The physics
Angular momentum about an axis is L = Iω. It changes only when an outside torque acts about that axis.
no outside torque: I₁ω₁ = I₂ω₂
A skater who pulls her arms in makes her I smaller. So she spins faster. A ring or blobs that land on a turntable make I bigger. So it slows down.
The kinetic energy KE = ½Iω² does not have to stay the same. Pulling the arms in adds KE. A sticky landing turns some KE into heat.
Something that starts at rest keeps a total L of zero. Spin a wheel one way, and you turn the other way.
A hinge or a pivot can give a big sudden force. Its torque about itself is zero. So keep L about the hinge through a hit. Then use energy for the swing.
m v L = I ω ½ I ω² = the gain in PE