摘要
大学物理教材及教学在刚体定轴转动一章中,往往不太重视刚体总角动量与角速度的关系,而只关注于沿轴向的角动量,有时甚至出现L=Jω这种容易误解的表述形式.实际上,一般情况下刚体定轴转动时的角动量与角速度方向不相同,且刚体匀速转动时受变外力矩作用.本文首先从理论层面上给出角动量与角速度方向不一致的一般性证明,并给出方向相同的两种特殊情况,其次用一个实例阐述刚体定轴转动时,刚体轴受到垂直于轴向的变力矩作用,最后将特例所得结论推广至一般刚体定轴转动,从而阐明重视两者方向关系的必要性.
In college physics textbooks and teaching, little emphasis is put on the relationship between the angular momentum and angular velocity of a rigid body when it rotates about a fixed axis. Instead, attention is focused on the projection of the angular momentum along the axis of rotation. Sometimes, we see equations, such as L= Jω, that are quite misleading. In fact, when a rigid body rotates about a fixed axis, its angular momentum and angular velocity generally point in different directions; there is normally a time-varying external torque acting on it even when it is rotating uniformly. Paper first present a general proof of this assertion and indicate two special situations in which L and ω point in the same direction. Then, by using a specific example, paper shows that when a rigid body rotates about a fixed axis, there is generally a changing external torque acting on the axis of rotation in a direction perpendicu- lar to the axis. Finally, paper generalize the conclusion drawn from this particular example, and further illustrate the importance of clarifying the relationship between the directions of L and ω.
出处
《物理与工程》
2016年第2期37-40,共4页
Physics and Engineering
基金
教育部在线教育研究中心在线教育研究基金(全通教育)重点课题
2016ZD312
江苏省高等教育教学改革项目(省教育厅)
2015JSJG118
关键词
刚体
定轴转动
角动量
角速度
方向
变力矩
rigid body
rotation about a fixed axis
angular momentum
angular velocity
direction
time-varying torque
