir-2864	52	4	law	law	NOUN
asir-2864	52	5	of	of	ADP
asir-2864	52	6	force	force	NOUN
asir-2864	52	7	we	we	PRON
asir-2864	52	8	use	use	VERB
asir-2864	52	9	the	the	DET
asir-2864	52	10	law	law	NOUN
asir-2864	52	11	of	of	ADP
asir-2864	52	12	areas	area	NOUN
asir-2864	52	13	in	in	ADP
asir-2864	52	14	the	the	DET
asir-2864	52	15	form	form	NOUN
asir-2864	52	16	𝑟	𝑟	X
asir-2864	52	17	·	·	PUNCT
asir-2864	52	18	𝑐𝑜𝑠𝜔	𝑐𝑜𝑠𝜔	X
asir-2864	52	19	·	·	PUNCT
asir-2864	52	20	𝑉	𝑉	NOUN
asir-2864	52	21	=	=	NOUN
asir-2864	52	22	ℎ	ℎ	NOUN
asir-2864	52	23	where	where	SCONJ
asir-2864	52	24	ω	ω	PROPN
asir-2864	52	25	is	be	AUX
asir-2864	52	26	the	the	DET
asir-2864	52	27	angle	angle	NOUN
asir-2864	52	28	between	between	ADP
asir-2864	52	29	the	the	DET
asir-2864	52	30	line	line	NOUN
asir-2864	52	31	r	r	NOUN
asir-2864	52	32	=	=	SYM
asir-2864	52	33	sm	sm	X
asir-2864	52	34	(	(	PUNCT
asir-2864	52	35	see	see	VERB
asir-2864	52	36	figure	figure	NOUN
asir-2864	52	37	3	3	NUM
asir-2864	52	38	)	)	PUNCT
asir-2864	52	39	and	and	CCONJ
asir-2864	52	40	the	the	DET
asir-2864	52	41	perpendicular	perpendicular	NOUN
asir-2864	52	42	on	on	ADP
asir-2864	52	43	the	the	DET
asir-2864	52	44	ellipse	ellipse	NOUN
asir-2864	52	45	.	.	PUNCT
asir-2864	53	1	to	to	PART
asir-2864	53	2	find	find	VERB
asir-2864	53	3	the	the	DET
asir-2864	53	4	cosω	cosω	NOUN
asir-2864	53	5	we	we	PRON
asir-2864	53	6	use	use	VERB
asir-2864	53	7	the	the	DET
asir-2864	53	8	parametric	parametric	ADJ
asir-2864	53	9	equations	equation	NOUN
asir-2864	53	10	of	of	ADP
asir-2864	53	11	the	the	DET
asir-2864	53	12	ellipse	ellipse	NOUN
asir-2864	53	13	with	with	ADP
asir-2864	53	14	semi	semi	NOUN
asir-2864	53	15	-	-	NOUN
asir-2864	53	16	axes	axis	NOUN
asir-2864	53	17	a	a	PRON
asir-2864	53	18	and	and	CCONJ
asir-2864	53	19	b	b	NOUN
asir-2864	53	20	as	as	ADP
asir-2864	53	21	x	x	X
asir-2864	53	22	=	=	SYM
asir-2864	53	23	a	a	DET
asir-2864	53	24	·	·	PUNCT
asir-2864	53	25	cosφ	cosφ	NOUN
asir-2864	53	26	,	,	PUNCT
asir-2864	53	27	y	y	PROPN
asir-2864	53	28	=	=	SYM
asir-2864	53	29	b	b	PROPN
asir-2864	53	30	·	·	PUNCT
asir-2864	53	31	sinφ	sinφ	NOUN
asir-2864	53	32	so	so	SCONJ
asir-2864	53	33	𝑑𝑦	𝑑𝑦	NOUN
asir-2864	53	34	𝑑𝑥	𝑑𝑥	NOUN
asir-2864	53	35	=	=	SYM
asir-2864	53	36	−	−	PROPN
asir-2864	53	37	𝑎·𝑠𝑖𝑛𝜑	𝑎·𝑠𝑖𝑛𝜑	X
asir-2864	53	38	𝑏·𝑐𝑜𝑠𝜑	𝑏·𝑐𝑜𝑠𝜑	ADV
asir-2864	53	39	,	,	PUNCT
asir-2864	53	40	with	with	ADP
asir-2864	53	41	unit	unit	NOUN
asir-2864	53	42	vector	vector	NOUN
asir-2864	53	43	𝑒	𝑒	PROPN
asir-2864	53	44	=	=	PRON
asir-2864	53	45	𝑎·𝑐𝑜𝑠𝜑+𝑐	𝑎·𝑐𝑜𝑠𝜑+𝑐	VERB
asir-2864	53	46	𝑟	𝑟	NOUN
asir-2864	53	47	,	,	PUNCT
asir-2864	53	48	𝑏·𝑠𝑖𝑛𝜑	𝑏·𝑠𝑖𝑛𝜑	ADP
asir-2864	53	49	𝑟	𝑟	NOUN
asir-2864	53	50	for	for	ADP
asir-2864	53	51	perpendicular	perpendicular	ADJ
asir-2864	53	52	�	�	NOUN
asir-2864	53	53	⃗⃗	⃗⃗	NOUN
asir-2864	53	54	�	�	PROPN
asir-2864	53	55	=	=	SYM
asir-2864	53	56	𝑏·𝑐𝑜𝑠𝜑	𝑏·𝑐𝑜𝑠𝜑	PROPN
asir-2864	53	57	√	√	PROPN
asir-2864	53	58	𝛼2·𝑠𝑖𝑛2𝜑+𝑏2·𝑐𝑜𝑠2𝜑	𝛼2·𝑠𝑖𝑛2𝜑+𝑏2·𝑐𝑜𝑠2𝜑	PROPN
asir-2864	53	59	,	,	PUNCT
asir-2864	54	1	𝑎·𝑠𝑖𝑛𝜑	𝑎·𝑠𝑖𝑛𝜑	X
asir-2864	55	1	√𝑎2·𝑠𝑖𝑛2𝜑+𝑏2·𝑐𝑜𝑠2𝜑	√𝑎2·𝑠𝑖𝑛2𝜑+𝑏2·𝑐𝑜𝑠2𝜑	PROPN
asir-2864	55	2	the	the	DET
asir-2864	55	3	force	force	NOUN
asir-2864	55	4	that	that	PRON
asir-2864	55	5	acts	act	VERB
asir-2864	55	6	as	as	ADP
asir-2864	55	7	centripetal	centripetal	NOUN
asir-2864	55	8	:	:	PUNCT
asir-2864	56	1	𝐹𝑘	𝐹𝑘	PROPN
asir-2864	56	2	=	=	SYM
asir-2864	56	3	𝐹	𝐹	PROPN
asir-2864	56	4	·	·	PUNCT
asir-2864	56	5	𝑐𝑜𝑠𝜔	𝑐𝑜𝑠𝜔	VERB
asir-2864	56	6	=	=	SYM
asir-2864	56	7	𝑚	𝑚	X
asir-2864	56	8	·	·	PUNCT
asir-2864	56	9	𝑉2	𝑉2	NOUN
asir-2864	56	10	𝜌	𝜌	X
asir-2864	56	11	=	=	SYM
asir-2864	56	12	𝑚·ℎ2	𝑚·ℎ2	X
asir-2864	56	13	(	(	PUNCT
asir-2864	56	14	𝑟·𝑐𝑜𝑠𝜔)2·𝜌	𝑟·𝑐𝑜𝑠𝜔)2·𝜌	NOUN
asir-2864	56	15	where	where	SCONJ
asir-2864	56	16	ρ	ρ	PROPN
asir-2864	56	17	is	be	AUX
asir-2864	56	18	the	the	DET
asir-2864	56	19	radius	radius	NOUN
asir-2864	56	20	of	of	ADP
asir-2864	56	21	curvature	curvature	NOUN
asir-2864	56	22	𝜌	𝜌	ADP
asir-2864	56	23	=	=	SYM
asir-2864	57	1	√(𝑎2·𝑠𝑖𝑛2𝜑+𝑏2·𝑐𝑜𝑠2𝜑)3	√(𝑎2·𝑠𝑖𝑛2𝜑+𝑏2·𝑐𝑜𝑠2𝜑)3	PROPN
asir-2864	57	2	𝑎·𝑏	𝑎·𝑏	NOUN
asir-2864	58	1	so	so	ADV
asir-2864	58	2	𝐹	𝐹	PROPN
asir-2864	58	3	=	=	SYM
asir-2864	58	4	𝑚·ℎ2	𝑚·ℎ2	ADJ
asir-2864	58	5	𝑟2·𝑐𝑜𝑠3𝜔·𝜌	𝑟2·𝑐𝑜𝑠3𝜔·𝜌	X
asir-2864	58	6	.	.	PUNCT
asir-2864	59	1	physical	physical	ADJ
asir-2864	59	2	entity	entity	NOUN
asir-2864	59	3	center	center	NOUN
asir-2864	59	4	at	at	ADP
asir-2864	59	5	left	left	ADJ
asir-2864	59	6	focus	focus	NOUN
asir-2864	59	7	center	center	NOUN
asir-2864	59	8	at	at	ADP
asir-2864	59	9	the	the	DET
asir-2864	59	10	center	center	NOUN
asir-2864	59	11	of	of	ADP
asir-2864	59	12	ellipse	ellipse	NOUN
asir-2864	59	13	center	center	NOUN
asir-2864	59	14	at	at	ADP
asir-2864	59	15	the	the	DET
asir-2864	59	16	right	right	ADJ
asir-2864	59	17	focus	focus	NOUN
asir-2864	59	18	r	r	NOUN
asir-2864	59	19	𝑎	𝑎	PROPN
asir-2864	59	20	+	+	X
asir-2864	59	21	𝑐	𝑐	NOUN
asir-2864	59	22	·	·	PUNCT
asir-2864	59	23	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	59	24	√	√	ADV
asir-2864	59	25	𝛼2	𝛼2	PROPN
asir-2864	59	26	·	·	PUNCT
asir-2864	59	27	𝑠𝑖𝑛2𝜑	𝑠𝑖𝑛2𝜑	PROPN
asir-2864	60	1	+	+	CCONJ
asir-2864	60	2	𝑏2	𝑏2	PROPN
asir-2864	60	3	·	·	PUNCT
asir-2864	60	4	𝑐𝑜𝑠2𝜑	𝑐𝑜𝑠2𝜑	PUNCT
asir-2864	61	1	𝑎	𝑎	X
asir-2864	61	2	−	−	PROPN
asir-2864	61	3	𝑐	𝑐	PROPN
asir-2864	61	4	·	·	PUNCT
asir-2864	61	5	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	61	6	cosω	cosω	NOUN
asir-2864	61	7	𝑏	𝑏	PROPN
asir-2864	61	8	·	·	PUNCT
asir-2864	61	9	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	61	10	√	√	ADV
asir-2864	61	11	𝛼2	𝛼2	PROPN
asir-2864	61	12	·	·	PUNCT
asir-2864	61	13	𝑠𝑖𝑛2𝜑	𝑠𝑖𝑛2𝜑	PROPN
asir-2864	62	1	+	+	CCONJ
asir-2864	62	2	𝑏2	𝑏2	PROPN
asir-2864	62	3	·	·	PUNCT
asir-2864	62	4	𝑐𝑜𝑠2𝜑	𝑐𝑜𝑠2𝜑	PUNCT
asir-2864	63	1	𝑎	𝑎	X
asir-2864	63	2	+	+	X
asir-2864	63	3	𝑏	𝑏	NOUN
asir-2864	63	4	·	·	PUNCT
asir-2864	63	5	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	63	6	𝑟√	𝑟√	PROPN
asir-2864	63	7	𝛼2	𝛼2	PROPN
asir-2864	63	8	·	·	PUNCT
asir-2864	63	9	𝑠𝑖𝑛2𝜑	𝑠𝑖𝑛2𝜑	PROPN
asir-2864	64	1	+	+	CCONJ
asir-2864	64	2	𝑏2	𝑏2	PROPN
asir-2864	64	3	·	·	PUNCT
asir-2864	64	4	𝑐𝑜𝑠2𝜑	𝑐𝑜𝑠2𝜑	PUNCT
asir-2864	65	1	𝑏	𝑏	X
asir-2864	65	2	·	·	PUNCT
asir-2864	65	3	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	65	4	√	√	ADV
asir-2864	65	5	𝛼2	𝛼2	PROPN
asir-2864	65	6	·	·	PUNCT
asir-2864	65	7	𝑠𝑖𝑛2𝜑	𝑠𝑖𝑛2𝜑	PROPN
asir-2864	66	1	+	+	CCONJ
asir-2864	66	2	𝑏2	𝑏2	PROPN
asir-2864	66	3	·	·	PUNCT
asir-2864	66	4	𝑐𝑜𝑠2𝜑	𝑐𝑜𝑠2𝜑	PUNCT
asir-2864	67	1	f	f	X
asir-2864	67	2	𝑚	𝑚	X
asir-2864	67	3	·	·	PUNCT
asir-2864	67	4	𝑎	𝑎	PRON
asir-2864	67	5	∙	∙	PROPN
asir-2864	67	6	ℎ2	ℎ2	ADJ
asir-2864	67	7	𝑟2	𝑟2	NOUN
asir-2864	67	8	·	·	PUNCT
asir-2864	67	9	𝑏2	𝑏2	PROPN
asir-2864	67	10	𝑚	𝑚	NOUN
asir-2864	67	11	·	·	PUNCT
asir-2864	67	12	ℎ2	ℎ2	ADJ
asir-2864	67	13	∙	∙	PROPN
asir-2864	67	14	𝑎	𝑎	X
asir-2864	67	15	∙	∙	PROPN
asir-2864	67	16	𝑏	𝑏	ADP
asir-2864	67	17	∙	∙	PROPN
asir-2864	67	18	𝑟	𝑟	X
asir-2864	67	19	(	(	PUNCT
asir-2864	67	20	𝑎	𝑎	X
asir-2864	67	21	+	+	NUM
asir-2864	67	22	𝑏)3	𝑏)3	NOUN
asir-2864	67	23	𝑚	𝑚	X
asir-2864	67	24	·	·	PUNCT
asir-2864	67	25	𝑎	𝑎	DET
asir-2864	67	26	∙	∙	PROPN
asir-2864	67	27	ℎ2	ℎ2	ADJ
asir-2864	67	28	𝑟2	𝑟2	NOUN
asir-2864	67	29	·	·	PUNCT
asir-2864	67	30	𝑏2	𝑏2	NOUN
asir-2864	67	31	by	by	ADP
asir-2864	67	32	using	use	VERB
asir-2864	67	33	the	the	DET
asir-2864	67	34	excel	excel	NOUN
asir-2864	67	35	file	file	NOUN
asir-2864	67	36	,	,	PUNCT
asir-2864	67	37	the	the	DET
asir-2864	67	38	user	user	NOUN
asir-2864	67	39	can	can	AUX
asir-2864	67	40	see	see	VERB
asir-2864	67	41	that	that	SCONJ
asir-2864	67	42	this	this	DET
asir-2864	67	43	method	method	NOUN
asir-2864	67	44	gives	give	VERB
asir-2864	67	45	correctly	correctly	ADV
asir-2864	67	46	the	the	DET
asir-2864	67	47	center	center	NOUN
asir-2864	67	48	of	of	ADP
asir-2864	67	49	the	the	DET
asir-2864	67	50	force	force	NOUN
asir-2864	67	51	for	for	ADP
asir-2864	67	52	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2864	67	53	applied	apply	VERB
asir-2864	67	54	science	science	NOUN
asir-2864	67	55	and	and	CCONJ
asir-2864	67	56	innovative	innovative	ADJ
asir-2864	67	57	research	research	NOUN
asir-2864	67	58	vol	vol	NOUN
asir-2864	67	59	.	.	PROPN
asir-2864	68	1	4	4	NUM
asir-2864	68	2	,	,	PUNCT
asir-2864	68	3	no	no	INTJ
asir-2864	68	4	.	.	NOUN
asir-2864	68	5	2	2	NUM
asir-2864	68	6	,	,	PUNCT
asir-2864	68	7	2020	2020	NUM
asir-2864	68	8	45	45	NUM
asir-2864	68	9	published	publish	VERB
asir-2864	68	10	by	by	ADP
asir-2864	68	11	scholink	scholink	PROPN
asir-2864	68	12	inc	inc	PROPN
asir-2864	68	13	.	.	PROPN
asir-2864	68	14	either	either	CCONJ
asir-2864	68	15	forces	force	NOUN
asir-2864	68	16	directed	direct	VERB
asir-2864	68	17	to	to	ADP
asir-2864	68	18	the	the	DET
asir-2864	68	19	foci	focus	NOUN
asir-2864	68	20	of	of	ADP
asir-2864	68	21	the	the	DET
asir-2864	68	22	ellipse	ellipse	NOUN
asir-2864	68	23	(	(	PUNCT
asir-2864	68	24	gravitational	gravitational	ADJ
asir-2864	68	25	attractive	attractive	ADJ
asir-2864	68	26	proportional	proportional	NOUN
asir-2864	68	27	to	to	ADP
asir-2864	68	28	the	the	DET
asir-2864	68	29	reciprocal	reciprocal	NOUN
asir-2864	68	30	of	of	ADP
asir-2864	68	31	the	the	DET
asir-2864	68	32	distance	distance	NOUN
asir-2864	68	33	from	from	ADP
asir-2864	68	34	the	the	DET
asir-2864	68	35	focus	focus	NOUN
asir-2864	68	36	)	)	PUNCT
asir-2864	68	37	or	or	CCONJ
asir-2864	68	38	to	to	ADP
asir-2864	68	39	the	the	DET
asir-2864	68	40	center	center	NOUN
asir-2864	68	41	of	of	ADP
asir-2864	68	42	the	the	DET
asir-2864	68	43	ellipse	ellipse	NOUN
asir-2864	68	44	(	(	PUNCT
asir-2864	68	45	proportional	proportional	ADJ
asir-2864	68	46	to	to	ADP
asir-2864	68	47	the	the	DET
asir-2864	68	48	distance	distance	NOUN
asir-2864	68	49	of	of	ADP
asir-2864	68	50	the	the	DET
asir-2864	68	51	particle	particle	NOUN
asir-2864	68	52	from	from	ADP
asir-2864	68	53	the	the	DET
asir-2864	68	54	center	center	NOUN
asir-2864	68	55	)	)	PUNCT
asir-2864	68	56	.	.	PUNCT
asir-2864	69	1	3	3	X
asir-2864	69	2	.	.	X
asir-2864	69	3	finding	find	VERB
asir-2864	69	4	the	the	DET
asir-2864	69	5	center	center	NOUN
asir-2864	69	6	in	in	ADP
asir-2864	69	7	the	the	DET
asir-2864	69	8	case	case	NOUN
asir-2864	69	9	of	of	ADP
asir-2864	69	10	hyperbola	hyperbola	PROPN
asir-2864	69	11	in	in	ADP
asir-2864	69	12	the	the	DET
asir-2864	69	13	case	case	NOUN
asir-2864	69	14	of	of	ADP
asir-2864	69	15	hyperbola	hyperbola	PROPN
asir-2864	69	16	there	there	PRON
asir-2864	69	17	are	be	VERB
asir-2864	69	18	three	three	NUM
asir-2864	69	19	cases	case	NOUN
asir-2864	69	20	of	of	ADP
asir-2864	69	21	force	force	NOUN
asir-2864	69	22	(	(	PUNCT
asir-2864	69	23	we	we	PRON
asir-2864	69	24	consider	consider	VERB
asir-2864	69	25	the	the	DET
asir-2864	69	26	movement	movement	NOUN
asir-2864	69	27	on	on	ADP
asir-2864	69	28	the	the	DET
asir-2864	69	29	right	right	ADJ
asir-2864	69	30	branch	branch	NOUN
asir-2864	69	31	of	of	ADP
asir-2864	69	32	the	the	DET
asir-2864	69	33	hyperbola	hyperbola	PROPN
asir-2864	69	34	)	)	PUNCT
asir-2864	69	35	.	.	PUNCT
asir-2864	70	1	a	a	X
asir-2864	70	2	)	)	PUNCT
asir-2864	70	3	an	an	DET
asir-2864	70	4	attractive	attractive	ADJ
asir-2864	70	5	force	force	NOUN
asir-2864	70	6	with	with	ADP
asir-2864	70	7	center	center	NOUN
asir-2864	70	8	of	of	ADP
asir-2864	70	9	force	force	NOUN
asir-2864	70	10	the	the	DET
asir-2864	70	11	focus	focus	NOUN
asir-2864	70	12	on	on	ADP
asir-2864	70	13	the	the	DET
asir-2864	70	14	right	right	ADJ
asir-2864	70	15	side	side	NOUN
asir-2864	70	16	of	of	ADP
asir-2864	70	17	the	the	DET
asir-2864	70	18	hyperbola	hyperbola	PROPN
asir-2864	70	19	.	.	PUNCT
asir-2864	71	1	this	this	DET
asir-2864	71	2	force	force	NOUN
asir-2864	71	3	is	be	AUX
asir-2864	71	4	reciprocal	reciprocal	ADJ
asir-2864	71	5	to	to	ADP
asir-2864	71	6	the	the	DET
asir-2864	71	7	square	square	NOUN
asir-2864	71	8	of	of	ADP
asir-2864	71	9	the	the	DET
asir-2864	71	10	distance	distance	NOUN
asir-2864	71	11	from	from	ADP
asir-2864	71	12	the	the	DET
asir-2864	71	13	focus	focus	NOUN
asir-2864	71	14	.	.	PUNCT
asir-2864	72	1	b	b	X
asir-2864	72	2	)	)	PUNCT
asir-2864	72	3	a	a	DET
asir-2864	72	4	repulsive	repulsive	ADJ
asir-2864	72	5	force	force	NOUN
asir-2864	72	6	with	with	ADP
asir-2864	72	7	center	center	NOUN
asir-2864	72	8	of	of	ADP
asir-2864	72	9	force	force	NOUN
asir-2864	72	10	the	the	DET
asir-2864	72	11	left	left	ADJ
asir-2864	72	12	focus	focus	NOUN
asir-2864	72	13	,	,	PUNCT
asir-2864	72	14	which	which	PRON
asir-2864	72	15	also	also	ADV
asir-2864	72	16	is	be	AUX
asir-2864	72	17	reciprocal	reciprocal	ADJ
asir-2864	72	18	to	to	ADP
asir-2864	72	19	the	the	DET
asir-2864	72	20	square	square	NOUN
asir-2864	72	21	of	of	ADP
asir-2864	72	22	the	the	DET
asir-2864	72	23	distance	distance	NOUN
asir-2864	72	24	from	from	ADP
asir-2864	72	25	the	the	DET
asir-2864	72	26	focus	focus	NOUN
asir-2864	72	27	.	.	PUNCT
asir-2864	73	1	c	c	X
asir-2864	73	2	)	)	PUNCT
asir-2864	73	3	a	a	DET
asir-2864	73	4	repulsive	repulsive	ADJ
asir-2864	73	5	force	force	NOUN
asir-2864	73	6	with	with	ADP
asir-2864	73	7	center	center	NOUN
asir-2864	73	8	of	of	ADP
asir-2864	73	9	force	force	NOUN
asir-2864	73	10	the	the	DET
asir-2864	73	11	origin	origin	NOUN
asir-2864	73	12	of	of	ADP
asir-2864	73	13	the	the	DET
asir-2864	73	14	coordinates	coordinate	NOUN
asir-2864	73	15	.	.	PUNCT
asir-2864	74	1	in	in	ADP
asir-2864	74	2	the	the	DET
asir-2864	74	3	figure	figure	NOUN
asir-2864	74	4	the	the	DET
asir-2864	74	5	particle	particle	NOUN
asir-2864	74	6	is	be	AUX
asir-2864	74	7	moving	move	VERB
asir-2864	74	8	to	to	ADP
asir-2864	74	9	the	the	DET
asir-2864	74	10	left	left	NOUN
asir-2864	74	11	.	.	PUNCT
asir-2864	75	1	it	it	PRON
asir-2864	75	2	is	be	AUX
asir-2864	75	3	clear	clear	ADJ
asir-2864	75	4	that	that	SCONJ
asir-2864	75	5	for	for	ADP
asir-2864	75	6	attractive	attractive	ADJ
asir-2864	75	7	force	force	NOUN
asir-2864	75	8	the	the	DET
asir-2864	75	9	velocity	velocity	NOUN
asir-2864	75	10	is	be	AUX
asir-2864	75	11	increasing	increase	VERB
asir-2864	75	12	as	as	SCONJ
asir-2864	75	13	the	the	DET
asir-2864	75	14	particle	particle	NOUN
asir-2864	75	15	moves	move	NOUN
asir-2864	75	16	to	to	ADP
asir-2864	75	17	the	the	DET
asir-2864	75	18	left	left	NOUN
asir-2864	75	19	.	.	PUNCT
asir-2864	76	1	for	for	ADP
asir-2864	76	2	the	the	DET
asir-2864	76	3	case	case	NOUN
asir-2864	76	4	of	of	ADP
asir-2864	76	5	elastic	elastic	ADJ
asir-2864	76	6	force	force	NOUN
asir-2864	76	7	the	the	DET
asir-2864	76	8	velocity	velocity	NOUN
asir-2864	76	9	increases	increase	NOUN
asir-2864	76	10	fast	fast	ADV
asir-2864	76	11	as	as	SCONJ
asir-2864	76	12	the	the	DET
asir-2864	76	13	body	body	NOUN
asir-2864	76	14	moves	move	VERB
asir-2864	76	15	away	away	ADV
asir-2864	76	16	to	to	ADP
asir-2864	76	17	the	the	DET
asir-2864	76	18	right	right	NOUN
asir-2864	76	19	,	,	PUNCT
asir-2864	76	20	while	while	SCONJ
asir-2864	76	21	for	for	ADP
asir-2864	76	22	repulsive	repulsive	ADJ
asir-2864	76	23	force	force	NOUN
asir-2864	76	24	the	the	DET
asir-2864	76	25	velocity	velocity	NOUN
asir-2864	76	26	increases	increase	NOUN
asir-2864	76	27	but	but	CCONJ
asir-2864	76	28	there	there	PRON
asir-2864	76	29	is	be	VERB
asir-2864	76	30	a	a	DET
asir-2864	76	31	limit	limit	NOUN
asir-2864	76	32	to	to	ADP
asir-2864	76	33	the	the	DET
asir-2864	76	34	velocity	velocity	NOUN
asir-2864	76	35	.	.	PUNCT
asir-2864	77	1	we	we	PRON
asir-2864	77	2	proceed	proceed	VERB
asir-2864	77	3	as	as	ADP
asir-2864	77	4	in	in	ADP
asir-2864	77	5	the	the	DET
asir-2864	77	6	case	case	NOUN
asir-2864	77	7	of	of	ADP
asir-2864	77	8	the	the	DET
asir-2864	77	9	ellipse	ellipse	NOUN
asir-2864	77	10	.	.	PUNCT
asir-2864	78	1	we	we	PRON
asir-2864	78	2	find	find	VERB
asir-2864	78	3	the	the	DET
asir-2864	78	4	points	point	NOUN
asir-2864	78	5	t	t	NOUN
asir-2864	78	6	and	and	CCONJ
asir-2864	78	7	z	z	NOUN
asir-2864	78	8	where	where	SCONJ
asir-2864	78	9	the	the	DET
asir-2864	78	10	lines	line	NOUN
asir-2864	78	11	of	of	ADP
asir-2864	78	12	the	the	DET
asir-2864	78	13	velocities	velocity	NOUN
asir-2864	78	14	𝑉𝑃⃗⃗⃗⃗⃗⃗	𝑉𝑃⃗⃗⃗⃗⃗⃗	PUNCT
asir-2864	78	15	,	,	PUNCT
asir-2864	78	16	𝑉𝑄⃗⃗⃗⃗	𝑉𝑄⃗⃗⃗⃗	PROPN
asir-2864	78	17	⃗⃗	⃗⃗	PROPN
asir-2864	78	18	and	and	CCONJ
asir-2864	78	19	𝑉𝑄⃗⃗⃗⃗	𝑉𝑄⃗⃗⃗⃗	ADJ
asir-2864	78	20	⃗⃗	⃗⃗	PROPN
asir-2864	78	21	,	,	PUNCT
asir-2864	79	1	𝑉𝑅⃗⃗⃗⃗	𝑉𝑅⃗⃗⃗⃗	PROPN
asir-2864	79	2	⃗⃗	⃗⃗	PROPN
asir-2864	79	3	⃗	⃗	PROPN
asir-2864	79	4	cut	cut	VERB
asir-2864	79	5	.	.	PUNCT
asir-2864	80	1	we	we	PRON
asir-2864	80	2	find	find	VERB
asir-2864	80	3	as	as	ADP
asir-2864	80	4	in	in	ADP
asir-2864	80	5	ellipse	ellipse	NOUN
asir-2864	80	6	the	the	DET
asir-2864	80	7	points	point	NOUN
asir-2864	80	8	,	,	PUNCT
asir-2864	80	9	e	e	NOUN
asir-2864	80	10	and	and	CCONJ
asir-2864	80	11	d	d	PROPN
asir-2864	80	12	and	and	CCONJ
asir-2864	80	13	draw	draw	VERB
asir-2864	80	14	the	the	DET
asir-2864	80	15	lines	line	NOUN
asir-2864	80	16	td	td	NOUN
asir-2864	80	17	and	and	CCONJ
asir-2864	80	18	ze	ze	PROPN
asir-2864	80	19	and	and	CCONJ
asir-2864	80	20	find	find	VERB
asir-2864	80	21	the	the	DET
asir-2864	80	22	point	point	NOUN
asir-2864	80	23	s	s	VERB
asir-2864	80	24	where	where	SCONJ
asir-2864	80	25	the	the	DET
asir-2864	80	26	two	two	NUM
asir-2864	80	27	lines	line	NOUN
asir-2864	80	28	cut	cut	VERB
asir-2864	80	29	each	each	DET
asir-2864	80	30	other	other	ADJ
asir-2864	80	31	.	.	PUNCT
asir-2864	81	1	at	at	ADP
asir-2864	81	2	the	the	DET
asir-2864	81	3	point	point	NOUN
asir-2864	81	4	s	s	VERB
asir-2864	81	5	the	the	DET
asir-2864	81	6	law	law	NOUN
asir-2864	81	7	of	of	ADP
asir-2864	81	8	areas	area	NOUN
asir-2864	81	9	holds	hold	VERB
asir-2864	81	10	for	for	ADP
asir-2864	81	11	all	all	DET
asir-2864	81	12	points	point	NOUN
asir-2864	81	13	,	,	PUNCT
asir-2864	81	14	so	so	CCONJ
asir-2864	81	15	this	this	PRON
asir-2864	81	16	is	be	AUX
asir-2864	81	17	the	the	DET
asir-2864	81	18	center	center	NOUN
asir-2864	81	19	of	of	ADP
asir-2864	81	20	force	force	NOUN
asir-2864	81	21	.	.	PUNCT
asir-2864	81	22	.	.	PUNCT
asir-2864	82	1	figure	figure	VERB
asir-2864	82	2	4	4	NUM
asir-2864	82	3	.	.	PUNCT
asir-2864	83	1	application	application	NOUN
asir-2864	83	2	of	of	ADP
asir-2864	83	3	newton	newton	PROPN
asir-2864	83	4	’s	’s	PART
asir-2864	83	5	ideas	idea	NOUN
asir-2864	83	6	for	for	ADP
asir-2864	83	7	hyperbola	hyperbola	PROPN
asir-2864	83	8	3.1	3.1	NUM
asir-2864	83	9	finding	find	VERB
asir-2864	83	10	the	the	DET
asir-2864	83	11	law	law	NOUN
asir-2864	83	12	of	of	ADP
asir-2864	83	13	force	force	NOUN
asir-2864	83	14	to	to	PART
asir-2864	83	15	find	find	VERB
asir-2864	83	16	the	the	DET
asir-2864	83	17	law	law	NOUN
asir-2864	83	18	of	of	ADP
asir-2864	83	19	the	the	DET
asir-2864	83	20	force	force	NOUN
asir-2864	83	21	we	we	PRON
asir-2864	83	22	need	need	VERB
asir-2864	83	23	to	to	PART
asir-2864	83	24	calculate	calculate	VERB
asir-2864	83	25	the	the	DET
asir-2864	83	26	velocity	velocity	NOUN
asir-2864	83	27	and	and	CCONJ
asir-2864	83	28	the	the	DET
asir-2864	83	29	radius	radius	NOUN
asir-2864	83	30	of	of	ADP
asir-2864	83	31	curvature	curvature	NOUN
asir-2864	83	32	ρ	ρ	PROPN
asir-2864	83	33	.	.	PUNCT
asir-2864	84	1	the	the	DET
asir-2864	84	2	radius	radius	NOUN
asir-2864	84	3	of	of	ADP
asir-2864	84	4	curvature	curvature	NOUN
asir-2864	84	5	is	be	AUX
asir-2864	84	6	ρ	ρ	NOUN
asir-2864	84	7	=	=	PUNCT
asir-2864	84	8	(	(	PUNCT
asir-2864	84	9	𝑎2∙𝑠𝑖𝑛(𝜑)2+𝑏2	𝑎2∙𝑠𝑖𝑛(𝜑)2+𝑏2	PROPN
asir-2864	84	10	)	)	PUNCT
asir-2864	84	11	3	3	NUM
asir-2864	84	12	2	2	NUM
asir-2864	84	13	𝑎∙𝑏∙𝑐𝑜𝑠(𝜑)3	𝑎∙𝑏∙𝑐𝑜𝑠(𝜑)3	PROPN
asir-2864	84	14	where	where	SCONJ
asir-2864	84	15	φ	φ	PROPN
asir-2864	84	16	is	be	AUX
asir-2864	84	17	the	the	DET
asir-2864	84	18	angle	angle	NOUN
asir-2864	84	19	from	from	ADP
asir-2864	84	20	which	which	PRON
asir-2864	84	21	we	we	PRON
asir-2864	84	22	calculate	calculate	VERB
asir-2864	84	23	the	the	DET
asir-2864	84	24	point	point	NOUN
asir-2864	84	25	of	of	ADP
asir-2864	84	26	the	the	DET
asir-2864	84	27	curve	curve	NOUN
asir-2864	84	28	:	:	PUNCT
asir-2864	84	29	(	(	PUNCT
asir-2864	84	30	𝑥	𝑥	NOUN
asir-2864	84	31	,	,	PUNCT
asir-2864	84	32	𝑦	𝑦	NOUN
asir-2864	84	33	)	)	PUNCT
asir-2864	84	34	=	=	SYM
asir-2864	84	35	(	(	PUNCT
asir-2864	84	36	𝑎	𝑎	X
asir-2864	84	37	𝑐𝑜𝑠(𝜑	𝑐𝑜𝑠(𝜑	NOUN
asir-2864	84	38	)	)	PUNCT
asir-2864	84	39	,	,	PUNCT
asir-2864	84	40	𝑏	𝑏	PROPN
asir-2864	84	41	∗	∗	NOUN
asir-2864	84	42	tan(𝜑	tan(𝜑	ADV
asir-2864	84	43	)	)	PUNCT
asir-2864	84	44	)	)	PUNCT
asir-2864	84	45	.	.	PUNCT
asir-2864	85	1	the	the	DET
asir-2864	85	2	tangent	tangent	NOUN
asir-2864	85	3	is	be	AUX
asir-2864	85	4	:	:	PUNCT
asir-2864	85	5	𝑦	𝑦	X
asir-2864	85	6	𝑑𝑥	𝑑𝑥	NOUN
asir-2864	85	7	=	=	SYM
asir-2864	85	8	𝑏	𝑏	NOUN
asir-2864	85	9	𝑎∗𝑠𝑖𝑛𝜑	𝑎∗𝑠𝑖𝑛𝜑	NOUN
asir-2864	85	10	,	,	PUNCT
asir-2864	85	11	and	and	CCONJ
asir-2864	85	12	the	the	DET
asir-2864	85	13	unit	unit	NOUN
asir-2864	85	14	vector	vector	NOUN
asir-2864	85	15	on	on	ADP
asir-2864	85	16	𝑟	𝑟	NOUN
asir-2864	85	17	is	be	AUX
asir-2864	85	18	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2864	85	19	applied	apply	VERB
asir-2864	85	20	science	science	NOUN
asir-2864	85	21	and	and	CCONJ
asir-2864	85	22	innovative	innovative	ADJ
asir-2864	85	23	research	research	NOUN
asir-2864	85	24	vol	vol	NOUN
asir-2864	85	25	.	.	PROPN
asir-2864	86	1	4	4	NUM
asir-2864	86	2	,	,	PUNCT
asir-2864	86	3	no	no	INTJ
asir-2864	86	4	.	.	NOUN
asir-2864	86	5	2	2	NUM
asir-2864	86	6	,	,	PUNCT
asir-2864	86	7	2020	2020	NUM
asir-2864	86	8	46	46	NUM
asir-2864	86	9	published	publish	VERB
asir-2864	86	10	by	by	ADP
asir-2864	86	11	scholink	scholink	PROPN
asir-2864	86	12	inc	inc	PROPN
asir-2864	86	13	.	.	PROPN
asir-2864	86	14	𝑒	𝑒	PROPN
asir-2864	87	1	=	=	PUNCT
asir-2864	87	2	(	(	PUNCT
asir-2864	87	3	𝑟𝑥	𝑟𝑥	NOUN
asir-2864	87	4	𝑟	𝑟	NOUN
asir-2864	87	5	,	,	PUNCT
asir-2864	87	6	𝑟𝑦	𝑟𝑦	X
asir-2864	87	7	𝑟	𝑟	NOUN
asir-2864	87	8	)	)	PUNCT
asir-2864	87	9	.	.	PUNCT
asir-2864	88	1	the	the	DET
asir-2864	88	2	perpendicular	perpendicular	NOUN
asir-2864	88	3	is	be	AUX
asir-2864	88	4	found	find	VERB
asir-2864	88	5	from	from	ADP
asir-2864	88	6	�	�	PROPN
asir-2864	88	7	⃗⃗	⃗⃗	PROPN
asir-2864	88	8	�	�	PROPN
asir-2864	88	9	=	=	PRON
asir-2864	88	10	(	(	PUNCT
asir-2864	88	11	𝑏	𝑏	PROPN
asir-2864	88	12	√𝑏2+α2∙sin2	√𝑏2+α2∙sin2	ADP
asir-2864	88	13	𝜑	𝜑	PROPN
asir-2864	88	14	,	,	PUNCT
asir-2864	88	15	−𝑎∙𝑠𝑖𝑛𝜑	−𝑎∙𝑠𝑖𝑛𝜑	PROPN
asir-2864	88	16	√𝑏2+α2∙sin2	√𝑏2+α2∙sin2	ADP
asir-2864	88	17	𝜑	𝜑	PROPN
asir-2864	88	18	)	)	PUNCT
asir-2864	88	19	and	and	CCONJ
asir-2864	88	20	the	the	DET
asir-2864	88	21	angle	angle	PROPN
asir-2864	88	22	ω	ω	PROPN
asir-2864	88	23	between	between	ADP
asir-2864	88	24	𝑒	𝑒	PROPN
asir-2864	88	25	and	and	CCONJ
asir-2864	88	26	�	�	PROPN
asir-2864	88	27	⃗⃗	⃗⃗	PROPN
asir-2864	88	28	�	�	PROPN
asir-2864	88	29	is	be	AUX
asir-2864	88	30	found	find	VERB
asir-2864	88	31	from	from	ADP
asir-2864	88	32	𝑐𝑜𝑠𝜔	𝑐𝑜𝑠𝜔	NOUN
asir-2864	88	33	=	=	SYM
asir-2864	88	34	�	�	PROPN
asir-2864	88	35	⃗⃗	⃗⃗	PROPN
asir-2864	88	36	�	�	PROPN
asir-2864	88	37	∙	∙	PROPN
asir-2864	88	38	𝑒	𝑒	PART
asir-2864	88	39	=	=	PUNCT
asir-2864	88	40	𝑟𝑥∙𝑏−𝑟𝑦∙𝑎∙𝑠𝑖𝑛𝜑	𝑟𝑥∙𝑏−𝑟𝑦∙𝑎∙𝑠𝑖𝑛𝜑	PROPN
asir-2864	88	41	𝑟∙√𝑏2+α2∙sin2	𝑟∙√𝑏2+α2∙sin2	NUM
asir-2864	88	42	𝜑	𝜑	NOUN
asir-2864	88	43	.	.	PUNCT
asir-2864	89	1	the	the	DET
asir-2864	89	2	velocity	velocity	NOUN
asir-2864	89	3	v	v	NOUN
asir-2864	89	4	is	be	AUX
asir-2864	89	5	found	find	VERB
asir-2864	89	6	from	from	ADP
asir-2864	89	7	the	the	DET
asir-2864	89	8	law	law	NOUN
asir-2864	89	9	of	of	ADP
asir-2864	89	10	areas	area	NOUN
asir-2864	89	11	:	:	PUNCT
asir-2864	89	12	if	if	SCONJ
asir-2864	89	13	ℎ	ℎ	X
asir-2864	89	14	=	=	SYM
asir-2864	89	15	𝑟	𝑟	X
asir-2864	89	16	×	×	PROPN
asir-2864	89	17	�	�	PROPN
asir-2864	89	18	⃗⃗	⃗⃗	PROPN
asir-2864	89	19	�	�	PROPN
asir-2864	89	20	then	then	ADV
asir-2864	89	21	𝑉	𝑉	PROPN
asir-2864	89	22	=	=	NOUN
asir-2864	89	23	ℎ	ℎ	PART
asir-2864	89	24	𝑟·𝑐𝑜𝑠𝜔	𝑟·𝑐𝑜𝑠𝜔	NOUN
asir-2864	89	25	and	and	CCONJ
asir-2864	89	26	we	we	PRON
asir-2864	89	27	find	find	VERB
asir-2864	89	28	the	the	DET
asir-2864	89	29	law	law	NOUN
asir-2864	89	30	of	of	ADP
asir-2864	89	31	the	the	DET
asir-2864	89	32	force	force	NOUN
asir-2864	89	33	from	from	ADP
asir-2864	89	34	the	the	DET
asir-2864	89	35	centripetal	centripetal	ADJ
asir-2864	89	36	force	force	NOUN
asir-2864	90	1	𝐹𝑘	𝐹𝑘	PROPN
asir-2864	90	2	=	=	PUNCT
asir-2864	90	3	𝐹	𝐹	PROPN
asir-2864	90	4	∙	∙	NOUN
asir-2864	90	5	𝑐𝑜𝑠𝜔	𝑐𝑜𝑠𝜔	VERB
asir-2864	90	6	=	=	PUNCT
asir-2864	90	7	𝑚	𝑚	ADP
asir-2864	90	8	∙	∙	PROPN
asir-2864	90	9	𝑉2	𝑉2	NOUN
asir-2864	90	10	𝜌	𝜌	ADP
asir-2864	90	11	=	=	SYM
asir-2864	90	12	𝑚	𝑚	ADP
asir-2864	90	13	∙	∙	PROPN
asir-2864	90	14	ℎ2	ℎ2	NOUN
asir-2864	90	15	𝜌∙(𝑟∙𝑐𝑜𝑠𝜔)2	𝜌∙(𝑟∙𝑐𝑜𝑠𝜔)2	VERB
asir-2864	91	1	so	so	ADV
asir-2864	91	2	𝐹	𝐹	PROPN
asir-2864	91	3	=	=	PUNCT
asir-2864	91	4	𝑚	𝑚	ADP
asir-2864	91	5	∙	∙	PROPN
asir-2864	91	6	ℎ2	ℎ2	ADJ
asir-2864	91	7	𝑟2∙cos3	𝑟2∙cos3	NUM
asir-2864	91	8	𝜔∙	𝜔∙	NOUN
asir-2864	91	9	(	(	PUNCT
asir-2864	91	10	𝑎2∙𝑠𝑖𝑛(𝜑)2+𝑏2	𝑎2∙𝑠𝑖𝑛(𝜑)2+𝑏2	ADJ
asir-2864	91	11	)	)	PUNCT
asir-2864	91	12	3	3	NUM
asir-2864	91	13	2	2	NUM
asir-2864	91	14	𝑎∙𝑏∙𝑐𝑜𝑠(𝜑)3	𝑎∙𝑏∙𝑐𝑜𝑠(𝜑)3	PROPN
asir-2864	91	15	.	.	PUNCT
asir-2864	92	1	center	center	NOUN
asir-2864	92	2	at	at	ADP
asir-2864	92	3	left	left	ADJ
asir-2864	92	4	focus	focus	NOUN
asir-2864	92	5	center	center	NOUN
asir-2864	92	6	at	at	ADP
asir-2864	92	7	the	the	DET
asir-2864	92	8	center	center	NOUN
asir-2864	92	9	of	of	ADP
asir-2864	92	10	ellipse	ellipse	NOUN
asir-2864	92	11	center	center	NOUN
asir-2864	92	12	at	at	ADP
asir-2864	92	13	the	the	DET
asir-2864	92	14	right	right	ADJ
asir-2864	92	15	focus	focus	NOUN
asir-2864	92	16	r	r	PROPN
asir-2864	92	17	𝑎	𝑎	PRON
asir-2864	92	18	·	·	PUNCT
asir-2864	92	19	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	92	20	+	+	CCONJ
asir-2864	92	21	𝑐	𝑐	PROPN
asir-2864	92	22	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	92	23	√𝛼2	√𝛼2	PROPN
asir-2864	92	24	∙	∙	PROPN
asir-2864	92	25	cos2	cos2	NOUN
asir-2864	92	26	𝜑	𝜑	PROPN
asir-2864	93	1	+	+	CCONJ
asir-2864	93	2	𝑏2	𝑏2	PROPN
asir-2864	93	3	∙	∙	PROPN
asir-2864	93	4	sin2	sin2	NOUN
asir-2864	93	5	𝜑	𝜑	ADP
asir-2864	93	6	𝑎	𝑎	PRON
asir-2864	93	7	·	·	PUNCT
asir-2864	93	8	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	93	9	−	−	PROPN
asir-2864	93	10	𝑐	𝑐	PROPN
asir-2864	93	11	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	93	12	cosω	cosω	NOUN
asir-2864	94	1	𝑏	𝑏	ADP
asir-2864	94	2	∙	∙	PROPN
asir-2864	94	3	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	94	4	√𝑏2	√𝑏2	PROPN
asir-2864	95	1	+	+	CCONJ
asir-2864	95	2	α2	α2	ADJ
asir-2864	95	3	∙	∙	PROPN
asir-2864	95	4	sin2	sin2	NOUN
asir-2864	95	5	𝜑	𝜑	PROPN
asir-2864	95	6	𝑎𝑏	𝑎𝑏	AUX
asir-2864	95	7	∙	∙	PROPN
asir-2864	95	8	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	95	9	𝑟	𝑟	NOUN
asir-2864	95	10	∙	∙	PROPN
asir-2864	95	11	√𝑏2	√𝑏2	PUNCT
asir-2864	96	1	+	+	CCONJ
asir-2864	96	2	α2	α2	ADJ
asir-2864	96	3	∙	∙	PROPN
asir-2864	96	4	sin2	sin2	NOUN
asir-2864	96	5	𝜑	𝜑	X
asir-2864	96	6	𝑏	𝑏	PROPN
asir-2864	96	7	·	·	PUNCT
asir-2864	96	8	𝑐𝑜𝑠𝜑	𝑐𝑜𝑠𝜑	ADJ
asir-2864	96	9	√𝑏2	√𝑏2	PROPN
asir-2864	96	10	+	+	CCONJ
asir-2864	96	11	α2	α2	ADJ
asir-2864	96	12	∙	∙	PROPN
asir-2864	96	13	sin2	sin2	NOUN
asir-2864	97	1	𝜑	𝜑	X
asir-2864	97	2	f	f	X
asir-2864	97	3	𝑚	𝑚	X
asir-2864	97	4	∙	∙	PROPN
asir-2864	97	5	ℎ2𝑎	ℎ2𝑎	NUM
asir-2864	97	6	𝑟2	𝑟2	NOUN
asir-2864	97	7	∙	∙	PROPN
asir-2864	97	8	𝑏2	𝑏2	PROPN
asir-2864	97	9	𝑚	𝑚	PROPN
asir-2864	97	10	·	·	SYM
asir-2864	97	11	ℎ2	ℎ2	ADJ
asir-2864	97	12	∙	∙	PROPN
asir-2864	97	13	𝑟	𝑟	X
asir-2864	97	14	(	(	PUNCT
asir-2864	97	15	𝑎𝑏)2	𝑎𝑏)2	PROPN
asir-2864	97	16	𝑚	𝑚	PROPN
asir-2864	97	17	·	·	PUNCT
asir-2864	97	18	ℎ2	ℎ2	NOUN
asir-2864	97	19	·	·	PUNCT
asir-2864	97	20	𝑎	𝑎	DET
asir-2864	97	21	𝑏2	𝑏2	NOUN
asir-2864	97	22	·	·	PUNCT
asir-2864	97	23	𝑟2	𝑟2	NOUN
asir-2864	97	24	4	4	NUM
asir-2864	97	25	.	.	PUNCT
asir-2864	98	1	parabola	parabola	PROPN
asir-2864	98	2	4.1	4.1	NUM
asir-2864	98	3	constant	constant	ADJ
asir-2864	98	4	force	force	NOUN
asir-2864	98	5	by	by	ADP
asir-2864	98	6	applying	apply	VERB
asir-2864	98	7	the	the	DET
asir-2864	98	8	same	same	ADJ
asir-2864	98	9	method	method	NOUN
asir-2864	98	10	we	we	PRON
asir-2864	98	11	get	get	VERB
asir-2864	98	12	two	two	NUM
asir-2864	98	13	parallel	parallel	ADJ
asir-2864	98	14	lines	line	NOUN
asir-2864	98	15	which	which	PRON
asir-2864	98	16	show	show	VERB
asir-2864	98	17	that	that	SCONJ
asir-2864	98	18	the	the	DET
asir-2864	98	19	center	center	NOUN
asir-2864	98	20	of	of	ADP
asir-2864	98	21	force	force	NOUN
asir-2864	98	22	is	be	AUX
asir-2864	98	23	at	at	ADP
asir-2864	98	24	an	an	DET
asir-2864	98	25	infinite	infinite	ADJ
asir-2864	98	26	distance	distance	NOUN
asir-2864	98	27	.	.	PUNCT
asir-2864	99	1	the	the	DET
asir-2864	99	2	user	user	NOUN
asir-2864	99	3	can	can	AUX
asir-2864	99	4	change	change	VERB
asir-2864	99	5	the	the	DET
asir-2864	99	6	initial	initial	ADJ
asir-2864	99	7	speed	speed	NOUN
asir-2864	99	8	and	and	CCONJ
asir-2864	99	9	the	the	DET
asir-2864	99	10	angle	angle	NOUN
asir-2864	99	11	of	of	ADP
asir-2864	99	12	the	the	DET
asir-2864	99	13	initial	initial	ADJ
asir-2864	99	14	velocity	velocity	NOUN
asir-2864	99	15	with	with	ADP
asir-2864	99	16	the	the	DET
asir-2864	99	17	horizontal	horizontal	NOUN
asir-2864	99	18	.	.	PUNCT
asir-2864	100	1	as	as	ADP
asir-2864	100	2	in	in	ADP
asir-2864	100	3	the	the	DET
asir-2864	100	4	case	case	NOUN
asir-2864	100	5	of	of	ADP
asir-2864	100	6	ellipse	ellipse	NOUN
asir-2864	100	7	he	he	PRON
asir-2864	100	8	can	can	AUX
asir-2864	100	9	change	change	VERB
asir-2864	100	10	the	the	DET
asir-2864	100	11	number	number	NOUN
asir-2864	100	12	of	of	ADP
asir-2864	100	13	steps	step	NOUN
asir-2864	100	14	and	and	CCONJ
asir-2864	100	15	see	see	VERB
asir-2864	100	16	the	the	DET
asir-2864	100	17	construction	construction	NOUN
asir-2864	100	18	of	of	ADP
asir-2864	100	19	the	the	DET
asir-2864	100	20	figure	figure	NOUN
asir-2864	100	21	.	.	PUNCT
asir-2864	101	1	the	the	DET
asir-2864	101	2	lines	line	NOUN
asir-2864	101	3	td	td	NOUN
asir-2864	101	4	and	and	CCONJ
asir-2864	101	5	ze	ze	PROPN
asir-2864	101	6	are	be	AUX
asir-2864	101	7	now	now	ADV
asir-2864	101	8	parallels	parallel	NOUN
asir-2864	101	9	and	and	CCONJ
asir-2864	101	10	so	so	ADV
asir-2864	101	11	the	the	DET
asir-2864	101	12	center	center	NOUN
asir-2864	101	13	of	of	ADP
asir-2864	101	14	force	force	NOUN
asir-2864	101	15	is	be	AUX
asir-2864	101	16	at	at	ADP
asir-2864	101	17	infinite	infinite	ADJ
asir-2864	101	18	distance	distance	NOUN
asir-2864	101	19	.	.	PUNCT
asir-2864	102	1	figure	figure	NOUN
asir-2864	102	2	5	5	NUM
asir-2864	102	3	.	.	PUNCT
asir-2864	103	1	application	application	NOUN
asir-2864	103	2	of	of	ADP
asir-2864	103	3	newton	newton	PROPN
asir-2864	103	4	’s	’s	PART
asir-2864	103	5	ideas	idea	NOUN
asir-2864	103	6	for	for	ADP
asir-2864	103	7	a	a	DET
asir-2864	103	8	parabola	parabola	NOUN
asir-2864	103	9	for	for	ADP
asir-2864	103	10	a	a	DET
asir-2864	103	11	force	force	NOUN
asir-2864	103	12	parallel	parallel	ADJ
asir-2864	103	13	to	to	ADP
asir-2864	103	14	y	y	PROPN
asir-2864	103	15	axis	axis	NOUN
asir-2864	103	16	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2864	103	17	applied	apply	VERB
asir-2864	103	18	science	science	NOUN
asir-2864	103	19	and	and	CCONJ
asir-2864	103	20	innovative	innovative	ADJ
asir-2864	103	21	research	research	NOUN
asir-2864	103	22	vol	vol	NOUN
asir-2864	103	23	.	.	PROPN
asir-2864	104	1	4	4	NUM
asir-2864	104	2	,	,	PUNCT
asir-2864	104	3	no	no	INTJ
asir-2864	104	4	.	.	NOUN
asir-2864	104	5	2	2	NUM
asir-2864	104	6	,	,	PUNCT
asir-2864	104	7	2020	2020	NUM
asir-2864	104	8	47	47	NUM
asir-2864	104	9	published	publish	VERB
asir-2864	104	10	by	by	ADP
asir-2864	104	11	scholink	scholink	PROPN
asir-2864	104	12	inc	inc	PROPN
asir-2864	104	13	.	.	PUNCT
asir-2864	105	1	we	we	PRON
asir-2864	105	2	can	can	AUX
asir-2864	105	3	prove	prove	VERB
asir-2864	105	4	that	that	SCONJ
asir-2864	105	5	t	t	PROPN
asir-2864	105	6	and	and	CCONJ
asir-2864	105	7	d	d	X
asir-2864	105	8	have	have	VERB
asir-2864	105	9	the	the	DET
asir-2864	105	10	same	same	ADJ
asir-2864	105	11	x	x	NOUN
asir-2864	105	12	_	_	PRON
asir-2864	105	13	component	component	NOUN
asir-2864	105	14	.	.	PUNCT
asir-2864	106	1	the	the	DET
asir-2864	106	2	tangent	tangent	NOUN
asir-2864	106	3	at	at	ADP
asir-2864	106	4	p	p	PROPN
asir-2864	106	5	is	be	AUX
asir-2864	106	6	𝑖𝑝	𝑖𝑝	INTJ
asir-2864	106	7	=	=	X
asir-2864	106	8	𝑑𝑦	𝑑𝑦	ADJ
asir-2864	106	9	𝑑𝑥	𝑑𝑥	NOUN
asir-2864	106	10	=	=	SYM
asir-2864	106	11	tan(𝜑	tan(𝜑	ADJ
asir-2864	106	12	)	)	PUNCT
asir-2864	106	13	−	−	PROPN
asir-2864	107	1	𝑗	𝑗	INTJ
asir-2864	107	2	𝑣0𝑥	𝑣0𝑥	PUNCT
asir-2864	107	3	2	2	NUM
asir-2864	107	4	(	(	PUNCT
asir-2864	107	5	𝑥𝑝	𝑥𝑝	ADV
asir-2864	107	6	−	−	PROPN
asir-2864	107	7	𝑥0	𝑥0	NOUN
asir-2864	107	8	)	)	PUNCT
asir-2864	107	9	where	where	SCONJ
asir-2864	107	10	𝑗	𝑗	ADJ
asir-2864	107	11	=	=	X
asir-2864	107	12	𝑔	𝑔	PROPN
asir-2864	107	13	𝑣0𝑥	𝑣0𝑥	NUM
asir-2864	107	14	2	2	NUM
asir-2864	107	15	and	and	CCONJ
asir-2864	107	16	φ	φ	NUM
asir-2864	107	17	the	the	DET
asir-2864	107	18	angle	angle	NOUN
asir-2864	107	19	of	of	ADP
asir-2864	107	20	the	the	DET
asir-2864	107	21	initial	initial	ADJ
asir-2864	107	22	velocity	velocity	NOUN
asir-2864	107	23	v0	v0	NOUN
asir-2864	107	24	with	with	ADP
asir-2864	107	25	the	the	DET
asir-2864	107	26	horizontal	horizontal	NOUN
asir-2864	107	27	.	.	PUNCT
asir-2864	108	1	we	we	PRON
asir-2864	108	2	find	find	VERB
asir-2864	108	3	that	that	SCONJ
asir-2864	108	4	the	the	DET
asir-2864	108	5	point	point	NOUN
asir-2864	108	6	t	t	PROPN
asir-2864	108	7	of	of	ADP
asir-2864	108	8	the	the	DET
asir-2864	108	9	intersections	intersection	NOUN
asir-2864	108	10	of	of	ADP
asir-2864	108	11	the	the	DET
asir-2864	108	12	lines	line	NOUN
asir-2864	108	13	of	of	ADP
asir-2864	108	14	the	the	DET
asir-2864	108	15	velocities	velocity	NOUN
asir-2864	108	16	is	be	AUX
asir-2864	108	17	given	give	VERB
asir-2864	108	18	by	by	ADP
asir-2864	108	19	:	:	PUNCT
asir-2864	108	20	𝑥𝑇	𝑥𝑇	PROPN
asir-2864	108	21	=	=	SYM
asir-2864	108	22	𝑆𝑝𝑞	𝑆𝑝𝑞	PROPN
asir-2864	108	23	𝑖𝑝−𝑖𝑞	𝑖𝑝−𝑖𝑞	PROPN
asir-2864	108	24	where	where	SCONJ
asir-2864	108	25	𝑆𝑝𝑞	𝑆𝑝𝑞	PROPN
asir-2864	108	26	−	−	PROPN
asir-2864	108	27	𝑦𝑞	𝑦𝑞	PROPN
asir-2864	108	28	−	−	PROPN
asir-2864	108	29	𝑦𝑝	𝑦𝑝	NOUN
asir-2864	108	30	+	+	CCONJ
asir-2864	108	31	𝑖𝑝𝑥𝑝	𝑖𝑝𝑥𝑝	NOUN
asir-2864	108	32	−	−	PROPN
asir-2864	108	33	𝑖𝑞𝑥𝑞.	𝑖𝑞𝑥𝑞.	VERB
asir-2864	108	34	the	the	DET
asir-2864	108	35	points	point	NOUN
asir-2864	108	36	a	a	PRON
asir-2864	108	37	,	,	PUNCT
asir-2864	108	38	and	and	CCONJ
asir-2864	108	39	b	b	NOUN
asir-2864	108	40	are	be	AUX
asir-2864	108	41	having	have	VERB
asir-2864	108	42	𝑥𝐴	𝑥𝐴	NOUN
asir-2864	108	43	=	=	SYM
asir-2864	108	44	𝑥𝑝	𝑥𝑝	NOUN
asir-2864	108	45	+	+	CCONJ
asir-2864	108	46	𝑑𝑝	𝑑𝑝	NUM
asir-2864	108	47	𝑠𝑖𝑛(atan(𝑖𝑝	𝑠𝑖𝑛(atan(𝑖𝑝	NUM
asir-2864	108	48	)	)	PUNCT
asir-2864	108	49	)	)	PUNCT
asir-2864	108	50	and	and	CCONJ
asir-2864	108	51	𝑥𝐵	𝑥𝐵	NOUN
asir-2864	108	52	=	=	SYM
asir-2864	108	53	𝑥𝑞	𝑥𝑞	PROPN
asir-2864	108	54	+	+	PROPN
asir-2864	108	55	𝑑𝑞	𝑑𝑞	PROPN
asir-2864	108	56	𝑠𝑖𝑛(atan(𝑖𝑞	𝑠𝑖𝑛(atan(𝑖𝑞	PROPN
asir-2864	108	57	)	)	PUNCT
asir-2864	108	58	)	)	PUNCT
asir-2864	108	59	where	where	SCONJ
asir-2864	108	60	𝑑𝑝	𝑑𝑝	ADV
asir-2864	108	61	=	=	SYM
asir-2864	108	62	𝑘	𝑘	X
asir-2864	108	63	𝑣𝑝	𝑣𝑝	INTJ
asir-2864	108	64	,	,	PUNCT
asir-2864	108	65	𝑑𝑞	𝑑𝑞	PROPN
asir-2864	109	1	=	=	SYM
asir-2864	109	2	𝑘	𝑘	PRON
asir-2864	109	3	𝑣𝑞	𝑣𝑞	NOUN
asir-2864	109	4	we	we	PRON
asir-2864	109	5	find	find	VERB
asir-2864	109	6	for	for	ADP
asir-2864	109	7	the	the	DET
asir-2864	109	8	point	point	NOUN
asir-2864	109	9	d	d	PROPN
asir-2864	109	10	that	that	SCONJ
asir-2864	109	11	it	it	PRON
asir-2864	109	12	has	have	VERB
asir-2864	109	13	as	as	ADP
asir-2864	109	14	x	x	NOUN
asir-2864	109	15	–	–	PUNCT
asir-2864	109	16	component	component	NOUN
asir-2864	109	17	𝑥𝐷	𝑥𝐷	NOUN
asir-2864	110	1	=	=	PUNCT
asir-2864	110	2	(	(	PUNCT
asir-2864	110	3	𝑆𝑝𝑞	𝑆𝑝𝑞	PROPN
asir-2864	110	4	−	−	PROPN
asir-2864	110	5	𝑑𝑞(1	𝑑𝑞(1	PROPN
asir-2864	110	6	+	+	CCONJ
asir-2864	110	7	𝑖𝑞	𝑖𝑞	PROPN
asir-2864	110	8	2	2	NUM
asir-2864	110	9	)	)	PUNCT
asir-2864	110	10	0,5	0,5	NOUN
asir-2864	111	1	+	+	PUNCT
asir-2864	111	2	𝑑𝑝(1	𝑑𝑝(1	NOUN
asir-2864	111	3	+	+	NUM
asir-2864	111	4	𝑡𝑝	𝑡𝑝	ADJ
asir-2864	111	5	2	2	NUM
asir-2864	111	6	)	)	PUNCT
asir-2864	111	7	0,5	0,5	NUM
asir-2864	111	8	)	)	PUNCT
asir-2864	111	9	/(𝑖𝑝	/(𝑖𝑝	PUNCT
asir-2864	112	1	−	−	PROPN
asir-2864	112	2	𝑖𝑞	𝑖𝑞	NOUN
asir-2864	112	3	)	)	PUNCT
asir-2864	113	1	but	but	CCONJ
asir-2864	113	2	the	the	DET
asir-2864	113	3	last	last	ADJ
asir-2864	113	4	two	two	NUM
asir-2864	113	5	terms	term	NOUN
asir-2864	113	6	on	on	ADP
asir-2864	113	7	the	the	DET
asir-2864	113	8	numerator	numerator	NOUN
asir-2864	113	9	have	have	VERB
asir-2864	113	10	a	a	DET
asir-2864	113	11	sum	sum	NOUN
asir-2864	113	12	of	of	ADP
asir-2864	113	13	zero	zero	NUM
asir-2864	113	14	since	since	SCONJ
asir-2864	113	15	−𝑑𝑞(1	−𝑑𝑞(1	PROPN
asir-2864	113	16	+	+	CCONJ
asir-2864	113	17	𝑖𝑞	𝑖𝑞	PROPN
asir-2864	113	18	2	2	NUM
asir-2864	113	19	)	)	PUNCT
asir-2864	113	20	0,5	0,5	NOUN
asir-2864	114	1	+	+	PUNCT
asir-2864	115	1	𝑑𝑝(1	𝑑𝑝(1	NOUN
asir-2864	115	2	+	+	NUM
asir-2864	115	3	𝑡𝑝	𝑡𝑝	ADJ
asir-2864	115	4	2	2	NUM
asir-2864	115	5	)	)	PUNCT
asir-2864	115	6	0,5	0,5	NOUN
asir-2864	115	7	=	=	PUNCT
asir-2864	116	1	−	−	PROPN
asir-2864	116	2	𝑘	𝑘	ADP
asir-2864	116	3	𝑣0𝑥	𝑣0𝑥	PUNCT
asir-2864	116	4	+	+	NOUN
asir-2864	116	5	𝑘	𝑘	DET
asir-2864	116	6	𝑣𝑜𝑥	𝑣𝑜𝑥	NOUN
asir-2864	116	7	=	=	NOUN
asir-2864	116	8	0	0	PUNCT
asir-2864	116	9	since	since	SCONJ
asir-2864	116	10	in	in	ADP
asir-2864	116	11	the	the	DET
asir-2864	116	12	parabola	parabola	NOUN
asir-2864	116	13	the	the	DET
asir-2864	116	14	horizontal	horizontal	ADJ
asir-2864	116	15	component	component	NOUN
asir-2864	116	16	is	be	AUX
asir-2864	116	17	constant	constant	ADJ
asir-2864	116	18	.	.	PUNCT
asir-2864	117	1	for	for	ADP
asir-2864	117	2	ellipse	ellipse	NOUN
asir-2864	117	3	and	and	CCONJ
asir-2864	117	4	hyperbola	hyperbola	PROPN
asir-2864	117	5	the	the	DET
asir-2864	117	6	expressions	expression	NOUN
asir-2864	117	7	become	become	VERB
asir-2864	117	8	very	very	ADV
asir-2864	117	9	complicated	complicated	ADJ
asir-2864	117	10	.	.	PUNCT
asir-2864	118	1	in	in	ADP
asir-2864	118	2	the	the	DET
asir-2864	118	3	case	case	NOUN
asir-2864	118	4	of	of	ADP
asir-2864	118	5	a	a	DET
asir-2864	118	6	force	force	NOUN
asir-2864	118	7	having	have	VERB
asir-2864	118	8	a	a	DET
asir-2864	118	9	constant	constant	ADJ
asir-2864	118	10	direction	direction	NOUN
asir-2864	118	11	we	we	PRON
asir-2864	118	12	can	can	AUX
asir-2864	118	13	prove	prove	VERB
asir-2864	118	14	that	that	SCONJ
asir-2864	118	15	this	this	DET
asir-2864	118	16	force	force	NOUN
asir-2864	118	17	is	be	AUX
asir-2864	118	18	constant	constant	ADJ
asir-2864	118	19	.	.	PUNCT
asir-2864	119	1	if	if	SCONJ
asir-2864	119	2	the	the	DET
asir-2864	119	3	parabola	parabola	NOUN
asir-2864	119	4	is	be	AUX
asir-2864	119	5	described	describe	VERB
asir-2864	119	6	by	by	ADP
asir-2864	119	7	the	the	DET
asir-2864	119	8	equation	equation	NOUN
asir-2864	119	9	y	y	PROPN
asir-2864	119	10	=	=	NOUN
asir-2864	119	11	a·x²	a·x²	PROPN
asir-2864	119	12	then	then	ADV
asir-2864	119	13	the	the	DET
asir-2864	119	14	radius	radius	NOUN
asir-2864	119	15	of	of	ADP
asir-2864	119	16	curvature	curvature	NOUN
asir-2864	119	17	is	be	AUX
asir-2864	119	18	𝜌	𝜌	ADP
asir-2864	119	19	=	=	SYM
asir-2864	119	20	|√1	|√1	PROPN
asir-2864	119	21	+	+	PROPN
asir-2864	119	22	(	(	PUNCT
asir-2864	119	23	𝑑𝑦	𝑑𝑦	NOUN
asir-2864	119	24	𝑑𝑥	𝑑𝑥	NOUN
asir-2864	119	25	)	)	PUNCT
asir-2864	119	26	2	2	NUM
asir-2864	120	1	|	|	ADV
asir-2864	120	2	3	3	NUM
asir-2864	120	3	|𝑑2𝑦/𝑑𝑥2	|𝑑2𝑦/𝑑𝑥2	NOUN
asir-2864	120	4	|	|	ADV
asir-2864	120	5	=	=	SYM
asir-2864	120	6	|√1+tan2	|√1+tan2	NUM
asir-2864	120	7	𝜔|	𝜔|	NOUN
asir-2864	120	8	3	3	NUM
asir-2864	120	9	2𝑎	2𝑎	NUM
asir-2864	120	10	=	=	SYM
asir-2864	120	11	1	1	NUM
asir-2864	120	12	2𝑎·cos3	2𝑎·cos3	NUM
asir-2864	120	13	𝜔	𝜔	ADP
asir-2864	120	14	where	where	SCONJ
asir-2864	120	15	ω	ω	NOUN
asir-2864	120	16	is	be	AUX
asir-2864	120	17	the	the	DET
asir-2864	120	18	angle	angle	NOUN
asir-2864	120	19	of	of	ADP
asir-2864	120	20	the	the	DET
asir-2864	120	21	tangent	tangent	NOUN
asir-2864	120	22	with	with	ADP
asir-2864	120	23	the	the	DET
asir-2864	120	24	horizontal	horizontal	NOUN
asir-2864	120	25	.	.	PUNCT
asir-2864	121	1	here	here	ADV
asir-2864	121	2	the	the	DET
asir-2864	121	3	horizontal	horizontal	ADJ
asir-2864	121	4	component	component	NOUN
asir-2864	121	5	of	of	ADP
asir-2864	121	6	the	the	DET
asir-2864	121	7	velocity	velocity	NOUN
asir-2864	121	8	remains	remain	VERB
asir-2864	121	9	constant	constant	ADJ
asir-2864	121	10	.	.	PUNCT
asir-2864	122	1	so	so	ADV
asir-2864	122	2	the	the	DET
asir-2864	122	3	velocity	velocity	NOUN
asir-2864	122	4	v	v	NOUN
asir-2864	122	5	is	be	AUX
asir-2864	122	6	found	find	VERB
asir-2864	122	7	from	from	ADP
asir-2864	122	8	ω	ω	NUM
asir-2864	122	9	by	by	ADP
asir-2864	122	10	v=	v=	PROPN
asir-2864	122	11	v0	v0	PROPN
asir-2864	122	12	/	/	SYM
asir-2864	122	13	cosω	cosω	NOUN
asir-2864	122	14	,	,	PUNCT
asir-2864	122	15	where	where	SCONJ
asir-2864	122	16	v0	v0	NOUN
asir-2864	122	17	is	be	AUX
asir-2864	122	18	the	the	DET
asir-2864	122	19	horizontal	horizontal	ADJ
asir-2864	122	20	component	component	NOUN
asir-2864	122	21	of	of	ADP
asir-2864	122	22	the	the	DET
asir-2864	122	23	velocity	velocity	NOUN
asir-2864	122	24	.	.	PUNCT
asir-2864	123	1	the	the	DET
asir-2864	123	2	law	law	NOUN
asir-2864	123	3	for	for	ADP
asir-2864	123	4	the	the	DET
asir-2864	123	5	force	force	NOUN
asir-2864	123	6	that	that	PRON
asir-2864	123	7	acts	act	VERB
asir-2864	123	8	on	on	ADP
asir-2864	123	9	the	the	DET
asir-2864	123	10	body	body	NOUN
asir-2864	123	11	is	be	AUX
asir-2864	123	12	found	find	VERB
asir-2864	123	13	by	by	ADP
asir-2864	123	14	:	:	PUNCT
asir-2864	123	15	𝐹	𝐹	PROPN
asir-2864	123	16	·	·	PUNCT
asir-2864	123	17	𝑐𝑜𝑠𝜔	𝑐𝑜𝑠𝜔	VERB
asir-2864	123	18	=	=	SYM
asir-2864	123	19	𝑚	𝑚	X
asir-2864	123	20	·	·	PUNCT
asir-2864	123	21	𝑉2	𝑉2	NOUN
asir-2864	123	22	𝜌	𝜌	X
asir-2864	123	23	=	=	SYM
asir-2864	123	24	2𝑎𝑚	2𝑎𝑚	NOUN
asir-2864	123	25	·	·	PUNCT
asir-2864	123	26	𝑉0	𝑉0	NOUN
asir-2864	123	27	2𝑐𝑜𝑠𝜔	2𝑐𝑜𝑠𝜔	NUM
asir-2864	123	28	so	so	CCONJ
asir-2864	123	29	f	f	PROPN
asir-2864	123	30	is	be	AUX
asir-2864	123	31	a	a	DET
asir-2864	123	32	constant	constant	ADJ
asir-2864	123	33	.	.	PUNCT
asir-2864	124	1	4.2	4.2	NUM
asir-2864	124	2	force	force	NOUN
asir-2864	124	3	directed	direct	VERB
asir-2864	124	4	to	to	ADP
asir-2864	124	5	a	a	DET
asir-2864	124	6	center	center	NOUN
asir-2864	124	7	in	in	ADP
asir-2864	124	8	this	this	DET
asir-2864	124	9	case	case	NOUN
asir-2864	124	10	the	the	DET
asir-2864	124	11	force	force	NOUN
asir-2864	124	12	is	be	AUX
asir-2864	124	13	directed	direct	VERB
asir-2864	124	14	to	to	ADP
asir-2864	124	15	the	the	DET
asir-2864	124	16	focus	focus	NOUN
asir-2864	124	17	.	.	PUNCT
asir-2864	125	1	the	the	DET
asir-2864	125	2	distance	distance	NOUN
asir-2864	125	3	r	r	NOUN
asir-2864	125	4	of	of	ADP
asir-2864	125	5	the	the	DET
asir-2864	125	6	point	point	NOUN
asir-2864	125	7	(	(	PUNCT
asir-2864	125	8	x	x	X
asir-2864	125	9	,	,	PUNCT
asir-2864	125	10	y	y	PROPN
asir-2864	125	11	)	)	PUNCT
asir-2864	125	12	on	on	ADP
asir-2864	125	13	the	the	DET
asir-2864	125	14	parabola	parabola	NOUN
asir-2864	125	15	from	from	ADP
asir-2864	125	16	the	the	DET
asir-2864	125	17	focus	focus	NOUN
asir-2864	125	18	is	be	AUX
asir-2864	125	19	found	find	VERB
asir-2864	125	20	to	to	PART
asir-2864	125	21	be	be	AUX
asir-2864	125	22	:	:	PUNCT
asir-2864	125	23	𝑟	𝑟	X
asir-2864	125	24	=	=	SYM
asir-2864	125	25	𝑎	𝑎	PRON
asir-2864	125	26	·	·	PUNCT
asir-2864	125	27	𝑥2	𝑥2	NOUN
asir-2864	125	28	+	+	CCONJ
asir-2864	125	29	1	1	NUM
asir-2864	125	30	4·𝑎	4·𝑎	NOUN
asir-2864	125	31	(	(	PUNCT
asir-2864	125	32	since	since	SCONJ
asir-2864	125	33	𝑦	𝑦	NOUN
asir-2864	125	34	=	=	SYM
asir-2864	125	35	𝑎	𝑎	PRON
asir-2864	125	36	·	·	PUNCT
asir-2864	125	37	𝑥2	𝑥2	NOUN
asir-2864	125	38	+	+	CCONJ
asir-2864	125	39	𝑐	𝑐	NOUN
asir-2864	125	40	,	,	PUNCT
asir-2864	125	41	𝑓	𝑓	PROPN
asir-2864	125	42	=	=	SYM
asir-2864	125	43	𝑐	𝑐	PROPN
asir-2864	125	44	+	+	NOUN
asir-2864	125	45	1	1	NUM
asir-2864	125	46	4·𝑎	4·𝑎	NOUN
asir-2864	125	47	)	)	PUNCT
asir-2864	125	48	.	.	PUNCT
asir-2864	126	1	the	the	DET
asir-2864	126	2	angle	angle	NOUN
asir-2864	126	3	θ	θ	PROPN
asir-2864	126	4	between	between	ADP
asir-2864	126	5	the	the	DET
asir-2864	126	6	r	r	NOUN
asir-2864	126	7	,	,	PUNCT
asir-2864	126	8	and	and	CCONJ
asir-2864	126	9	the	the	DET
asir-2864	126	10	perpendicular	perpendicular	NOUN
asir-2864	126	11	is	be	AUX
asir-2864	126	12	found	find	VERB
asir-2864	126	13	from	from	ADP
asir-2864	126	14	𝑐𝑜𝑠𝜃	𝑐𝑜𝑠𝜃	NOUN
asir-2864	126	15	=	=	PUNCT
asir-2864	126	16	(	(	PUNCT
asir-2864	126	17	𝑥	𝑥	NOUN
asir-2864	126	18	𝑟	𝑟	NOUN
asir-2864	126	19	,	,	PUNCT
asir-2864	126	20	𝑦−𝑓	𝑦−𝑓	PROPN
asir-2864	126	21	𝑟	𝑟	NOUN
asir-2864	126	22	)	)	PUNCT
asir-2864	126	23	·	·	PUNCT
asir-2864	127	1	(	(	PUNCT
asir-2864	127	2	𝑑𝑦	𝑑𝑦	ADP
asir-2864	127	3	𝑑𝑥	𝑑𝑥	ADP
asir-2864	127	4	√1	√1	ADV
asir-2864	127	5	+	+	ADJ
asir-2864	127	6	(	(	PUNCT
asir-2864	127	7	𝑑𝑦	𝑑𝑦	NOUN
asir-2864	127	8	𝑑𝑥	𝑑𝑥	NOUN
asir-2864	127	9	)	)	PUNCT
asir-2864	127	10	2	2	NUM
asir-2864	127	11	,	,	PUNCT
asir-2864	127	12	−	−	PROPN
asir-2864	127	13	1	1	NUM
asir-2864	127	14	√1	√1	ADJ
asir-2864	127	15	+	+	ADJ
asir-2864	127	16	(	(	PUNCT
asir-2864	127	17	𝑑𝑦	𝑑𝑦	NOUN
asir-2864	127	18	𝑑𝑥	𝑑𝑥	NOUN
asir-2864	127	19	)	)	PUNCT
asir-2864	127	20	2	2	NUM
asir-2864	127	21	)	)	PUNCT
asir-2864	127	22	=	=	SYM
asir-2864	128	1	1	1	NUM
asir-2864	128	2	√1	√1	PROPN
asir-2864	128	3	+	+	ADJ
asir-2864	128	4	(	(	PUNCT
asir-2864	128	5	𝑑𝑦	𝑑𝑦	NOUN
asir-2864	128	6	𝑑𝑥	𝑑𝑥	NOUN
asir-2864	128	7	)	)	SYM
asir-2864	128	8	2	2	NUM
asir-2864	128	9	,	,	PUNCT
asir-2864	128	10	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	VERB
asir-2864	128	11	applied	apply	VERB
asir-2864	128	12	science	science	NOUN
asir-2864	128	13	and	and	CCONJ
asir-2864	128	14	innovative	innovative	ADJ
asir-2864	128	15	research	research	NOUN
asir-2864	128	16	vol	vol	NOUN
asir-2864	128	17	.	.	PROPN
asir-2864	129	1	4	4	NUM
asir-2864	129	2	,	,	PUNCT
asir-2864	129	3	no	no	INTJ
asir-2864	129	4	.	.	NOUN
asir-2864	129	5	2	2	NUM
asir-2864	129	6	,	,	PUNCT
asir-2864	129	7	2020	2020	NUM
asir-2864	129	8	48	48	NUM
asir-2864	129	9	published	publish	VERB
asir-2864	129	10	by	by	ADP
asir-2864	129	11	scholink	scholink	PROPN
asir-2864	129	12	inc	inc	PROPN
asir-2864	129	13	.	.	PROPN
asir-2864	129	14	figure	figure	NOUN
asir-2864	129	15	6	6	NUM
asir-2864	129	16	.	.	PUNCT
asir-2864	129	17	parabolic	parabolic	ADJ
asir-2864	129	18	motion	motion	NOUN
asir-2864	129	19	with	with	ADP
asir-2864	129	20	a	a	DET
asir-2864	129	21	force	force	NOUN
asir-2864	129	22	directed	direct	VERB
asir-2864	129	23	towards	towards	ADP
asir-2864	129	24	the	the	DET
asir-2864	129	25	focus	focus	NOUN
asir-2864	129	26	and	and	CCONJ
asir-2864	129	27	proportional	proportional	ADJ
asir-2864	129	28	to	to	ADP
asir-2864	129	29	1	1	NUM
asir-2864	129	30	/	/	SYM
asir-2864	129	31	r	r	NOUN
asir-2864	129	32	2	2	NUM
asir-2864	129	33	since	since	SCONJ
asir-2864	129	34	this	this	DET
asir-2864	129	35	case	case	NOUN
asir-2864	129	36	the	the	DET
asir-2864	129	37	particle	particle	NOUN
asir-2864	129	38	stars	star	NOUN
asir-2864	129	39	with	with	ADP
asir-2864	129	40	zero	zero	NUM
asir-2864	129	41	velocity	velocity	NOUN
asir-2864	129	42	at	at	ADP
asir-2864	129	43	infinity	infinity	NOUN
asir-2864	129	44	and	and	CCONJ
asir-2864	129	45	gets	get	VERB
asir-2864	129	46	its	its	PRON
asir-2864	129	47	maximum	maximum	ADJ
asir-2864	129	48	velocity	velocity	NOUN
asir-2864	129	49	at	at	ADP
asir-2864	129	50	the	the	DET
asir-2864	129	51	apex	apex	NOUN
asir-2864	129	52	.	.	PUNCT
asir-2864	130	1	since	since	SCONJ
asir-2864	130	2	𝜌	𝜌	X
asir-2864	130	3	=	=	SYM
asir-2864	130	4	|√1	|√1	PROPN
asir-2864	130	5	+	+	PROPN
asir-2864	130	6	(	(	PUNCT
asir-2864	130	7	𝑑𝑦	𝑑𝑦	NOUN
asir-2864	130	8	𝑑𝑥	𝑑𝑥	NOUN
asir-2864	130	9	)	)	PUNCT
asir-2864	130	10	2	2	NUM
asir-2864	130	11	|	|	ADV
asir-2864	130	12	3	3	NUM
asir-2864	130	13	|	|	ADV
asir-2864	130	14	𝑑2𝑦	𝑑2𝑦	VERB
asir-2864	130	15	𝑑𝑥2|	𝑑𝑥2|	PROPN
asir-2864	130	16	=	=	PUNCT
asir-2864	130	17	1	1	NUM
asir-2864	130	18	⌊cos3	⌊cos3	NOUN
asir-2864	130	19	𝜃∙2𝑎⌋	𝜃∙2𝑎⌋	NOUN
asir-2864	130	20	we	we	PRON
asir-2864	130	21	see	see	VERB
asir-2864	130	22	that	that	SCONJ
asir-2864	130	23	𝐹𝑘	𝐹𝑘	PROPN
asir-2864	130	24	=	=	SYM
asir-2864	130	25	𝑚	𝑚	PROPN
asir-2864	130	26	·	·	PUNCT
asir-2864	130	27	𝑉2	𝑉2	NOUN
asir-2864	130	28	𝜌·𝑐𝑜𝑠𝜃	𝜌·𝑐𝑜𝑠𝜃	NOUN
asir-2864	131	1	=	=	SYM
asir-2864	131	2	𝑚∙𝑉𝑜	𝑚∙𝑉𝑜	NOUN
asir-2864	131	3	2	2	NUM
asir-2864	131	4	𝑟2∙𝜌∙cos3	𝑟2∙𝜌∙cos3	NUM
asir-2864	131	5	𝜃	𝜃	NUM
asir-2864	131	6	=	=	SYM
asir-2864	131	7	2𝑎∙𝑚∙𝑉0	2𝑎∙𝑚∙𝑉0	NUM
asir-2864	131	8	2	2	NUM
asir-2864	131	9	𝑟2	𝑟2	NOUN
asir-2864	131	10	and	and	CCONJ
asir-2864	131	11	so	so	ADV
asir-2864	131	12	𝐹_𝑘	𝐹_𝑘	PROPN
asir-2864	131	13	∝	∝	NOUN
asir-2864	131	14	1	1	NUM
asir-2864	131	15	𝑟2	𝑟2	NOUN
asir-2864	131	16	.	.	PUNCT
asir-2864	132	1	in	in	ADP
asir-2864	132	2	this	this	DET
asir-2864	132	3	case	case	NOUN
asir-2864	132	4	if	if	SCONJ
asir-2864	132	5	the	the	DET
asir-2864	132	6	particle	particle	NOUN
asir-2864	132	7	starts	start	VERB
asir-2864	132	8	with	with	ADP
asir-2864	132	9	zero	zero	NUM
asir-2864	132	10	velocity	velocity	NOUN
asir-2864	132	11	at	at	ADP
asir-2864	132	12	infinity	infinity	NOUN
asir-2864	132	13	and	and	CCONJ
asir-2864	132	14	has	have	VERB
asir-2864	132	15	maximum	maximum	ADJ
asir-2864	132	16	velocity	velocity	NOUN
asir-2864	132	17	at	at	ADP
asir-2864	132	18	the	the	DET
asir-2864	132	19	apex	apex	NOUN
asir-2864	132	20	.	.	PUNCT
asir-2864	133	1	5	5	X
asir-2864	133	2	.	.	X
asir-2864	133	3	circular	circular	ADJ
asir-2864	133	4	movements	movement	NOUN
asir-2864	133	5	5.1	5.1	NUM
asir-2864	133	6	circle	circle	NOUN
asir-2864	133	7	and	and	CCONJ
asir-2864	133	8	forces	force	NOUN
asir-2864	133	9	which	which	PRON
asir-2864	133	10	are	be	AUX
asir-2864	133	11	parallel	parallel	ADJ
asir-2864	133	12	in	in	ADP
asir-2864	133	13	this	this	DET
asir-2864	133	14	case	case	NOUN
asir-2864	133	15	a	a	DET
asir-2864	133	16	body	body	NOUN
asir-2864	133	17	describes	describe	VERB
asir-2864	133	18	a	a	DET
asir-2864	133	19	semicircle	semicircle	NOUN
asir-2864	133	20	under	under	ADP
asir-2864	133	21	the	the	DET
asir-2864	133	22	influence	influence	NOUN
asir-2864	133	23	of	of	ADP
asir-2864	133	24	a	a	DET
asir-2864	133	25	force	force	NOUN
asir-2864	133	26	which	which	PRON
asir-2864	133	27	has	have	VERB
asir-2864	133	28	a	a	DET
asir-2864	133	29	direction	direction	NOUN
asir-2864	133	30	parallel	parallel	NOUN
asir-2864	133	31	to	to	ADP
asir-2864	133	32	the	the	DET
asir-2864	133	33	y	y	PROPN
asir-2864	133	34	axis	axis	NOUN
asir-2864	133	35	(	(	PUNCT
asir-2864	133	36	figure	figure	NOUN
asir-2864	133	37	7	7	NUM
asir-2864	133	38	)	)	PUNCT
asir-2864	133	39	.	.	PUNCT
asir-2864	134	1	figure	figure	VERB
asir-2864	134	2	7	7	NUM
asir-2864	134	3	.	.	PUNCT
asir-2864	134	4	application	application	NOUN
asir-2864	134	5	of	of	ADP
asir-2864	134	6	newton	newton	PROPN
asir-2864	134	7	’s	’s	PART
asir-2864	134	8	ideas	idea	NOUN
asir-2864	134	9	for	for	ADP
asir-2864	134	10	a	a	DET
asir-2864	134	11	force	force	NOUN
asir-2864	134	12	parallel	parallel	ADJ
asir-2864	134	13	to	to	ADP
asir-2864	134	14	y	y	NOUN
asir-2864	134	15	-	-	PUNCT
asir-2864	134	16	axis	axis	NOUN
asir-2864	134	17	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2864	134	18	applied	apply	VERB
asir-2864	134	19	science	science	NOUN
asir-2864	134	20	and	and	CCONJ
asir-2864	134	21	innovative	innovative	ADJ
asir-2864	134	22	research	research	NOUN
asir-2864	134	23	vol	vol	NOUN
asir-2864	134	24	.	.	PROPN
asir-2864	135	1	4	4	NUM
asir-2864	135	2	,	,	PUNCT
asir-2864	135	3	no	no	INTJ
asir-2864	135	4	.	.	NOUN
asir-2864	135	5	2	2	NUM
asir-2864	135	6	,	,	PUNCT
asir-2864	135	7	2020	2020	NUM
asir-2864	135	8	49	49	NUM
asir-2864	135	9	published	publish	VERB
asir-2864	135	10	by	by	ADP
asir-2864	135	11	scholink	scholink	PROPN
asir-2864	135	12	inc	inc	PROPN
asir-2864	135	13	.	.	PROPN
asir-2864	135	14	in	in	ADP
asir-2864	135	15	this	this	DET
asir-2864	135	16	case	case	NOUN
asir-2864	135	17	newton	newton	PROPN
asir-2864	135	18	proves	prove	VERB
asir-2864	135	19	that	that	SCONJ
asir-2864	135	20	the	the	DET
asir-2864	135	21	force	force	NOUN
asir-2864	135	22	is	be	AUX
asir-2864	135	23	inversely	inversely	ADV
asir-2864	135	24	proportional	proportional	ADJ
asir-2864	135	25	to	to	ADP
asir-2864	135	26	y3	y3	NOUN
asir-2864	135	27	.	.	PUNCT
asir-2864	136	1	we	we	PRON
asir-2864	136	2	can	can	AUX
asir-2864	136	3	use	use	VERB
asir-2864	136	4	the	the	DET
asir-2864	136	5	constancy	constancy	NOUN
asir-2864	136	6	of	of	ADP
asir-2864	136	7	vx	vx	PROPN
asir-2864	136	8	to	to	PART
asir-2864	136	9	find	find	VERB
asir-2864	136	10	the	the	DET
asir-2864	136	11	centripetal	centripetal	ADJ
asir-2864	136	12	force	force	NOUN
asir-2864	136	13	.	.	PUNCT
asir-2864	137	1	if	if	SCONJ
asir-2864	137	2	v0	v0	NOUN
asir-2864	137	3	is	be	AUX
asir-2864	137	4	the	the	DET
asir-2864	137	5	velocity	velocity	NOUN
asir-2864	137	6	at	at	ADP
asir-2864	137	7	the	the	DET
asir-2864	137	8	highest	high	ADJ
asir-2864	137	9	point	point	NOUN
asir-2864	137	10	then	then	ADV
asir-2864	137	11	the	the	DET
asir-2864	137	12	horizontal	horizontal	ADJ
asir-2864	137	13	component	component	NOUN
asir-2864	137	14	of	of	ADP
asir-2864	137	15	the	the	DET
asir-2864	137	16	velocity	velocity	NOUN
asir-2864	137	17	v	v	NOUN
asir-2864	137	18	is	be	AUX
asir-2864	137	19	vx=	vx=	NOUN
asir-2864	137	20	v0	v0	NOUN
asir-2864	137	21	=	=	SYM
asir-2864	137	22	v	v	PROPN
asir-2864	137	23	·	·	PUNCT
asir-2864	137	24	cosω	cosω	NOUN
asir-2864	137	25	where	where	SCONJ
asir-2864	137	26	ω	ω	PROPN
asir-2864	137	27	is	be	AUX
asir-2864	137	28	the	the	DET
asir-2864	137	29	angle	angle	NOUN
asir-2864	137	30	of	of	ADP
asir-2864	137	31	the	the	DET
asir-2864	137	32	radius	radius	NOUN
asir-2864	137	33	at	at	ADP
asir-2864	137	34	the	the	DET
asir-2864	137	35	point	point	NOUN
asir-2864	137	36	p	p	NOUN
asir-2864	137	37	with	with	ADP
asir-2864	137	38	the	the	DET
asir-2864	137	39	perpendicular	perpendicular	NOUN
asir-2864	137	40	.	.	PUNCT
asir-2864	138	1	then	then	ADV
asir-2864	138	2	the	the	DET
asir-2864	138	3	centripetal	centripetal	ADJ
asir-2864	138	4	force	force	NOUN
asir-2864	138	5	for	for	ADP
asir-2864	138	6	the	the	DET
asir-2864	138	7	circular	circular	ADJ
asir-2864	138	8	movement	movement	NOUN
asir-2864	138	9	is	be	AUX
asir-2864	138	10	𝐹	𝐹	PROPN
asir-2864	138	11	·	·	PUNCT
asir-2864	138	12	𝑐𝑜𝑠𝜔	𝑐𝑜𝑠𝜔	X
asir-2864	138	13	=	=	SYM
asir-2864	138	14	𝑚·𝑉2	𝑚·𝑉2	PROPN
asir-2864	138	15	𝑅	𝑅	PROPN
asir-2864	138	16	=	=	NOUN
asir-2864	138	17	𝑚·𝑉0	𝑚·𝑉0	NOUN
asir-2864	138	18	2	2	NUM
asir-2864	138	19	𝑐𝑜𝑠2𝜔·𝑅	𝑐𝑜𝑠2𝜔·𝑅	PUNCT
asir-2864	138	20	.	.	PUNCT
asir-2864	139	1	thus	thus	ADV
asir-2864	139	2	𝐹	𝐹	PROPN
asir-2864	139	3	∝	∝	NOUN
asir-2864	139	4	1	1	NUM
asir-2864	139	5	𝑐𝑜𝑠3	𝑐𝑜𝑠3	NOUN
asir-2864	139	6	𝜔	𝜔	ADP
asir-2864	139	7	∝	∝	PROPN
asir-2864	139	8	1	1	NUM
asir-2864	139	9	𝑦3	𝑦3	PROPN
asir-2864	139	10	since	since	SCONJ
asir-2864	139	11	y	y	PROPN
asir-2864	139	12	=	=	SYM
asir-2864	139	13	r	r	NOUN
asir-2864	139	14	·	·	PUNCT
asir-2864	139	15	cosω	cosω	PROPN
asir-2864	139	16	newton	newton	PROPN
asir-2864	139	17	gives	give	VERB
asir-2864	139	18	examples	example	NOUN
asir-2864	139	19	of	of	ADP
asir-2864	139	20	circular	circular	ADJ
asir-2864	139	21	movements	movement	NOUN
asir-2864	139	22	as	as	ADP
asir-2864	139	23	an	an	DET
asir-2864	139	24	introduction	introduction	NOUN
asir-2864	139	25	for	for	ADP
asir-2864	139	26	the	the	DET
asir-2864	139	27	way	way	NOUN
asir-2864	139	28	to	to	PART
asir-2864	139	29	determine	determine	VERB
asir-2864	139	30	the	the	DET
asir-2864	139	31	centripetal	centripetal	ADJ
asir-2864	139	32	attraction	attraction	NOUN
asir-2864	139	33	from	from	ADP
asir-2864	139	34	the	the	DET
asir-2864	139	35	orbit	orbit	NOUN
asir-2864	139	36	.	.	PUNCT
asir-2864	140	1	his	his	PRON
asir-2864	140	2	examples	example	NOUN
asir-2864	140	3	can	can	AUX
asir-2864	140	4	be	be	AUX
asir-2864	140	5	also	also	ADV
asir-2864	140	6	used	use	VERB
asir-2864	140	7	to	to	PART
asir-2864	140	8	demonstrate	demonstrate	VERB
asir-2864	140	9	that	that	SCONJ
asir-2864	140	10	his	his	PRON
asir-2864	140	11	method	method	NOUN
asir-2864	140	12	for	for	ADP
asir-2864	140	13	finding	find	VERB
asir-2864	140	14	the	the	DET
asir-2864	140	15	center	center	NOUN
asir-2864	140	16	of	of	ADP
asir-2864	140	17	the	the	DET
asir-2864	140	18	force	force	NOUN
asir-2864	140	19	is	be	AUX
asir-2864	140	20	applicable	applicable	ADJ
asir-2864	140	21	to	to	ADP
asir-2864	140	22	these	these	DET
asir-2864	140	23	circular	circular	ADJ
asir-2864	140	24	orbits	orbit	NOUN
asir-2864	140	25	.	.	PUNCT
asir-2864	141	1	a	a	DET
asir-2864	141	2	body	body	NOUN
asir-2864	141	3	describes	describe	VERB
asir-2864	141	4	a	a	DET
asir-2864	141	5	semicircle	semicircle	NOUN
asir-2864	141	6	under	under	ADP
asir-2864	141	7	the	the	DET
asir-2864	141	8	influence	influence	NOUN
asir-2864	141	9	of	of	ADP
asir-2864	141	10	a	a	DET
asir-2864	141	11	force	force	NOUN
asir-2864	141	12	which	which	PRON
asir-2864	141	13	has	have	VERB
asir-2864	141	14	a	a	DET
asir-2864	141	15	direction	direction	NOUN
asir-2864	141	16	parallel	parallel	NOUN
asir-2864	141	17	to	to	ADP
asir-2864	141	18	the	the	DET
asir-2864	141	19	y	y	PROPN
asir-2864	141	20	axis	axis	NOUN
asir-2864	141	21	.	.	PUNCT
asir-2864	142	1	in	in	ADP
asir-2864	142	2	this	this	DET
asir-2864	142	3	case	case	NOUN
asir-2864	142	4	newton	newton	PROPN
asir-2864	142	5	proves	prove	VERB
asir-2864	142	6	that	that	SCONJ
asir-2864	142	7	the	the	DET
asir-2864	142	8	force	force	NOUN
asir-2864	142	9	is	be	AUX
asir-2864	142	10	inversely	inversely	ADV
asir-2864	142	11	proportional	proportional	ADJ
asir-2864	142	12	to	to	ADP
asir-2864	142	13	y3	y3	NOUN
asir-2864	142	14	.	.	PUNCT
asir-2864	143	1	we	we	PRON
asir-2864	143	2	can	can	AUX
asir-2864	143	3	use	use	VERB
asir-2864	143	4	the	the	DET
asir-2864	143	5	constancy	constancy	NOUN
asir-2864	143	6	of	of	ADP
asir-2864	143	7	vx	vx	PROPN
asir-2864	143	8	to	to	PART
asir-2864	143	9	find	find	VERB
asir-2864	143	10	the	the	DET
asir-2864	143	11	centripetal	centripetal	ADJ
asir-2864	143	12	force	force	NOUN
asir-2864	143	13	.	.	PUNCT
asir-2864	144	1	if	if	SCONJ
asir-2864	144	2	v0	v0	NOUN
asir-2864	144	3	is	be	AUX
asir-2864	144	4	the	the	DET
asir-2864	144	5	velocity	velocity	NOUN
asir-2864	144	6	at	at	ADP
asir-2864	144	7	the	the	DET
asir-2864	144	8	highest	high	ADJ
asir-2864	144	9	point	point	NOUN
asir-2864	144	10	then	then	ADV
asir-2864	144	11	the	the	DET
asir-2864	144	12	horizontal	horizontal	ADJ
asir-2864	144	13	component	component	NOUN
asir-2864	144	14	of	of	ADP
asir-2864	144	15	the	the	DET
asir-2864	144	16	velocity	velocity	NOUN
asir-2864	144	17	v	v	NOUN
asir-2864	144	18	is	be	AUX
asir-2864	144	19	vx	vx	ADP
asir-2864	144	20	=	=	PROPN
asir-2864	144	21	v0	v0	NOUN
asir-2864	144	22	=	=	SYM
asir-2864	144	23	v*sinω	v*sinω	X
asir-2864	144	24	where	where	SCONJ
asir-2864	144	25	ω	ω	PROPN
asir-2864	144	26	is	be	AUX
asir-2864	144	27	the	the	DET
asir-2864	144	28	angle	angle	NOUN
asir-2864	144	29	of	of	ADP
asir-2864	144	30	the	the	DET
asir-2864	144	31	radius	radius	NOUN
asir-2864	144	32	at	at	ADP
asir-2864	144	33	the	the	DET
asir-2864	144	34	point	point	NOUN
asir-2864	144	35	p	p	NOUN
asir-2864	144	36	with	with	ADP
asir-2864	144	37	the	the	DET
asir-2864	144	38	horizontal	horizontal	NOUN
asir-2864	144	39	.	.	PUNCT
asir-2864	145	1	then	then	ADV
asir-2864	145	2	the	the	DET
asir-2864	145	3	centripetal	centripetal	ADJ
asir-2864	145	4	force	force	NOUN
asir-2864	145	5	for	for	ADP
asir-2864	145	6	the	the	DET
asir-2864	145	7	circular	circular	ADJ
asir-2864	145	8	movement	movement	NOUN
asir-2864	145	9	is	be	AUX
asir-2864	145	10	𝐹	𝐹	PROPN
asir-2864	145	11	∙	∙	NOUN
asir-2864	145	12	𝑠𝑖𝑛𝜔	𝑠𝑖𝑛𝜔	NOUN
asir-2864	146	1	=	=	PRON
asir-2864	146	2	𝑚𝑉2	𝑚𝑉2	PROPN
asir-2864	146	3	𝑅	𝑅	PROPN
asir-2864	146	4	=	=	PUNCT
asir-2864	146	5	𝑚𝑉0	𝑚𝑉0	PROPN
asir-2864	146	6	2	2	NUM
asir-2864	146	7	sin2	sin2	NOUN
asir-2864	146	8	𝜔∙𝑅	𝜔∙𝑅	PUNCT
asir-2864	146	9	so	so	ADV
asir-2864	146	10	f	f	X
asir-2864	146	11	~1	~1	ADV
asir-2864	146	12	/	/	SYM
asir-2864	146	13	sinω3	sinω3	ADJ
asir-2864	146	14	~1	~1	NOUN
asir-2864	146	15	/	/	SYM
asir-2864	146	16	y3	y3	NOUN
asir-2864	146	17	,	,	PUNCT
asir-2864	146	18	since	since	SCONJ
asir-2864	146	19	y	y	PROPN
asir-2864	146	20	=	=	SYM
asir-2864	146	21	r·sinω	r·sinω	PROPN
asir-2864	146	22	.	.	NOUN
asir-2864	147	1	5.2	5.2	NUM
asir-2864	147	2	attractive	attractive	ADJ
asir-2864	147	3	force	force	NOUN
asir-2864	147	4	towards	towards	ADP
asir-2864	147	5	a	a	DET
asir-2864	147	6	point	point	NOUN
asir-2864	147	7	on	on	ADP
asir-2864	147	8	a	a	DET
asir-2864	147	9	circumference	circumference	NOUN
asir-2864	147	10	figure	figure	NOUN
asir-2864	147	11	8	8	NUM
asir-2864	147	12	.	.	PUNCT
asir-2864	147	13	application	application	NOUN
asir-2864	147	14	of	of	ADP
asir-2864	147	15	newton	newton	PROPN
asir-2864	147	16	’s	’s	PART
asir-2864	147	17	ideas	idea	NOUN
asir-2864	147	18	for	for	ADP
asir-2864	147	19	the	the	DET
asir-2864	147	20	case	case	NOUN
asir-2864	147	21	of	of	ADP
asir-2864	147	22	force	force	NOUN
asir-2864	147	23	directed	direct	VERB
asir-2864	147	24	to	to	ADP
asir-2864	147	25	a	a	DET
asir-2864	147	26	point	point	NOUN
asir-2864	147	27	on	on	ADP
asir-2864	147	28	the	the	DET
asir-2864	147	29	circumference	circumference	NOUN
asir-2864	147	30	a	a	DET
asir-2864	147	31	circular	circular	ADJ
asir-2864	147	32	(	(	PUNCT
asir-2864	147	33	almost	almost	ADV
asir-2864	147	34	)	)	PUNCT
asir-2864	147	35	orbit	orbit	NOUN
asir-2864	147	36	under	under	ADP
asir-2864	147	37	the	the	DET
asir-2864	147	38	influence	influence	NOUN
asir-2864	147	39	of	of	ADP
asir-2864	147	40	a	a	DET
asir-2864	147	41	force	force	NOUN
asir-2864	147	42	directed	direct	VERB
asir-2864	147	43	to	to	ADP
asir-2864	147	44	a	a	DET
asir-2864	147	45	point	point	NOUN
asir-2864	147	46	directed	direct	VERB
asir-2864	147	47	to	to	ADP
asir-2864	147	48	a	a	DET
asir-2864	147	49	point	point	NOUN
asir-2864	147	50	on	on	ADP
asir-2864	147	51	the	the	DET
asir-2864	147	52	circumference	circumference	NOUN
asir-2864	147	53	.	.	PUNCT
asir-2864	148	1	in	in	ADP
asir-2864	148	2	this	this	DET
asir-2864	148	3	case	case	NOUN
asir-2864	148	4	the	the	DET
asir-2864	148	5	force	force	NOUN
asir-2864	148	6	is	be	AUX
asir-2864	148	7	proportional	proportional	ADJ
asir-2864	148	8	to	to	ADP
asir-2864	148	9	the	the	DET
asir-2864	148	10	inverse	inverse	NOUN
asir-2864	148	11	of	of	ADP
asir-2864	148	12	the	the	DET
asir-2864	148	13	5th	5th	ADJ
asir-2864	148	14	power	power	NOUN
asir-2864	148	15	of	of	ADP
asir-2864	148	16	the	the	DET
asir-2864	148	17	distance	distance	NOUN
asir-2864	148	18	sr	sr	PROPN
asir-2864	148	19	of	of	ADP
asir-2864	148	20	the	the	DET
asir-2864	148	21	body	body	NOUN
asir-2864	148	22	r	r	NOUN
asir-2864	148	23	from	from	ADP
asir-2864	148	24	the	the	DET
asir-2864	148	25	center	center	NOUN
asir-2864	148	26	of	of	ADP
asir-2864	148	27	force	force	NOUN
asir-2864	148	28	s.	s.	PROPN
asir-2864	148	29	here	here	ADV
asir-2864	148	30	we	we	PRON
asir-2864	148	31	apply	apply	VERB
asir-2864	148	32	the	the	DET
asir-2864	148	33	law	law	NOUN
asir-2864	148	34	of	of	ADP
asir-2864	148	35	constant	constant	ADJ
asir-2864	148	36	angular	angular	ADJ
asir-2864	148	37	momentum	momentum	NOUN
asir-2864	148	38	:	:	PUNCT
asir-2864	148	39	in	in	ADP
asir-2864	148	40	the	the	DET
asir-2864	148	41	highest	high	ADJ
asir-2864	148	42	point	point	NOUN
asir-2864	148	43	v	v	NOUN
asir-2864	148	44	=	=	SYM
asir-2864	148	45	v0	v0	NOUN
asir-2864	148	46	so	so	ADV
asir-2864	148	47	𝑚	𝑚	PROPN
asir-2864	148	48	·	·	PUNCT
asir-2864	148	49	𝑉0	𝑉0	NOUN
asir-2864	148	50	∙	∙	PROPN
asir-2864	148	51	2	2	NUM
asir-2864	148	52	·	·	PUNCT
asir-2864	148	53	𝜌	𝜌	ADP
asir-2864	148	54	=	=	SYM
asir-2864	148	55	𝑚𝑉	𝑚𝑉	PROPN
asir-2864	148	56	·	·	PUNCT
asir-2864	148	57	𝑟	𝑟	X
asir-2864	148	58	·	·	PUNCT
asir-2864	148	59	𝑐𝑜𝑠𝜃	𝑐𝑜𝑠𝜃	NOUN
asir-2864	148	60	where	where	SCONJ
asir-2864	148	61	θ	θ	PROPN
asir-2864	148	62	is	be	AUX
asir-2864	148	63	the	the	DET
asir-2864	148	64	angle	angle	NOUN
asir-2864	148	65	of	of	ADP
asir-2864	148	66	the	the	DET
asir-2864	148	67	r	r	NOUN
asir-2864	148	68	=	=	SYM
asir-2864	148	69	sr=2ρcosθ	sr=2ρcosθ	PROPN
asir-2864	148	70	with	with	ADP
asir-2864	148	71	the	the	DET
asir-2864	148	72	radius	radius	NOUN
asir-2864	148	73	ρ	ρ	NOUN
asir-2864	148	74	at	at	ADP
asir-2864	148	75	point	point	NOUN
asir-2864	148	76	r.	r.	PROPN
asir-2864	149	1	the	the	DET
asir-2864	149	2	component	component	NOUN
asir-2864	149	3	of	of	ADP
asir-2864	149	4	f	f	PROPN
asir-2864	149	5	o	o	NOUN
asir-2864	149	6	r	r	NOUN
asir-2864	149	7	is	be	AUX
asir-2864	149	8	the	the	DET
asir-2864	149	9	centripetal	centripetal	ADJ
asir-2864	149	10	force	force	NOUN
asir-2864	149	11	so	so	ADV
asir-2864	149	12	mv2	mv2	PROPN
asir-2864	149	13	/	/	SYM
asir-2864	149	14	ρ	ρ	NOUN
asir-2864	149	15	=	=	SYM
asir-2864	149	16	f·cosθ	f·cosθ	X
asir-2864	149	17	or	or	CCONJ
asir-2864	149	18	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2864	149	19	applied	apply	VERB
asir-2864	149	20	science	science	NOUN
asir-2864	149	21	and	and	CCONJ
asir-2864	149	22	innovative	innovative	ADJ
asir-2864	149	23	research	research	NOUN
asir-2864	149	24	vol	vol	NOUN
asir-2864	149	25	.	.	PROPN
asir-2864	150	1	4	4	NUM
asir-2864	150	2	,	,	PUNCT
asir-2864	150	3	no	no	INTJ
asir-2864	150	4	.	.	NOUN
asir-2864	150	5	2	2	NUM
asir-2864	150	6	,	,	PUNCT
asir-2864	150	7	2020	2020	NUM
asir-2864	150	8	50	50	NUM
asir-2864	150	9	published	publish	VERB
asir-2864	150	10	by	by	ADP
asir-2864	150	11	scholink	scholink	PROPN
asir-2864	150	12	inc	inc	PROPN
asir-2864	150	13	.	.	PROPN
asir-2864	151	1	mv0	mv0	VERB
asir-2864	151	2	2/(2ρ*cos2θ)=	2/(2ρ*cos2θ)=	PROPN
asir-2864	151	3	f*cosθ	f*cosθ	PUNCT
asir-2864	151	4	so	so	ADV
asir-2864	151	5	𝐹~	𝐹~	NOUN
asir-2864	151	6	1	1	NUM
asir-2864	151	7	𝑐𝑜𝑠𝜃3	𝑐𝑜𝑠𝜃3	NOUN
asir-2864	151	8	~	~	SYM
asir-2864	151	9	1	1	NUM
asir-2864	151	10	𝑆𝑅3	𝑆𝑅3	PROPN
asir-2864	151	11	.	.	PUNCT
asir-2864	152	1	5.3	5.3	NUM
asir-2864	152	2	circular	circular	ADJ
asir-2864	152	3	orbit	orbit	NOUN
asir-2864	152	4	with	with	ADP
asir-2864	152	5	the	the	DET
asir-2864	152	6	center	center	NOUN
asir-2864	152	7	of	of	ADP
asir-2864	152	8	the	the	DET
asir-2864	152	9	force	force	NOUN
asir-2864	152	10	inside	inside	ADP
asir-2864	152	11	the	the	DET
asir-2864	152	12	circle	circle	NOUN
asir-2864	152	13	a	a	DET
asir-2864	152	14	circular	circular	ADJ
asir-2864	152	15	orbit	orbit	NOUN
asir-2864	152	16	on	on	ADP
asir-2864	152	17	a	a	DET
asir-2864	152	18	center	center	NOUN
asir-2864	152	19	which	which	PRON
asir-2864	152	20	is	be	AUX
asir-2864	152	21	inside	inside	ADP
asir-2864	152	22	the	the	DET
asir-2864	152	23	circle	circle	NOUN
asir-2864	152	24	.	.	PUNCT
asir-2864	153	1	in	in	ADP
asir-2864	153	2	this	this	DET
asir-2864	153	3	case	case	NOUN
asir-2864	153	4	the	the	DET
asir-2864	153	5	force	force	NOUN
asir-2864	153	6	is	be	AUX
asir-2864	153	7	expressed	express	VERB
asir-2864	153	8	as	as	ADP
asir-2864	153	9	𝐹	𝐹	PROPN
asir-2864	153	10	=	=	PROPN
asir-2864	153	11	𝑘	𝑘	PROPN
asir-2864	153	12	𝑅𝑉3∗𝑆𝑅2	𝑅𝑉3∗𝑆𝑅2	PROPN
asir-2864	153	13	where	where	SCONJ
asir-2864	153	14	sr	sr	PROPN
asir-2864	153	15	is	be	AUX
asir-2864	153	16	the	the	DET
asir-2864	153	17	distance	distance	NOUN
asir-2864	153	18	of	of	ADP
asir-2864	153	19	the	the	DET
asir-2864	153	20	center	center	NOUN
asir-2864	153	21	of	of	ADP
asir-2864	153	22	force	force	NOUN
asir-2864	153	23	s	s	VERB
asir-2864	153	24	from	from	ADP
asir-2864	153	25	the	the	DET
asir-2864	153	26	body	body	NOUN
asir-2864	153	27	r	r	NOUN
asir-2864	153	28	and	and	CCONJ
asir-2864	153	29	rv	rv	PROPN
asir-2864	153	30	is	be	AUX
asir-2864	153	31	the	the	DET
asir-2864	153	32	distance	distance	NOUN
asir-2864	153	33	of	of	ADP
asir-2864	153	34	the	the	DET
asir-2864	153	35	body	body	NOUN
asir-2864	153	36	p	p	NOUN
asir-2864	153	37	from	from	ADP
asir-2864	153	38	the	the	DET
asir-2864	153	39	point	point	NOUN
asir-2864	153	40	v	v	ADP
asir-2864	153	41	found	find	VERB
asir-2864	153	42	by	by	ADP
asir-2864	153	43	extending	extend	VERB
asir-2864	153	44	the	the	DET
asir-2864	153	45	line	line	NOUN
asir-2864	153	46	sr	sr	PROPN
asir-2864	153	47	and	and	CCONJ
asir-2864	153	48	finding	find	VERB
asir-2864	153	49	the	the	DET
asir-2864	153	50	point	point	NOUN
asir-2864	153	51	v	v	NOUN
asir-2864	153	52	on	on	ADP
asir-2864	153	53	the	the	DET
asir-2864	153	54	circle	circle	NOUN
asir-2864	153	55	.	.	PUNCT
asir-2864	154	1	again	again	ADV
asir-2864	154	2	here	here	ADV
asir-2864	154	3	𝑣	𝑣	ADP
asir-2864	154	4	=	=	PUNCT
asir-2864	154	5	𝑉0	𝑉0	NOUN
asir-2864	154	6	∙	∙	PROPN
asir-2864	154	7	𝜌	𝜌	ADP
asir-2864	154	8	∙	∙	PROPN
asir-2864	154	9	1+𝛼	1+𝛼	NUM
asir-2864	154	10	𝑆𝑃∙𝑠𝑖𝑛𝜀	𝑆𝑃∙𝑠𝑖𝑛𝜀	ADJ
asir-2864	154	11	if	if	SCONJ
asir-2864	154	12	ε	ε	PROPN
asir-2864	154	13	is	be	AUX
asir-2864	154	14	the	the	DET
asir-2864	154	15	angle	angle	NOUN
asir-2864	154	16	of	of	ADP
asir-2864	154	17	the	the	DET
asir-2864	154	18	velocity	velocity	NOUN
asir-2864	154	19	at	at	ADP
asir-2864	154	20	r	r	NOUN
asir-2864	154	21	with	with	ADP
asir-2864	154	22	sr	sr	PROPN
asir-2864	154	23	then	then	ADV
asir-2864	154	24	𝐹	𝐹	PROPN
asir-2864	154	25	∙	∙	PROPN
asir-2864	154	26	𝑠𝑖𝑛𝜀	𝑠𝑖𝑛𝜀	NOUN
asir-2864	154	27	=	=	PUNCT
asir-2864	155	1	𝑚∙𝑉0	𝑚∙𝑉0	PROPN
asir-2864	155	2	2(1+𝛼)2	2(1+𝛼)2	NUM
asir-2864	155	3	(	(	PUNCT
asir-2864	155	4	𝑆𝑅∙𝑠𝑖𝑛𝜀)2	𝑆𝑅∙𝑠𝑖𝑛𝜀)2	ADJ
asir-2864	155	5	𝑠𝑖𝑛𝜀	𝑠𝑖𝑛𝜀	NOUN
asir-2864	155	6	=	=	SYM
asir-2864	155	7	𝑅𝑉	𝑅𝑉	NOUN
asir-2864	155	8	2𝜌	2𝜌	NOUN
asir-2864	155	9	.	.	PUNCT
asir-2864	156	1	by	by	ADP
asir-2864	156	2	combining	combine	VERB
asir-2864	156	3	these	these	PRON
asir-2864	156	4	we	we	PRON
asir-2864	156	5	find	find	VERB
asir-2864	156	6	that	that	SCONJ
asir-2864	156	7	𝐹~	𝐹~	NOUN
asir-2864	156	8	1	1	NUM
asir-2864	156	9	𝑆𝑅2∗𝑅𝑉^3	𝑆𝑅2∗𝑅𝑉^3	NOUN
asir-2864	156	10	.	.	PUNCT
asir-2864	157	1	6	6	X
asir-2864	157	2	.	.	X
asir-2864	157	3	newton	newton	PROPN
asir-2864	157	4	’s	’s	PART
asir-2864	157	5	isogonal	isogonal	ADJ
asir-2864	157	6	spiral	spiral	ADJ
asir-2864	157	7	figure	figure	NOUN
asir-2864	157	8	9	9	NUM
asir-2864	157	9	.	.	PUNCT
asir-2864	157	10	application	application	NOUN
asir-2864	157	11	of	of	ADP
asir-2864	157	12	newton	newton	PROPN
asir-2864	157	13	’s	’s	PART
asir-2864	157	14	ideas	idea	NOUN
asir-2864	157	15	for	for	ADP
asir-2864	157	16	a	a	DET
asir-2864	157	17	force	force	NOUN
asir-2864	157	18	directed	direct	VERB
asir-2864	157	19	to	to	ADP
asir-2864	157	20	a	a	DET
asir-2864	157	21	center	center	NOUN
asir-2864	157	22	not	not	PART
asir-2864	157	23	on	on	ADP
asir-2864	157	24	the	the	DET
asir-2864	157	25	circumference	circumference	NOUN
asir-2864	157	26	figure	figure	NOUN
asir-2864	157	27	10	10	NUM
asir-2864	157	28	.	.	PUNCT
asir-2864	158	1	application	application	NOUN
asir-2864	158	2	of	of	ADP
asir-2864	158	3	newton	newton	PROPN
asir-2864	158	4	’s	’s	PART
asir-2864	158	5	ideas	idea	NOUN
asir-2864	158	6	for	for	ADP
asir-2864	158	7	a	a	DET
asir-2864	158	8	movement	movement	NOUN
asir-2864	158	9	under	under	ADP
asir-2864	158	10	the	the	DET
asir-2864	158	11	influence	influence	NOUN
asir-2864	158	12	of	of	ADP
asir-2864	158	13	a	a	DET
asir-2864	158	14	force	force	NOUN
asir-2864	158	15	directed	direct	VERB
asir-2864	158	16	towards	towards	ADP
asir-2864	158	17	the	the	DET
asir-2864	158	18	origin	origin	NOUN
asir-2864	158	19	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2864	158	20	applied	apply	VERB
asir-2864	158	21	science	science	NOUN
asir-2864	158	22	and	and	CCONJ
asir-2864	158	23	innovative	innovative	ADJ
asir-2864	158	24	research	research	NOUN
asir-2864	158	25	vol	vol	NOUN
asir-2864	158	26	.	.	PROPN
asir-2864	159	1	4	4	NUM
asir-2864	159	2	,	,	PUNCT
asir-2864	159	3	no	no	INTJ
asir-2864	159	4	.	.	NOUN
asir-2864	159	5	2	2	NUM
asir-2864	159	6	,	,	PUNCT
asir-2864	159	7	2020	2020	NUM
asir-2864	159	8	51	51	NUM
asir-2864	159	9	published	publish	VERB
asir-2864	159	10	by	by	ADP
asir-2864	159	11	scholink	scholink	PROPN
asir-2864	159	12	inc	inc	PROPN
asir-2864	159	13	.	.	PUNCT
asir-2864	160	1	the	the	DET
asir-2864	160	2	last	last	ADJ
asir-2864	160	3	application	application	NOUN
asir-2864	160	4	of	of	ADP
asir-2864	160	5	the	the	DET
asir-2864	160	6	ideas	idea	NOUN
asir-2864	160	7	is	be	AUX
asir-2864	160	8	on	on	ADP
asir-2864	160	9	newton	newton	PROPN
asir-2864	160	10	’s	’s	PART
asir-2864	160	11	isogonal	isogonal	ADJ
asir-2864	160	12	spiral	spiral	NOUN
asir-2864	160	13	which	which	PRON
asir-2864	160	14	is	be	AUX
asir-2864	160	15	proposition	proposition	NOUN
asir-2864	160	16	9	9	NUM
asir-2864	160	17	problem	problem	NOUN
asir-2864	160	18	3	3	NUM
asir-2864	160	19	let	let	VERB
asir-2864	160	20	a	a	DET
asir-2864	160	21	body	body	NOUN
asir-2864	160	22	revolve	revolve	NOUN
asir-2864	160	23	in	in	ADP
asir-2864	160	24	a	a	DET
asir-2864	160	25	spiral	spiral	ADJ
asir-2864	160	26	pqs	pqs	NOUN
asir-2864	160	27	intersection	intersection	NOUN
asir-2864	160	28	all	all	DET
asir-2864	160	29	its	its	PRON
asir-2864	160	30	radii	radii	NOUN
asir-2864	160	31	sp	sp	NOUN
asir-2864	160	32	,	,	PUNCT
asir-2864	160	33	sq	sq	ADJ
asir-2864	160	34	,	,	PUNCT
asir-2864	160	35	…	…	PUNCT
asir-2864	160	36	of	of	ADP
asir-2864	160	37	a	a	DET
asir-2864	160	38	given	give	VERB
asir-2864	160	39	angle	angle	NOUN
asir-2864	160	40	;	;	PUNCT
asir-2864	160	41	it	it	PRON
asir-2864	160	42	is	be	AUX
asir-2864	160	43	required	require	VERB
asir-2864	160	44	to	to	PART
asir-2864	160	45	find	find	VERB
asir-2864	160	46	the	the	DET
asir-2864	160	47	law	law	NOUN
asir-2864	160	48	of	of	ADP
asir-2864	160	49	the	the	DET
asir-2864	160	50	centripetal	centripetal	ADJ
asir-2864	160	51	force	force	NOUN
asir-2864	160	52	tending	tend	VERB
asir-2864	160	53	toward	toward	ADP
asir-2864	160	54	the	the	DET
asir-2864	160	55	center	center	NOUN
asir-2864	160	56	of	of	ADP
asir-2864	160	57	the	the	DET
asir-2864	160	58	spiral	spiral	NOUN
asir-2864	160	59	.	.	PUNCT
asir-2864	161	1	we	we	PRON
asir-2864	161	2	can	can	AUX
asir-2864	161	3	prove	prove	VERB
asir-2864	161	4	that	that	SCONJ
asir-2864	161	5	the	the	DET
asir-2864	161	6	force	force	NOUN
asir-2864	161	7	is	be	AUX
asir-2864	161	8	proportional	proportional	ADJ
asir-2864	161	9	to	to	ADP
asir-2864	161	10	r-2	r-2	NUM
asir-2864	161	11	where	where	SCONJ
asir-2864	161	12	r	r	NOUN
asir-2864	161	13	is	be	AUX
asir-2864	161	14	the	the	DET
asir-2864	161	15	distance	distance	NOUN
asir-2864	161	16	of	of	ADP
asir-2864	161	17	the	the	DET
asir-2864	161	18	point	point	NOUN
asir-2864	161	19	to	to	ADP
asir-2864	161	20	the	the	DET
asir-2864	161	21	point	point	NOUN
asir-2864	161	22	s.	s.	PROPN
asir-2864	161	23	we	we	PRON
asir-2864	161	24	apply	apply	VERB
asir-2864	161	25	again	again	ADV
asir-2864	161	26	the	the	DET
asir-2864	161	27	law	law	NOUN
asir-2864	161	28	of	of	ADP
asir-2864	161	29	areas	area	NOUN
asir-2864	161	30	and	and	CCONJ
asir-2864	161	31	if	if	SCONJ
asir-2864	161	32	at	at	ADP
asir-2864	161	33	an	an	DET
asir-2864	161	34	initial	initial	ADJ
asir-2864	161	35	point	point	NOUN
asir-2864	161	36	the	the	DET
asir-2864	161	37	velocity	velocity	NOUN
asir-2864	161	38	is	be	AUX
asir-2864	161	39	v0	v0	NOUN
asir-2864	161	40	and	and	CCONJ
asir-2864	161	41	the	the	DET
asir-2864	161	42	initial	initial	ADJ
asir-2864	161	43	radius	radius	NOUN
asir-2864	161	44	of	of	ADP
asir-2864	161	45	curvature	curvature	NOUN
asir-2864	161	46	is	be	AUX
asir-2864	161	47	ρ0	ρ0	PROPN
asir-2864	161	48	then	then	ADV
asir-2864	161	49	at	at	ADP
asir-2864	161	50	the	the	DET
asir-2864	161	51	point	point	NOUN
asir-2864	161	52	z	z	NOUN
asir-2864	161	53	ρ·v	ρ·v	NOUN
asir-2864	161	54	=	=	SYM
asir-2864	161	55	ρ0·v0	ρ0·v0	PROPN
asir-2864	161	56	to	to	PART
asir-2864	161	57	find	find	VERB
asir-2864	161	58	the	the	DET
asir-2864	161	59	law	law	NOUN
asir-2864	161	60	of	of	ADP
asir-2864	161	61	the	the	DET
asir-2864	161	62	force	force	NOUN
asir-2864	161	63	we	we	PRON
asir-2864	161	64	note	note	VERB
asir-2864	161	65	that	that	SCONJ
asir-2864	161	66	the	the	DET
asir-2864	161	67	centripetal	centripetal	ADJ
asir-2864	161	68	force	force	NOUN
asir-2864	161	69	will	will	AUX
asir-2864	161	70	be	be	AUX
asir-2864	161	71	f·sinε	f·sinε	PROPN
asir-2864	161	72	=	=	PRON
asir-2864	161	73	m·v2	m·v2	PROPN
asir-2864	161	74	/	/	SYM
asir-2864	161	75	ρ	ρ	PROPN
asir-2864	161	76	=	=	SYM
asir-2864	161	77	m·v0	m·v0	ADJ
asir-2864	161	78	2	2	NUM
asir-2864	162	1	ρ0²/ρ	ρ0²/ρ	ADP
asir-2864	162	2	3	3	X
asir-2864	162	3	.	.	PUNCT
asir-2864	163	1	since	since	SCONJ
asir-2864	163	2	the	the	DET
asir-2864	163	3	radius	radius	NOUN
asir-2864	163	4	of	of	ADP
asir-2864	163	5	curvature	curvature	NOUN
asir-2864	163	6	is	be	AUX
asir-2864	163	7	ρ	ρ	NOUN
asir-2864	163	8	=	=	SYM
asir-2864	163	9	r	r	NOUN
asir-2864	163	10	/	/	SYM
asir-2864	163	11	sinε	sinε	NOUN
asir-2864	163	12	and	and	CCONJ
asir-2864	163	13	we	we	PRON
asir-2864	163	14	find	find	VERB
asir-2864	163	15	that	that	SCONJ
asir-2864	163	16	𝐹~1/𝑟3	𝐹~1/𝑟3	NOUN
asir-2864	163	17	.	.	PUNCT
asir-2864	164	1	7	7	X
asir-2864	164	2	.	.	X
asir-2864	164	3	fixing	fix	VERB
asir-2864	164	4	the	the	DET
asir-2864	164	5	velocities	velocity	NOUN
asir-2864	164	6	in	in	ADP
asir-2864	164	7	excel	excel	NOUN
asir-2864	164	8	to	to	PART
asir-2864	164	9	move	move	VERB
asir-2864	164	10	the	the	DET
asir-2864	164	11	body	body	NOUN
asir-2864	164	12	around	around	ADP
asir-2864	164	13	we	we	PRON
asir-2864	164	14	need	need	VERB
asir-2864	164	15	to	to	PART
asir-2864	164	16	have	have	VERB
asir-2864	164	17	velocities	velocity	NOUN
asir-2864	164	18	that	that	PRON
asir-2864	164	19	really	really	ADV
asir-2864	164	20	correspond	correspond	VERB
asir-2864	164	21	to	to	ADP
asir-2864	164	22	the	the	DET
asir-2864	164	23	ellipse	ellipse	NOUN
asir-2864	164	24	with	with	ADP
asir-2864	164	25	semi	semi	NOUN
asir-2864	164	26	-	-	NOUN
asir-2864	164	27	axes	axis	NOUN
asir-2864	164	28	a	a	DET
asir-2864	164	29	,	,	PUNCT
asir-2864	164	30	b	b	NOUN
asir-2864	164	31	and	and	CCONJ
asir-2864	164	32	foci	focus	NOUN
asir-2864	164	33	at	at	ADP
asir-2864	164	34	c,-c	c,-c	NOUN
asir-2864	164	35	:	:	PUNCT
asir-2864	164	36	the	the	DET
asir-2864	164	37	velocity	velocity	NOUN
asir-2864	164	38	in	in	ADP
asir-2864	164	39	the	the	DET
asir-2864	164	40	farthest	farth	ADJ
asir-2864	164	41	point	point	NOUN
asir-2864	164	42	is	be	AUX
asir-2864	164	43	given	give	VERB
asir-2864	164	44	the	the	DET
asir-2864	164	45	value	value	NOUN
asir-2864	164	46	voo	voo	NOUN
asir-2864	164	47	and	and	CCONJ
asir-2864	164	48	then	then	ADV
asir-2864	164	49	by	by	ADP
asir-2864	164	50	the	the	DET
asir-2864	164	51	constancy	constancy	NOUN
asir-2864	164	52	of	of	ADP
asir-2864	164	53	the	the	DET
asir-2864	164	54	angular	angular	ADJ
asir-2864	164	55	momentum	momentum	NOUN
asir-2864	164	56	the	the	DET
asir-2864	164	57	velocity	velocity	NOUN
asir-2864	164	58	at	at	ADP
asir-2864	164	59	the	the	DET
asir-2864	164	60	nearest	near	ADJ
asir-2864	164	61	point	point	NOUN
asir-2864	164	62	𝑣_𝑜𝑜	𝑣_𝑜𝑜	NOUN
asir-2864	164	63	=	=	NOUN
asir-2864	164	64	𝑣𝑜𝑜	𝑣𝑜𝑜	NOUN
asir-2864	164	65	·	·	PUNCT
asir-2864	164	66	𝑎+𝑐	𝑎+𝑐	X
asir-2864	164	67	𝑎−𝑐	𝑎−𝑐	PUNCT
asir-2864	164	68	and	and	CCONJ
asir-2864	164	69	then	then	ADV
asir-2864	164	70	by	by	ADP
asir-2864	164	71	the	the	DET
asir-2864	164	72	law	law	NOUN
asir-2864	164	73	of	of	ADP
asir-2864	164	74	conservation	conservation	NOUN
asir-2864	164	75	of	of	ADP
asir-2864	164	76	energy	energy	NOUN
asir-2864	164	77	we	we	PRON
asir-2864	164	78	can	can	AUX
asir-2864	164	79	find	find	VERB
asir-2864	164	80	the	the	DET
asir-2864	164	81	constant	constant	NOUN
asir-2864	164	82	of	of	ADP
asir-2864	164	83	the	the	DET
asir-2864	164	84	law	law	NOUN
asir-2864	164	85	by	by	ADP
asir-2864	164	86	1	1	NUM
asir-2864	164	87	2	2	NUM
asir-2864	164	88	·	·	PUNCT
asir-2864	164	89	𝑚	𝑚	X
asir-2864	164	90	·	·	PUNCT
asir-2864	164	91	𝑣𝑜𝑜2	𝑣𝑜𝑜2	PROPN
asir-2864	164	92	−	−	PROPN
asir-2864	164	93	𝑘·𝑚	𝑘·𝑚	ADJ
asir-2864	164	94	𝑎+𝑐	𝑎+𝑐	PROPN
asir-2864	164	95	=	=	SYM
asir-2864	164	96	1	1	NUM
asir-2864	164	97	2	2	NUM
asir-2864	164	98	𝑚	𝑚	NOUN
asir-2864	164	99	·	·	PUNCT
asir-2864	164	100	𝑣𝑜𝑜	𝑣𝑜𝑜	NOUN
asir-2864	164	101	2	2	NUM
asir-2864	164	102	−	−	NOUN
asir-2864	164	103	𝑘·𝑚	𝑘·𝑚	ADJ
asir-2864	164	104	𝑎−𝑐	𝑎−𝑐	PROPN
asir-2864	164	105	.	.	PUNCT
asir-2864	165	1	we	we	PRON
asir-2864	165	2	can	can	AUX
asir-2864	165	3	proceed	proceed	VERB
asir-2864	165	4	on	on	ADP
asir-2864	165	5	the	the	DET
asir-2864	165	6	same	same	ADJ
asir-2864	165	7	manner	manner	NOUN
asir-2864	165	8	for	for	ADP
asir-2864	165	9	the	the	DET
asir-2864	165	10	case	case	NOUN
asir-2864	165	11	of	of	ADP
asir-2864	165	12	hyperbola	hyperbola	PROPN
asir-2864	165	13	.	.	PUNCT
asir-2864	166	1	in	in	ADP
asir-2864	166	2	the	the	DET
asir-2864	166	3	case	case	NOUN
asir-2864	166	4	of	of	ADP
asir-2864	166	5	hyperbola	hyperbola	PROPN
asir-2864	166	6	we	we	PRON
asir-2864	166	7	can	can	AUX
asir-2864	166	8	have	have	VERB
asir-2864	166	9	for	for	ADP
asir-2864	166	10	a	a	DET
asir-2864	166	11	particle	particle	NOUN
asir-2864	166	12	moving	move	VERB
asir-2864	166	13	on	on	ADP
asir-2864	166	14	the	the	DET
asir-2864	166	15	right	right	ADJ
asir-2864	166	16	branch	branch	NOUN
asir-2864	166	17	either	either	CCONJ
asir-2864	166	18	an	an	DET
asir-2864	166	19	attractive	attractive	ADJ
asir-2864	166	20	gravitational	gravitational	ADJ
asir-2864	166	21	force	force	NOUN
asir-2864	166	22	directed	direct	VERB
asir-2864	166	23	to	to	ADP
asir-2864	166	24	the	the	DET
asir-2864	166	25	right	right	ADJ
asir-2864	166	26	focus	focus	NOUN
asir-2864	166	27	,	,	PUNCT
asir-2864	166	28	or	or	CCONJ
asir-2864	166	29	a	a	DET
asir-2864	166	30	repulsive	repulsive	ADJ
asir-2864	166	31	–	–	PUNCT
asir-2864	166	32	1	1	NUM
asir-2864	166	33	/	/	SYM
asir-2864	166	34	r²	r²	NOUN
asir-2864	166	35	or	or	CCONJ
asir-2864	166	36	a	a	DET
asir-2864	166	37	repulsive	repulsive	ADJ
asir-2864	166	38	directed	direct	VERB
asir-2864	166	39	to	to	ADP
asir-2864	166	40	the	the	DET
asir-2864	166	41	center	center	NOUN
asir-2864	166	42	.	.	PUNCT
asir-2864	167	1	we	we	PRON
asir-2864	167	2	note	note	VERB
asir-2864	167	3	that	that	SCONJ
asir-2864	167	4	for	for	ADP
asir-2864	167	5	the	the	DET
asir-2864	167	6	repulsive	repulsive	ADJ
asir-2864	167	7	force	force	NOUN
asir-2864	167	8	from	from	ADP
asir-2864	167	9	the	the	DET
asir-2864	167	10	left	left	ADJ
asir-2864	167	11	focus	focus	NOUN
asir-2864	167	12	,	,	PUNCT
asir-2864	167	13	we	we	PRON
asir-2864	167	14	can	can	AUX
asir-2864	167	15	see	see	VERB
asir-2864	167	16	that	that	SCONJ
asir-2864	167	17	the	the	DET
asir-2864	167	18	velocity	velocity	NOUN
asir-2864	167	19	for	for	ADP
asir-2864	167	20	infinite	infinite	ADJ
asir-2864	167	21	distance	distance	NOUN
asir-2864	167	22	is	be	AUX
asir-2864	167	23	not	not	PART
asir-2864	167	24	zero	zero	NUM
asir-2864	167	25	but	but	CCONJ
asir-2864	167	26	equal	equal	ADJ
asir-2864	167	27	to	to	ADP
asir-2864	167	28	𝑣∞	𝑣∞	NUM
asir-2864	167	29	=	=	SYM
asir-2864	167	30	𝑣_00	𝑣_00	NOUN
asir-2864	167	31	·	·	PUNCT
asir-2864	167	32	(	(	PUNCT
asir-2864	167	33	𝑐	𝑐	NOUN
asir-2864	167	34	+	+	NUM
asir-2864	167	35	𝑎)/𝑏	𝑎)/𝑏	PROPN
asir-2864	167	36	while	while	SCONJ
asir-2864	167	37	for	for	ADP
asir-2864	167	38	the	the	DET
asir-2864	167	39	elastic	elastic	ADJ
asir-2864	167	40	force	force	NOUN
asir-2864	167	41	the	the	DET
asir-2864	167	42	velocity	velocity	NOUN
asir-2864	167	43	is	be	AUX
asir-2864	167	44	infinite	infinite	ADJ
asir-2864	167	45	.	.	PUNCT
asir-2864	168	1	8	8	X
asir-2864	168	2	.	.	PUNCT
asir-2864	168	3	analytic	analytic	ADJ
asir-2864	168	4	solution	solution	NOUN
asir-2864	168	5	the	the	DET
asir-2864	168	6	distance	distance	NOUN
asir-2864	168	7	of	of	ADP
asir-2864	168	8	the	the	DET
asir-2864	168	9	center	center	NOUN
asir-2864	168	10	of	of	ADP
asir-2864	168	11	force	force	NOUN
asir-2864	168	12	(	(	PUNCT
asir-2864	168	13	sx	sx	PROPN
asir-2864	168	14	,	,	PUNCT
asir-2864	168	15	sy	sy	PROPN
asir-2864	168	16	)	)	PUNCT
asir-2864	168	17	from	from	ADP
asir-2864	168	18	the	the	DET
asir-2864	168	19	velocities	velocity	NOUN
asir-2864	168	20	is	be	AUX
asir-2864	168	21	𝑑	𝑑	NOUN
asir-2864	168	22	=	=	NOUN
asir-2864	168	23	±(𝑠𝑖𝑛𝜑𝑠𝑥	±(𝑠𝑖𝑛𝜑𝑠𝑥	NOUN
asir-2864	168	24	−	−	NOUN
asir-2864	168	25	𝑐𝑜𝑠𝜑𝑠𝑦	𝑐𝑜𝑠𝜑𝑠𝑦	PROPN
asir-2864	168	26	+	+	CCONJ
asir-2864	168	27	𝑐𝑜𝑠𝜑𝑦1	𝑐𝑜𝑠𝜑𝑦1	NOUN
asir-2864	168	28	−	−	NOUN
asir-2864	168	29	𝑠𝑖𝑛𝜑𝑥1	𝑠𝑖𝑛𝜑𝑥1	NOUN
asir-2864	168	30	)	)	PUNCT
asir-2864	168	31	where	where	SCONJ
asir-2864	168	32	(	(	PUNCT
asir-2864	168	33	x1	x1	ADJ
asir-2864	168	34	,	,	PUNCT
asir-2864	168	35	y1	y1	PROPN
asir-2864	168	36	)	)	PUNCT
asir-2864	168	37	is	be	AUX
asir-2864	168	38	the	the	DET
asir-2864	168	39	point	point	NOUN
asir-2864	168	40	where	where	SCONJ
asir-2864	168	41	the	the	DET
asir-2864	168	42	velocity	velocity	NOUN
asir-2864	168	43	is	be	AUX
asir-2864	168	44	v1	v1	PROPN
asir-2864	168	45	and	and	CCONJ
asir-2864	168	46	φ	φ	NUM
asir-2864	168	47	the	the	DET
asir-2864	168	48	angle	angle	NOUN
asir-2864	168	49	of	of	ADP
asir-2864	168	50	inclination	inclination	NOUN
asir-2864	168	51	.	.	PUNCT
asir-2864	169	1	for	for	ADP
asir-2864	169	2	x_1	x_1	PROPN
asir-2864	169	3	we	we	PRON
asir-2864	169	4	take	take	VERB
asir-2864	169	5	the	the	DET
asir-2864	169	6	negative	negative	ADJ
asir-2864	169	7	since	since	SCONJ
asir-2864	169	8	the	the	DET
asir-2864	169	9	numerator	numerator	NOUN
asir-2864	169	10	is	be	AUX
asir-2864	169	11	negative	negative	ADJ
asir-2864	169	12	(	(	PUNCT
asir-2864	169	13	we	we	PRON
asir-2864	169	14	expect	expect	VERB
asir-2864	169	15	sy	sy	INTJ
asir-2864	169	16	to	to	PART
asir-2864	169	17	be	be	AUX
asir-2864	169	18	zero	zero	NUM
asir-2864	169	19	)	)	PUNCT
asir-2864	169	20	.	.	PUNCT
asir-2864	170	1	by	by	ADP
asir-2864	170	2	demanding	demand	VERB
asir-2864	170	3	that	that	SCONJ
asir-2864	170	4	the	the	DET
asir-2864	170	5	law	law	NOUN
asir-2864	170	6	of	of	ADP
asir-2864	170	7	areas	area	NOUN
asir-2864	170	8	is	be	AUX
asir-2864	170	9	valid	valid	ADJ
asir-2864	170	10	we	we	PRON
asir-2864	170	11	get	get	VERB
asir-2864	170	12	the	the	DET
asir-2864	170	13	equations	equation	NOUN
asir-2864	170	14	:	:	PUNCT
asir-2864	170	15	𝑑1𝑉1	𝑑1𝑉1	PROPN
asir-2864	170	16	=	=	SYM
asir-2864	170	17	𝑑2𝑉2	𝑑2𝑉2	X
asir-2864	170	18	=	=	SYM
asir-2864	170	19	𝑑3𝑉3	𝑑3𝑉3	PROPN
asir-2864	170	20	or	or	CCONJ
asir-2864	170	21	:	:	PUNCT
asir-2864	170	22	we	we	PRON
asir-2864	170	23	denote	denote	VERB
asir-2864	170	24	by	by	ADP
asir-2864	170	25	v_1y	v_1y	NOUN
asir-2864	170	26	=	=	SYM
asir-2864	170	27	v_1sinφ_1	v_1sinφ_1	NOUN
asir-2864	170	28	,	,	PUNCT
asir-2864	170	29	v_1x	v_1x	NOUN
asir-2864	170	30	=	=	SYM
asir-2864	170	31	v_1cosφ_1	v_1cosφ_1	NOUN
asir-2864	170	32	,	,	PUNCT
asir-2864	170	33	etc	etc	X
asir-2864	170	34	.	.	X
asir-2864	170	35	(	(	PUNCT
asir-2864	170	36	𝑉1𝑦	𝑉1𝑦	INTJ
asir-2864	170	37	+	+	NUM
asir-2864	170	38	𝑉2𝑦)𝑆𝑥	𝑉2𝑦)𝑆𝑥	ADJ
asir-2864	170	39	−	−	PROPN
asir-2864	170	40	(	(	PUNCT
asir-2864	170	41	𝑉1𝑥	𝑉1𝑥	PROPN
asir-2864	170	42	+	+	CCONJ
asir-2864	170	43	𝑉2𝑋)𝑆𝑌	𝑉2𝑋)𝑆𝑌	PROPN
asir-2864	170	44	=	=	PUNCT
asir-2864	170	45	(	(	PUNCT
asir-2864	170	46	𝑟𝑄⃗⃗	𝑟𝑄⃗⃗	NUM
asir-2864	170	47	⃗⃗	⃗⃗	PROPN
asir-2864	170	48	⃗𝑋𝑉2	⃗𝑋𝑉2	PROPN
asir-2864	170	49	⃗⃗	⃗⃗	PROPN
asir-2864	170	50	⃗⃗	⃗⃗	PROPN
asir-2864	170	51	+	+	CCONJ
asir-2864	170	52	𝑟𝑃⃗⃗⃗⃗⃗	𝑟𝑃⃗⃗⃗⃗⃗	ADV
asir-2864	170	53	𝑋	𝑋	PROPN
asir-2864	170	54	𝑉1	𝑉1	PROPN
asir-2864	170	55	⃗⃗	⃗⃗	PROPN
asir-2864	170	56	⃗⃗	⃗⃗	PROPN
asir-2864	170	57	)	)	PUNCT
asir-2864	171	1	(	(	PUNCT
asir-2864	171	2	𝑉1𝑦	𝑉1𝑦	INTJ
asir-2864	171	3	+	+	NUM
asir-2864	171	4	𝑉3𝑦)𝑆𝑥	𝑉3𝑦)𝑆𝑥	NUM
asir-2864	171	5	−	−	PROPN
asir-2864	171	6	(	(	PUNCT
asir-2864	171	7	𝑉1𝑥	𝑉1𝑥	PROPN
asir-2864	171	8	+	+	CCONJ
asir-2864	171	9	𝑉3𝑥)𝑆𝑌	𝑉3𝑥)𝑆𝑌	PROPN
asir-2864	171	10	=	=	SYM
asir-2864	171	11	(	(	PUNCT
asir-2864	171	12	𝑟𝑅⃗⃗⃗⃗⃗𝑋	𝑟𝑅⃗⃗⃗⃗⃗𝑋	PROPN
asir-2864	171	13	𝑉3	𝑉3	PROPN
asir-2864	171	14	⃗⃗	⃗⃗	PROPN
asir-2864	171	15	⃗⃗	⃗⃗	PROPN
asir-2864	172	1	+	+	CCONJ
asir-2864	172	2	𝑟𝑃⃗⃗⃗⃗⃗	𝑟𝑃⃗⃗⃗⃗⃗	ADV
asir-2864	173	1	𝑋	𝑋	PROPN
asir-2864	173	2	𝑉1	𝑉1	PROPN
asir-2864	173	3	⃗⃗	⃗⃗	PROPN
asir-2864	173	4	⃗⃗	⃗⃗	PROPN
asir-2864	173	5	)	)	PUNCT
asir-2864	173	6	by	by	ADP
asir-2864	173	7	solving	solve	VERB
asir-2864	173	8	these	these	DET
asir-2864	173	9	equations	equation	NOUN
asir-2864	173	10	we	we	PRON
asir-2864	173	11	find	find	VERB
asir-2864	173	12	the	the	DET
asir-2864	173	13	center	center	NOUN
asir-2864	173	14	.	.	PUNCT
asir-2864	174	1	excel	excel	VERB
asir-2864	174	2	files	file	NOUN
asir-2864	174	3	for	for	ADP
asir-2864	174	4	ellipses	ellipsis	NOUN
asir-2864	174	5	and	and	CCONJ
asir-2864	174	6	parabolas	parabola	NOUN
asir-2864	174	7	,	,	PUNCT
asir-2864	174	8	the	the	DET
asir-2864	174	9	_	_	PROPN
asir-2864	174	10	le	le	X
asir-2864	174	11	is	be	AUX
asir-2864	174	12	downloadable	downloadable	ADJ
asir-2864	174	13	from	from	ADP
asir-2864	174	14	:	:	PUNCT
asir-2864	174	15	http://www.kyriakosxolio.gr/2_dimensional_motiona/newtonstheoryofellipse2_2.xlsm	http://www.kyriakosxolio.gr/2_dimensional_motiona/newtonstheoryofellipse2_2.xlsm	NOUN
asir-2864	174	16	the	the	DET
asir-2864	174	17	corresponding	corresponding	PROPN
asir-2864	174	18	_	_	PROPN
asir-2864	174	19	le	le	X
asir-2864	174	20	for	for	ADP
asir-2864	174	21	hyperbolas	hyperbola	NOUN
asir-2864	174	22	is	be	AUX
asir-2864	174	23	downloadable	downloadable	ADJ
asir-2864	174	24	from	from	ADP
asir-2864	174	25	:	:	PUNCT
asir-2864	174	26	http://www.kyriakosxolio.gr/2_dimensional_motiona/hyperobolas_newton_find_center	http://www.kyriakosxolio.gr/2_dimensional_motiona/hyperobolas_newton_find_center	X
asir-2864	174	27	_	_	PRON
asir-2864	174	28	without_macros.xlsm	without_macros.xlsm	PUNCT
asir-2864	174	29	a	a	DET
asir-2864	174	30	zip	zip	NOUN
asir-2864	174	31	_	_	NOUN
asir-2864	174	32	e	e	NOUN
asir-2864	174	33	with	with	ADP
asir-2864	174	34	the	the	DET
asir-2864	174	35	excel	excel	NOUN
asir-2864	174	36	_	_	PUNCT
asir-2864	174	37	les	le	NOUN
asir-2864	174	38	for	for	ADP
asir-2864	174	39	circular	circular	ADJ
asir-2864	174	40	motions	motion	NOUN
asir-2864	174	41	and	and	CCONJ
asir-2864	174	42	newton	newton	PROPN
asir-2864	174	43	’s	’s	PART
asir-2864	174	44	spiral	spiral	NOUN
asir-2864	174	45	is	be	AUX
asir-2864	174	46	downloadable	downloadable	ADJ
asir-2864	174	47	from	from	ADP
asir-2864	174	48	:	:	PUNCT
asir-2864	174	49	http://www.kyriakosxolio.gr/2_dimensional_motiona/circular_spiral.zip	http://www.kyriakosxolio.gr/2_dimensional_motiona/circular_spiral.zip	NOUN
asir-2864	174	50	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2864	174	51	applied	apply	VERB
asir-2864	174	52	science	science	NOUN
asir-2864	174	53	and	and	CCONJ
asir-2864	174	54	innovative	innovative	ADJ
asir-2864	174	55	research	research	NOUN
asir-2864	174	56	vol	vol	NOUN
asir-2864	174	57	.	.	PROPN
asir-2864	175	1	4	4	NUM
asir-2864	175	2	,	,	PUNCT
asir-2864	175	3	no	no	INTJ
asir-2864	175	4	.	.	NOUN
asir-2864	175	5	2	2	NUM
asir-2864	175	6	,	,	PUNCT
asir-2864	175	7	2020	2020	NUM
asir-2864	175	8	52	52	NUM
asir-2864	175	9	published	publish	VERB
asir-2864	175	10	by	by	ADP
asir-2864	175	11	scholink	scholink	PROPN
asir-2864	175	12	inc	inc	PROPN
asir-2864	175	13	.	.	PROPN
asir-2864	175	14	references	references	PROPN
asir-2864	175	15	alfred	alfred	PROPN
asir-2864	175	16	m.	m.	PROPN
asir-2864	175	17	b.	b.	PROPN
asir-2864	176	1	(	(	PUNCT
asir-2864	176	2	1964	1964	NUM
asir-2864	176	3	)	)	PUNCT
asir-2864	176	4	.	.	PUNCT
asir-2864	177	1	newton	newton	PROPN
asir-2864	177	2	in	in	ADP
asir-2864	177	3	the	the	DET
asir-2864	177	4	college	college	NOUN
asir-2864	177	5	classroom	classroom	NOUN
asir-2864	177	6	.	.	PUNCT
asir-2864	178	1	american	american	PROPN
asir-2864	178	2	journal	journal	PROPN
asir-2864	178	3	of	of	ADP
asir-2864	178	4	physics	physics	PROPN
asir-2864	178	5	,	,	PUNCT
asir-2864	178	6	32	32	NUM
asir-2864	178	7	,	,	PUNCT
asir-2864	178	8	959	959	NUM
asir-2864	178	9	.	.	PUNCT
asir-2864	179	1	https://doi.org/10.1119/1.1970038	https://doi.org/10.1119/1.1970038	PROPN
asir-2864	179	2	bernard	bernard	PROPN
asir-2864	179	3	,	,	PUNCT
asir-2864	179	4	c.	c.	PROPN
asir-2864	179	5	(	(	PUNCT
asir-2864	179	6	1981	1981	NUM
asir-2864	179	7	)	)	PUNCT
asir-2864	179	8	.	.	PUNCT
asir-2864	180	1	newton	newton	PROPN
asir-2864	180	2	’s	’s	PART
asir-2864	180	3	discovery	discovery	NOUN
asir-2864	180	4	of	of	ADP
asir-2864	180	5	gravity	gravity	NOUN
asir-2864	180	6	.	.	PUNCT
asir-2864	181	1	scientific	scientific	ADJ
asir-2864	181	2	american	american	PROPN
asir-2864	181	3	,	,	PUNCT
asir-2864	181	4	244(3	244(3	NUM
asir-2864	181	5	)	)	PUNCT
asir-2864	181	6	,	,	PUNCT
asir-2864	181	7	123	123	NUM
asir-2864	181	8	-	-	SYM
asir-2864	181	9	133	133	NUM
asir-2864	181	10	.	.	PUNCT
asir-2864	182	1	https://doi.org/10.1038/scientificamerican0381-166	https://doi.org/10.1038/scientificamerican0381-166	PROPN
asir-2864	182	2	chandrasekhar	chandrasekhar	PROPN
asir-2864	182	3	,	,	PUNCT
asir-2864	182	4	s.	s.	PROPN
asir-2864	182	5	(	(	PUNCT
asir-2864	182	6	1995	1995	NUM
asir-2864	182	7	)	)	PUNCT
asir-2864	182	8	.	.	PUNCT
asir-2864	183	1	newton	newton	PROPN
asir-2864	183	2	’s	’s	PART
asir-2864	183	3	principia	principia	PROPN
asir-2864	183	4	for	for	ADP
asir-2864	183	5	the	the	DET
asir-2864	183	6	common	common	ADJ
asir-2864	183	7	reader	reader	NOUN
asir-2864	183	8	(	(	PUNCT
asir-2864	183	9	p.	p.	NOUN
asir-2864	183	10	75	75	NUM
asir-2864	183	11	)	)	PUNCT
asir-2864	183	12	.	.	PUNCT
asir-2864	184	1	clarendon	clarendon	PROPN
asir-2864	184	2	press	press	PROPN
asir-2864	184	3	.	.	PUNCT
asir-2864	185	1	michael	michael	PROPN
asir-2864	185	2	,	,	PUNCT
asir-2864	185	3	n.	n.	PROPN
asir-2864	185	4	(	(	PUNCT
asir-2864	185	5	1994	1994	NUM
asir-2864	185	6	)	)	PUNCT
asir-2864	185	7	.	.	PUNCT
asir-2864	186	1	hooke	hooke	PROPN
asir-2864	186	2	,	,	PUNCT
asir-2864	186	3	orbital	orbital	ADJ
asir-2864	186	4	motion	motion	NOUN
asir-2864	186	5	,	,	PUNCT
asir-2864	186	6	and	and	CCONJ
asir-2864	186	7	newton	newton	PROPN
asir-2864	186	8	’s	’s	PART
asir-2864	186	9	principia	principia	PROPN
asir-2864	186	10	.	.	PROPN
asir-2864	186	11	american	american	PROPN
asir-2864	186	12	journal	journal	PROPN
asir-2864	186	13	of	of	ADP
asir-2864	186	14	physics	physics	PROPN
asir-2864	186	15	,	,	PUNCT
asir-2864	186	16	62	62	NUM
asir-2864	186	17	,	,	PUNCT
asir-2864	186	18	331	331	NUM
asir-2864	186	19	.	.	PUNCT
asir-2864	187	1	https://doi.org/10.1119/1.17576	https://doi.org/10.1119/1.17576	PROPN
asir-2864	187	2	murray	murray	PROPN
asir-2864	187	3	,	,	PUNCT
asir-2864	187	4	r.	r.	PROPN
asir-2864	187	5	s.	s.	PROPN
asir-2864	187	6	(	(	PUNCT
asir-2864	187	7	1967	1967	NUM
asir-2864	187	8	)	)	PUNCT
asir-2864	187	9	.	.	PUNCT
asir-2864	188	1	theoretical	theoretical	ADJ
asir-2864	188	2	mechanics	mechanic	NOUN
asir-2864	188	3	(	(	PUNCT
asir-2864	188	4	p.	p.	NOUN
asir-2864	188	5	127	127	NUM
asir-2864	188	6	)	)	PUNCT
asir-2864	188	7	.	.	PUNCT
asir-2864	189	1	si	si	PROPN
asir-2864	189	2	edition	edition	PROPN
asir-2864	189	3	,	,	PUNCT
asir-2864	189	4	schaum	schaum	PROPN
asir-2864	189	5	’s	’s	PART
asir-2864	189	6	outline	outline	PROPN
asir-2864	189	7	series	series	PROPN
asir-2864	189	8	,	,	PUNCT
asir-2864	189	9	mcgraw	mcgraw	PROPN
asir-2864	189	10	-	-	PUNCT
asir-2864	189	11	hill	hill	NOUN
asir-2864	189	12	book	book	NOUN
asir-2864	189	13	company	company	NOUN
asir-2864	189	14	.	.	PUNCT
asir-2864	190	1	newton	newton	PROPN
asir-2864	190	2	and	and	CCONJ
asir-2864	190	3	kepler	kepler	PROPN
asir-2864	190	4	ex	ex	PROPN
asir-2864	190	5	libris	libris	PROPN
asir-2864	190	6	.	.	PUNCT
asir-2864	191	1	(	(	PUNCT
asir-2864	191	2	n.d	n.d	PROPN
asir-2864	191	3	.	.	PROPN
asir-2864	191	4	)	)	PUNCT
asir-2864	191	5	.	.	PUNCT
asir-2864	192	1	retrieved	retrieve	VERB
asir-2864	192	2	from	from	ADP
asir-2864	192	3	http://www.nonagon.org/exlibris/newton-keplers-laws	http://www.nonagon.org/exlibris/newton-keplers-laws	PROPN
asir-2864	192	4	newton	newton	PROPN
asir-2864	192	5	,	,	PUNCT
asir-2864	192	6	i.	i.	PROPN
asir-2864	192	7	(	(	PUNCT
asir-2864	192	8	1999	1999	NUM
asir-2864	192	9	)	)	PUNCT
asir-2864	192	10	.	.	PUNCT
asir-2864	193	1	the	the	DET
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asir-2864	193	3	:	:	PUNCT
asir-2864	193	4	the	the	DET
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asir-2864	193	6	translation	translation	NOUN
asir-2864	193	7	and	and	CCONJ
asir-2864	193	8	guide	guide	NOUN
asir-2864	193	9	:	:	PUNCT
asir-2864	193	10	mathematical	mathematical	ADJ
asir-2864	193	11	principles	principle	NOUN
asir-2864	193	12	of	of	ADP
asir-2864	193	13	natural	natural	ADJ
asir-2864	193	14	philosophy	philosophy	NOUN
asir-2864	193	15	(	(	PUNCT
asir-2864	193	16	bernard	bernard	PROPN
asir-2864	193	17	cohen	cohen	PROPN
asir-2864	193	18	,	,	PUNCT
asir-2864	193	19	anne	anne	PROPN
asir-2864	193	20	whitman	whitman	PROPN
asir-2864	193	21	,	,	PUNCT
asir-2864	193	22	&	&	CCONJ
asir-2864	193	23	julia	julia	PROPN
asir-2864	193	24	budenz	budenz	PROPN
asir-2864	193	25	,	,	PUNCT
asir-2864	193	26	trans	trans	PROPN
asir-2864	193	27	.	.	PROPN
asir-2864	193	28	,	,	PUNCT
asir-2864	193	29	p.	p.	NOUN
asir-2864	193	30	454	454	NUM
asir-2864	193	31	)	)	PUNCT
asir-2864	193	32	.	.	PUNCT
asir-2864	194	1	university	university	PROPN
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asir-2864	194	3	california	california	PROPN
asir-2864	194	4	press	press	PROPN
asir-2864	194	5	.	.	PUNCT
asir-2864	195	1	newton	newton	PROPN
asir-2864	195	2	,	,	PUNCT
asir-2864	195	3	i.	i.	PROPN
asir-2864	195	4	(	(	PUNCT
asir-2864	195	5	n.d	n.d	PROPN
asir-2864	195	6	.	.	PROPN
asir-2864	195	7	)	)	PUNCT
asir-2864	195	8	.	.	PUNCT
asir-2864	196	1	the	the	DET
asir-2864	196	2	mathematical	mathematical	ADJ
asir-2864	196	3	principles	principle	NOUN
asir-2864	196	4	of	of	ADP
asir-2864	196	5	natural	natural	ADJ
asir-2864	196	6	philosophy	philosophy	NOUN
asir-2864	196	7	(	(	PUNCT
asir-2864	196	8	andrew	andrew	PROPN
asir-2864	196	9	motte	motte	PROPN
asir-2864	196	10	,	,	PUNCT
asir-2864	196	11	trans	trans	PROPN
asir-2864	196	12	.	.	PUNCT
asir-2864	196	13	)	)	PUNCT
asir-2864	196	14	.	.	PUNCT