A solid uniform disk and a thin hoop have the same mass and radius
PHYSICS · Single correct · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A solid uniform disk and a thin hoop have the same mass and radius. Each is released from rest and rolls without slipping down the same frictionless incline. Which statement best describes their motion at the bottom of the incline?
(a) The hoop reaches the bottom first because its larger moment of inertia means a greater share of its gravitational potential energy is converted into rotational kinetic energy, resulting in more total kinetic energy at the bottom.
(b) The disk reaches the bottom first because its smaller moment of inertia allows a larger fraction of its gravitational potential energy to become translational kinetic energy.
(c) Both objects reach the bottom at the same time because, having the same mass and starting from the same height, they experience the same acceleration down the incline.
(d) The disk reaches the bottom first mainly because the static friction force on it is larger than on the hoop, giving it a greater net downhill force.