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A skater is spinning on the ice and extends her arms out straight. Discuss the effect...

A skater is spinning on the ice and extends her arms out straight. Discuss the effect this will have on her moment of inertia, her angular momentum, and her angular velocity. Will each increase, decrease, or stay the same? Explain. Please be specific?

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Answer #1

Moment of inertia of the skater here will be:

where mr2 is the momentum of inertia due to the hands and their distance from the torso.

Therefore, the moment of inertia increases if the hands are extended outwards.

The angular momentum of the skater is conserved at all times regardless of the position of the arm.

so, if the arms are extended outwards, an increased moment of inertia must be compensated by a decrease by an equal factor in the rotation speed of the skater. Similarly, a decreased moment of inertia must be compensated by an increase in the rotation speed of the skater. This means that the skater slows down when the arms are extended outwards.

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