A round object has a rotational inertia of I = ?MR2, where ? is a constant, M is its mass and R is its radius. It starts at rest and its center-of-mass rolls a distance d down a plane inclined at an angle ??, without slipping. As it rolls, it gains a center-of-mass speed of v and a rotational speed of ? over the distance d.

A) What is the change in rotational kinetic energy of the round object after it has moved the distance d?

B) What is the change in potential energy of the round object after it has moved the distance d?

C) Use the conservation of mechanical energy to determine the object's speed v at the distance d. Express the answer in terms of d, ?, ?, and any other constants necessary.

D) What fraction of the total kinetic energy of the rolling object is rotational? Express your answer in terms of ? alone.