A holiday ornament in the shape of a hollow sphere with a mass of 10 grams and a radius of 4.5 cm is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a physical pendulum. You can ignore any possible friction at the pivot.

a.) What is the rotational inertia for the hollow spherical ornament about the pivot at the tree limb? The rotational inertia for a hollow sphere about its center of mass is 2/3(MR^2)

b.) Suppose the ornament were displaced from equilibrium by an angle of 4.5 degrees and released from rest. Calculate the magnitude of the torque on the ornament, about the pivot at the tree limb, at the instant immediately after release.

c.) Calculate the angular frequency and the period of the motion of the swinging ornament. Give your answers as an ordered pair, with the angular frequency first, followed by a comma, followed by the period.

d.) Calculate the maximum kinetic energy of the swinging ornament if it is displaced from equilibrium by an angle of 4.5 degreesand released from rest. Give your answer in millijoules.