Vector Properties of Rotational Quantities

Rotation Vectors

旋转矢量

Angular motion has direction associated with it and is inherently a vector process. But a point on a rotating wheel is continuously changing direction and it is inconvenient to track that direction. The only fixed, unique direction for a rotating wheel is the axis of rotation, so it is logical to choose this axis direction as the direction of the angular velocity. Left with two choices about direction, it is customary to use the right hand rule to specify the direction of angular quantities.

角运动具有方向性，并本质上是一个矢量过程。但是，旋转轮上的一个点方向不断变化，跟踪这种方向是不方便的。旋转轮中唯一固定且唯一的方向是旋转轴，因此选择旋转轴方向作为角速度的方向是合乎逻辑的。在两个方向选择中，习惯上使用右手法则来指定角量的方向。

Direction of other angular quantities

其他角量的方向

Vector rotation examples

矢量旋转示例

Directions of Angular Quantities

角量的方向

As an example of the directions of angular quantities, consider a vector angular velocity as shown. If a force acts tangential to the wheel to speed it up, it follows that the change in angular velocity and therefore the angular acceleration are in the direction of the axis. Newton's 2nd law for rotation implies that the torque is also in the axis direction. The angular momentum will also be in this direction, so in this example, all of these angular quantities act along the axis of rotation as shown.

作为角量方向的一个例子，考虑所示的角速度矢量。如果一个力作用在轮子上以加快其转动，那么角速度的变化以及因此的角加速度都沿着轴的方向。牛顿第二定律对于旋转的推论表明，力矩也沿着轴的方向。角动量也将沿着这个方向，因此在这个例子中，所有这些角量都沿着旋转轴方向，如图所示。

What if the torque is perpendicular to the angular momentum?

如果力矩垂直于角动量呢？

Angular Momentum Change

角动量变化

A force tangential to the wheel produces a torque along the axis as shown (right hand rule). The change in angular momentum is therefore along the axis and the wheel increases in angular velocity. However, if the torque direction is perpendicular to the axis of the wheel the effect is very different. The change in angular velocity is perpendicular to the angular velocity vector, changing its direction but not its magnitude. The resultant motion of the wheel around a vertical axis is called precession.

作用在轮子上的切向力会产生沿轴的力矩，如图所示（右手法则）。因此，角动量的变化沿轴方向，轮子的角速度会增加。然而，如果力矩方向垂直于轮子的轴，效果则截然不同。角速度的变化方向垂直于角速度矢量，改变其方向但不改变其大小。轮子围绕垂直轴的 resultant 运动称为进动。