A solid cylinder of mass and radius slides across a rough horizontal surface with…

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A solid cylinder of mass

M

and radius

r

slides across a rough horizontal surface with initial speed

v_0

and no initial rotation. Kinetic friction acts until the cylinder begins rolling without slipping. What is the speed

v_f

of the center of mass at the instant pure rolling starts? (The cylinder’s moment of inertia about its center is

\tfrac{1}{2}Mr^2

.) (a)

v_f = \dfrac{1}{2}v_0

(b)

v_f = \dfrac{2}{3}v_0

(c)

v_f = \dfrac{3}{4}v_0

(d)

v_f = \sqrt{\dfrac{2}{3}}v_0