Question

When a spinning star shrinks in radius, it speeds up. Why does this happen?

Answer 1

Because of conservation of angular momentum.

Explanation:

Consider a spinning skater. Who draws in his or her arms and then spins faster. The star is no different.

Let's look at a simple example - a point mass rotating in a circular path. It's momentum at any point is `mv` where `v` is the linear instantaneous value of its velocity. Now imagine the same mass with the same momentum hauled into a lower orbit. It has the same (conserved) momentum and its mass remains the same as does its linear velocity, but now it's traveling in a smaller circle. The only way this can happen is if it speeds up, just like a star.

Answer 2

When a spinning star shrinks in radius, it loses some of its rotational inertia, and due to the conservation of angular momentum , it will gain rotational speed.

Explanation:

You can be a star (even without skates) and try this out for yourself. You will need four friends and the gym or a wide hallway. To begin, walk up to a mark located in the center of the area and invite your four friends to form a line beside you, all facing the same direction. You now have one spoke of a wheel with you as the hub. Start walking together in step, then move the entire line to mimic the rotation of the spoke with you as the hub. It’s like a marching band or skaters turning in a wheel formation. Everyone must stay in line.

You will find the work you are doing in the center is easy, and the same may be said for the friend next to you, but for the friends towards the outer end of the spoke, their work will become increasingly harder. This is because their rotational inertia increases with distance from the center. You can confirm this by linking arms as you walk around in formation. You will notice an outward pull that also increases from person to person moving outward.

Now we can get back to the star. As you all walk in rotation, ask the outermost friend to drop out. Rotation will get somewhat easier. Then ask the next outermost friend to drop out. Easier yet. This trend will continue until only you are left. And if you are still using the same energy, you will find yourself rotating faster on your own than you were when with the group. Your rotational inertia has been minimized.

There is more information, with math, here:
https://en.wikipedia.org/wiki/Angular_momentum