1.A solid sphere of mass $M$ and radius $R$ rolls without slipping down an inclined plane of inclination $\theta$. Find acceleration of its center of mass.
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.
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.
