Consider a uniform solid sphere of radius R and mass M rolling without slipping.Which form of its kinetic energy is larger,translational or rotational?
A) Its translational kinetic energy is larger than its rotational kinetic energy.
B) Its rotational kinetic energy is larger than its translational kinetic energy.
C) Both forms of energy are equal.
D) You need to know the speed of the sphere to tell.

Question

Quizplus · Accepted Answer

For a rolling sphere, the total kinetic energy consists of both translational and rotational kinetic energies. 
The translational kinetic energy is given by KE_trans = 1/2 Mv^2, where v is the velocity of the center of mass. 
The rotational kinetic energy is given by KE_rot = 1/2 I ω^2, where I is the moment of inertia of the sphere (I = 2/5 MR^2 for a solid sphere) and ω is the angular velocity of the sphere. 
Since the sphere rolls without slipping, v = Rω, and substituting this in the above equations, we get KE_trans = 1/2 Mv^2 = 1/2 (2/5 MR^2 ω^2) and KE_rot = 1/2 I ω^2 = 1/2 (2/5 MR^2 ω^2). 
Thus, we see that both forms of energy are equal, i.e., KE_trans = KE_rot.

Consider a Uniform Solid Sphere of Radius R and Mass