A child holds dumbbells with his hands straightened and lifted on both sides, and slowly rotates on a swivel chair. When he suddenly pulls his hands close to his body, he finds that his rotation speed has significantly increased. No one pushed himāhe simply pulled his arms back. Why would the rotation speed change? Let's start with the opening and closing of a door, which is easier to understand. A door can rotate around a pivot axis. When we open the door, the force we apply is usually perpendicular to the pivot axis. Try this: If you apply downward force to the door handle (with the force direction parallel to the pivot axis) or direct the force toward the pivot axis, the door won't rotate. The simple fact of opening the door contains many mechanical principles. We can at least conclude that if the applied force is parallel to the pivot axis or directed toward it, it has no effect on the door's rotation. Of course, we can replace the door with other objects. In the child's rotation problem, the only external forces acting on him are gravity and the chair's support on the ground, and these forces are all parallel to the pivot axis. According to our previous conclusion, these forces have no effect on the rotationāif the amount of rotation is the same before and after the child pulls his arms back, it would mean there's an "influence." However, the rotation speed clearly changes before and after the child pulls his arms back. So, what is the invariant quantity that represents the "system's rotation" during the rotation process? First, analyze the changes in the relevant physical quantities in the child's rotation problem. Before and after the child pulls his arms back, the phenomenon is: the mass of the dumbbells doesn't change, but its distance to the pivot axis decreases, so the system's rotation speed increases.
And the previous analysis shows that there are invariant quantities. So it's natural to think: if the rotation speed and distance change separately, could their sum be invariant? Impossible! Because the units of these two quantities are different and cannot be added. So could the "product of rotation speed and distance" be invariant? If you think this way, congratulations! You've guessed it right! The conclusion you've guessed is actually the "law of conservation of angular momentum" in physics, also known as the "law of conservation of momentum torque" in mechanics. With this conclusion, it's easy to understand why figure skaters quickly spin when they pull in their limbs: the skaters first open their arms and slowly rotate, and the friction on the ice is very small, so it has no effect on the rotation speed. And gravity and support forces are parallel to the pivot axis, so they also have no effect on the system's rotation. According to the "law of conservation of angular momentum" that the "product of rotation speed and distance" is invariant, pulling in the limbs is equivalent to decreasing the distance to the pivot axis, so the rotation speed will naturally increase.