When an object is effectively isolated from external torques, like an ice skater

Question

When an object is effectively isolated from external torques, like an ice skater twirling on the tip of one skate, the angular momentum of the object

a. can be increased by shifting mass out away from the axis of rotation
b. can be decreased by shifting mass out away from the axis of rotation
c. can be increased by shifting mass in toward the axis of rotation
d. can be decreased by shifting mass in toward the axis of rotation
e. cannot be changed except by friction at the point of contact

(please provide a very detailed explanation for your answer)

Explanation / Answer

Angular Momentum cannot be changed because it is a conservative force. In fact, it is especially because of conservation of angular momentum that forces a skater to speed up when she pulls her arms in because then r is reduced for the arms and her moment of inertia is reduced.  Since the angular momentum Iw remains constant, if I decreases, then w must increase.

On the other hand, there is a small torque due to friction. That is why the skater cannot spin forever.

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