A student observes a uniform cylinder that is both translating and rotating while…
PHYSICS · Single correct · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A student observes a uniform cylinder that is both translating and rotating while sliding across a rough horizontal table. During the slide, the cylinder’s center-of-mass speed decreases, but its angular speed increases until pure rolling begins. Which of the following best explains this simultaneous decrease in translational kinetic energy and increase in rotational kinetic energy?
(a) Conservation of linear momentum requires the cylinder’s translation to slow while its rotation speeds up, so the total mechanical energy stays constant because friction does no work.
(b) Static friction converts the cylinder’s translational kinetic energy entirely into rotational kinetic energy, so the cylinder slows down while spinning up without any energy dissipation.
(c) Kinetic friction does negative work on the center-of-mass motion while exerting a torque that increases the cylinder’s rotation, converting part of the lost translational energy into rotational energy and the rest into thermal energy.
(d) Because the point of contact is instantaneously at rest, kinetic friction does no work, yet the torque it exerts boosts the cylinder’s rotation; translation slows solely to keep the total mechanical energy constant.