A figure skater is spinning slowly with arms outstretched. He brings his arms in close to...

A figure skater is spinning slowly with arms outstretched. He brings his arms in close to his body and his angular velocity changes by a factor of 4. By what factor does his moment of inertia change, and why?

Solutions

Expert Solution

Let L be the total angular momentum of the skater when he is spinning with his arms outstretched, and L' be the angular momentum of the skater when he brings his arms close to his body.

Now as angular momentum of the spinning skater will be conserved, therefore:

As angular momentum is given by:

Where I is the inertia of the body.

is the angular velocity

Let I and be the inertia and the angular velocity of the skater when his arms are outstretched

Let I' and be the inertia and the angular velocity of the skater after he has brought the arms close to his body

Therefore, using conservation of angular momentum we have:

As angular velocity changes by factor of 4, therefore :

Therefore, momentum of inertia changes by a factor of 1/4 th.

As angular momentum is conserved (), therefore when angular velocity increases, then the moment of inertia should decrease in order to keep the angular momentum constant (conserved).

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genius_generous answered 1 year ago

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