Physics

Problem

A solid cylinder of mass

M

rolls without slipping at speed

v

on a horizontal surface. Student A models the cylinder as a single particle and calculates its kinetic energy as

K_A=\frac12 M v^{2}

. Student B treats the cylinder as a rigid system and includes both translation and rotation, obtaining

K_B=\frac12 M v^{2}+\frac12 I\omega^{2}

with

I=\frac12 M R^{2}

. By what factor does Student A’s value differ from Student B’s correct value? a)

\dfrac12

\dfrac43

\dfrac23

1