Question

A man stands on a freely rotating platform. With his arms extended, his rotation frequency is 0.25 rev/s. But when he draws them in, his frequency is 0.8 rev/s. Find the ratio of his moment of inertia in the first case to that of the second.

Answer 1

$I_1\omega_1=I_2\omega_2\to\frac{I_1}{I_2}=\frac{\omega_2}{\omega_1}=\frac{2\pi\nu_2}{2\pi\nu_1}=\frac{\nu_2}{\nu_1}=\frac{0.8}{0.25}=3.2$ . Answer