Angular Momentum Demonstrations

The subject of mechanics depends strongly upon the conservation laws, such as conservation of energy, conservation of momentum, and conservation of angular momentum. The first two demonstrations show the conservation of angular momentum, and the third shows the vector nature of angular momentum when an unbalanced torque acts on the system.

As an example of the mechanics of angular momentum, spinning on a stool with masses held out demonstrates conservation of angular momentum. Bringing the masses in makes the stool spin faster. The angular momentum is equal to the moment of inertia times the angular velocity, so if you reduce the moment of inertia by a factor of two by pulling the masses in, the spin speed will double. 作为角动量力学的一个例子，人在旋转的椅子上手持质量向外伸展时，演示了角动量的守恒。将质量向内收拢会使椅子转得更快。角动量等于转动惯量乘以角速度，因此如果通过将质量向内收拢使转动惯量减少一半，转速将加倍。

Another way to demonstrate conservation of angular momentum is to spin a wheel and hold it on the rotatable stool. If you turn the wheel over to reverse the direction of its angular momentum, then the stool counter-rotates to keep the vector angular momentum the same. In the ideal case of no frictional torque from the stool, the total angular momentum of the system must remain the same in both magnitude and direction. 另一种展示角动量守恒的方法是旋转一个轮子并将其固定在可旋转的凳子上。如果你将轮子翻转以改变其角动量的方向，那么凳子会反向旋转以保持角动量矢量保持不变。在理想情况下，凳子与轮子之间没有摩擦力矩，系统总角动量在大小和方向上都必须保持不变。

If a spinning wheel is supported on an axis point so that there is a net torque on it, the torque will change the angular momentum in a manner which is called "precession". Both angular momentum and torque are vector quantities, and if the applied torque has a component perpendicular to the angular momentum, it will produce a rate of change of the direction of the spin axis. 如果一个旋转的轮子被支承在轴的某一点上，使得其存在净力矩，那么这个力矩将改变其角动量，这种改变被称为'进动'。角动量和力矩都是矢量，如果施加的力矩有一个垂直于角动量的分量，它将导致自旋轴方向的变化率。