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

Question

Quizplus · Accepted Answer

For a uniform hoop rolling without slipping, the translational kinetic energy and the rotational kinetic energy are equal. This is a consequence of the parallel-axis theorem. Therefore, both kinetic energies have the same value: K = (1/2)MV^2 + (1/2)Iω^2, where V is the speed of the hoop's center of mass, ω is the angular speed of the hoop, M is the mass of the hoop, and I is the moment of inertia of the hoop about an axis passing through its center of mass.

Consider a Uniform Hoop of Radius R and Mass M