A hollow sphere of radius 0.15 m, with rotational inertia I = 0.082 kg m^2 about a line through its center of mass, rolls without slipping up a surface inclined at 30° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 50 J.
(a) How much of this initial kinetic energy is rotational?
(b) What is the speed of the center of mass of the sphere at the initial position?
Now, the sphere moves 1.0 m up the incline from its initial position.
(c) What is its total kinetic energy now?
(d) What is the speed of its center of mass now?