I have an question about rotational motion of the following system
There is a hollow symmetric cylinder on a friction-less inclined plane (mass M, moment of inertia I, radius R, incline angle a). We place a small metallic sphere (mass m) inside the cylinder in an equilibrium state, but it can move inside without friction.
The cylinder is kept in place by external force and the small sphere is in equilibrium and not moving. The external force is removed at t=0.
Will the cylinder rotate while going down the plane? It so, how to calculate the rotational acceleration?
(I assume that a symmetric cylinder without a sphere inside will not rotate)