1. A thin spherical shell of mass 13.5 kg is rotating through its center of mass. It has a radius of 4.11 m. a) What is its moment of inertia? b) If it is rotating with a rotational velocity of 2.32 rad/ s, what is its rotational kinetic energy? 2. A hollow cylinder is spinning around its center of mass at a constant rotational speed of 9.73 radXs. It has an inner radius of 1.3 m and an outer radius of 2.4 m. It has a mass of 35.5 kg. a) What is its moment of inertia? b) What are the velocities of the cylinder at its inner and outer radii? 3. A solid sphere of mass 12 kg and radius 0.56 m is rotating around a parallel axis 0.2 m away from its center of mass. What is its moment of inertia? 4. Normally, if you spin a uniform rigid rod through its center of mass, it will have a moment ofinertia of1/12 * M * L2 , where M is its mass and L is its full length. Use the parallel axis theorem to prove that if you instead rotate the rod at one of its ends, the moment of inertia will instead be 1/3 * M * L2