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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 2. By what factor does his moment of inertia change, and why?

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Answer #1

(1) when arms are outstretched, the angular speed and moment of inertia are and I respectively. for the 2nd case when arm close to his body the angular speed changed by a factor of two, therefore new angular speed is;

' = 2 and assuming new moment of inertia as I'.

Since, there is no external torque in the system, angular momentum is conserved, so apply conservaton of angular momentum;

moment of inertia changes due to the change in position of arms.

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