A solid uniform cylinder of mass and radius rests on a long horizontal surface
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A solid uniform cylinder of mass m and radius R rests on a long horizontal surface. A light, inextensible string is wound around the cylinder’s rim.
Scenario A: A student pulls the free end of the string with a constant horizontal force F, and the string remains taut so that it unwinds without slipping relative to the cylinder as the cylinder moves a distance d to the right.
Scenario B: The same force F is applied horizontally to the top point of the cylinder by a rough belt that slides over the cylinder’s surface without sticking, so the belt does not cause the cylinder to rotate while it moves the same distance d.
Assume no other external forces do work and neglect rolling friction and air resistance.
(a) For each scenario, state whether the cylinder is rotating after it has moved the distance d, and explain how you know.
(b) For Scenario A, derive an expression for the cylinder’s translational speed vA after it has traveled the distance d. Express your answer in terms of F,d, and m only.
(c) For Scenario B, determine the cylinder’s translational speed vB after moving the same distance d.
(d) Compare vA and vB. Discuss the physical reason for any difference in the two speeds, referring explicitly to energy transfers in each scenario.