Angular momentum conservation by video analysis using the flat balls toy

Abstract The angular momentum of a particle system and its division into an orbital term and a spin term is a subject usually relegated to the background, or even absent, in introductory mechanics courses in undergraduate courses. In addition, the angular momentum conservation of a system, in the absence of external torques, can often be counterintuitive. The present work uses a toy called flat ball, which has a format similar to discs, in the context of a two-dimensional collision. Two identical flat balls are launched spinning in opposite directions and collide on a negligible friction surface. The experiment has great pedagogical potential because it provides a qualitative and quantitative analysis of the magnitude of the linear and angular momenta of the system, as well as its conservation, using the technique of video analysis. The surprising result of the experiment has the potential to arouse students' curiosity, as well as opening the way to address the transition of the system's absolute values of the orbital angular momentum and spin angular momentum, before and after the collision.

摘要 粒子系统的角动量及其分解为轨道项与自旋项的相关内容，在本科入门力学课程中常被置于次要地位，甚至完全未被纳入教学范畴。此外，无外力矩时系统的角动量守恒规律往往具有反直觉性。本研究采用一种外形类似圆盘、被称为平球（flat ball）的教具，在二维碰撞场景中开展实验：将两个完全相同的平球以反向自旋状态抛出，在近似无摩擦的表面上发生碰撞。本实验具备极高的教学价值，通过视频分析技术，可对系统的线动量、角动量大小及其守恒性开展定性与定量分析。实验得到的反常结果能够激发学生的探究兴趣，同时可为讲解碰撞前后系统轨道角动量与自旋角动量的绝对值转换问题提供教学切入点。