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) Both are equal.
C) Rotational kinetic energy is larger.
D) You need to know the speed of the hoop to tell.

Question

Quizplus · Accepted Answer

For a hoop rolling without slipping, the translational kinetic energy (associated with the motion of the center of mass) and the rotational kinetic energy (associated with rotation around the center of mass) are equal. This is because the translational kinetic energy is given by (1/2)Mv^2 and the rotational kinetic energy by (1/2)Iω^2, where I is the moment of inertia of the hoop (I = MR^2 for a hoop) and ω is the angular velocity. Since v = ωR for rolling without slipping, both expressions yield the same value for kinetic energy.

Consider a Uniform Hoop of Radius R and Mass M