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

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%.

本文探讨了一项视频分析实验的结果，该实验通过拍摄自行车车轮的圆周运动，用以研究匀速圆周运动（uniform circular motion, UCM）与简谐运动（simple harmonic motion, SHM）之间的内在关联。选取车轮边缘的固定点P，当其开展半径为R、角坐标为φ的圆周运动时，可通过视频分析获取其笛卡尔坐标分量x与y，观测可见二者随时间呈现周期性振荡。假设该点P的运动为匀速圆周运动，我们可通过解析方法推导得到其x、y坐标，并将其与视频分析得到的坐标进行比对。该模型不仅可清晰展现匀速圆周运动与简谐运动的关联机制，还能以1%的精度测算自行车车轮的半径。