Acessibilidade / Reportar erro

Brasil

Revista Brasileira de Ensino de Física

Español English

Brasil

Español English

sumário « anterior atual seguinte »

Sumário

Artigos Gerais • Rev. Bras. Ensino Fís. 40 (2) • 2018 • https://doi.org/10.1590/1806-9126-RBEF-2017-0152 copy

Study of the relationship between circular uniform movement and simple harmonic movement using video analysis of a bicycle wheel

Authorship SCIMAGO INSTITUTIONS RANKINGS

In this article we discuss the results of a video analysis that allows us to study the relationship between uniform circular motion (UCM) and simple harmonic motion (SHM), from the filming of the circular motion of a bicycle wheel. Considering a fixed point P at the wheel's edge, in a circular motion of radius R and angular coordinate $φ$ , we can obtain its Cartesian components x and y by means of video analysis, observing that they oscillate over time. Assuming the motion of P as an MCU, we obtain analytically the x and y coordinates, comparing them with the coordinates obtained by video analysis. The model allows explicit study of the relationship between UCM and SHM, in addition to providing the bicycle radius with accuracy of 1%.

Keywords:
UCM; SHM; Video analysis; Mathematical modeling

$t$ (s)	$δ_{x}$ (cm)	$δ_{y}$ (cm)
0,00	3,86 × 10 $^{-9}$	4,90 × 10 $^{-12}$
0,03	3,89 × 10 $^{-9}$	4,36 × 10 $^{-11}$
0,07	3,69 × 10 $^{-10}$	1,83 × 10 $^{-10}$
0,10	6,38 × 10 $^{-10}$	4,76 × 10 $^{-9}$
0,13	3,31 × 10 $^{-9}$	2,61 × 10 $^{-9}$
0,17	1,01 × 10 $^{-9}$	6,14 × 10 $^{-9}$
0,20	2,60 × 10 $^{-9}$	1,23 × 10 $^{-9}$
0,23	4,54 × 10 $^{-9}$	3,76 × 10 $^{-9}$
0,27	1,22 × 10 $^{-9}$	7,31 × 10 $^{-9}$
0,30	2,31 × 10 $^{-9}$	1,18 × 10 $^{-9}$
0,33	3,27 × 10 $^{-10}$	4,18 × 10 $^{-9}$
0,37	2,28 × 10 $^{-10}$	8,13 × 10 $^{-9}$
0,40	7,99 × 10 $^{-10}$	3,03 × 10 $^{-9}$
0,43	1,60 × 10 $^{-9}$	4,91 × 10 $^{-10}$
0,47	1,51 × 10 $^{-8}$	7,91 × 10 $^{-10}$
0,50	1,79 × 10 $^{-8}$	1,41 × 10 $^{-8}$
0,53	2,10 × 10 $^{-10}$	1,70 × 10 $^{-9}$
0,57	6,64 × 10 $^{-9}$	1,40 × 10 $^{-9}$
0,60	1,29 × 10 $^{-9}$	3,99 × 10 $^{-9}$
0,63	2,67 × 10 $^{-9}$	5,63 × 10 $^{-9}$
0,66	1,41 × 10 $^{-9}$	5,73 × 10 $^{-9}$
0,70	3,10 × 10 $^{-9}$	2,25 × 10 $^{-8}$
0,73	3,25 × 10 $^{-9}$	1,73 × 10 $^{-8}$

$t$	$x$ (cm)	$y$ (cm)	$R$ (cm)	$ε$ %
0,00	28,34	0,84	28,35	0,6
0,03	28,07	4,70	28,46	1,0
0,07	27,19	8,44	28,47	1,0
0,10	25,79	12,14	28,51	1,1
0,13	24,06	15,30	28,51	1,1
0,17	21,78	18,39	28,50	1,1
0,20	19,05	21,14	28,46	0,9
0,23	16,10	23,55	28,53	1,2
0,27	12,62	25,63	28,57	1,3
0,30	8,95	27,05	28,49	1,1
0,33	5,18	28,00	28,47	1,0
0,37	1,48	28,40	28,44	0,9
0,40	-2,53	28,22	28,34	0,5
0,43	-6,43	27,64	28,37	0,6
0,47	-10,09	26,49	28,34	0,5
0,50	-13,67	24,73	28,25	0,2
0,53	-17,03	22,49	28,21	0,1
0,57	-19,96	19,81	28,12	0,2
0,60	-22,56	16,70	28,07	0,5
0,63	-24,68	13,29	28,03	0,6
0,66	-26,28	9,64	27,99	0,7
0,70	-27,32	5,74	27,91	1,0
0,73	-27,86	1,84	27,92	1,0

Sociedade Brasileira de Física Caixa Postal 66328, 05389-970 São Paulo SP - Brazil - São Paulo - SP - Brazil
E-mail: marcio@sbfisica.org.br

Acompanhe os números deste periódico no seu leitor de RSS