Question

suppose you sit on a rotating stool, holding a big mass in each outstretched hand. if you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? explain.

Answer 1

When the masses drop, they move with the same angular velocity as you before hitting the ground. i.e., they leave your hand with their angular momentum. So, in one view, you can think the mass decreases, which means the moment of inertia also decreases. Therefore, the angular velocity should increase.