转动刚体角动量的复杂关系——兼谈不同参考系选择的意义

Complex relationships of angular momentum of rotating rigid-bodies——Discussing the significance of choosing the right reference frame

一道貌似简单的刚性陀螺运动题,牵扯出大学物理教学中一个被忽略的问题——刚体同时绕相互垂直的轴旋转时角动量的计算.本文从一道题目的解答入手,阐述刚体(陀螺)旋转的角动量复杂关系,推导出简易、约束陀螺的正确角动量变换关系.同时讨论选择惯性参考系与非惯性参考系时对问题求解有不同难度的问题.

A seemingly simple rigid-gyro-motion problem involves an overlooked aspect in university physics teaching,namely,the calculation of angular momentum when rigid bodies rotate simultaneously around mutually perpendicular axes.Starting from the solution of question,this paper elaborates the complex relationship of angular momentum of rigid-body(gyro)rotation,and derives the correct angular momentum transformation relationship of simple and constrained gyroscope.At the same time,it shows that,this kind of problems can be greatly simplified when selecting the appropriate reference frame.