2.Find the moment of inertia of a uniform solid cylinder of mass $M$, radius $R$, and length $L$ about its central longitudinal axis and about an axis passing through its center perpendicular to length.
Sol: Longitudinal axis: $I_{axis} = \frac{1}{2} M R^2$. Perpendicular central axis: $I_{perp} = M \left( \frac{R^2}{4} + \frac{L^2}{12} \right)$.
3.A child stands at the center of a turntable rotating with angular velocity $\omega_0$. If the child walks to the outer edge of radius $R$, find the new angular velocity.
Sol: Conservation of angular momentum: $I_0 \omega_0 = (I_0 + m R^2) \omega \implies \omega = \frac{I_0 \omega_0}{I_0 + m R^2}$.
