Question

Explain, in the terms of physics, How figure skaters do spins on the ice. Explain Inertia and use two formulas that support how the skaters spin.

Answer 1

In figure skating, when a figure skater is rotating with her arms extended, the greater moment of inertia will make her rotate slower. Now, if she brings both arms inward, decreasing the distance between axis of rotation and arm, the inertia will decrease. Now to conserve momentum, the angular velocity must increase.  A change in rotational inertia is compensated by a change in rotation speed.

So, what we can say is that when a figure skater needs to speed up, she need to make sure that the inertia of rotation is the least and in order to slow down, she can again increase her inertia by extending her arms.

Here the conservation of angular momentum says

I₁₁ = I₂₂