An ice skater spins with her arms extended and then pulls her arms in and spins faster. Which statement is correct?

Question

A. Her kinetic energy of rotation increases because of the work she does to pull her arms in.
B. Her kinetic energy of rotation does not change because, by conservation of angular momentum, the fraction by which her angular velocity increases is the same as the fraction by which her rotational inertia decreases.
C. Her kinetic energy of rotation decreases because of the decrease in her rotational inertia; she does loses energy because she gradually gets tired.

I'm not sure of this one because, I know for sure that the angular rotation increases and the rotational inertia decreases, but does the kinetic energy changes or is it conserved?

A solid sphere rolls without slipping down an incline, starting from rest. At the same time, a box starts from rest at the same altitude and slides down the same incline, with negligible friction. Which object arrives at the bottom first?
A. Both arrive at the same time.
B. It is impossible to determine.
C. The box arrives first.
D. The solid sphere arrives first.

I think it's A.

Please help, I'm not sure of these.

Answer 1

first one: KE remains the same.

second: The inertia of the sphere causes it to absorb energy as rotational, the box all converts to translational. The box arrives first.

Answer 2

Thanks... now I understand, but when I choose B in the first one it says that it's wrong...