$!$

Required information

Problem $16\mathrm{.}073-$ DEPENDENT MULTI$-$PART PROBLEM $-$ ASSIGN ALL PARTS

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

A uniform sphere of radius $\backslash ($ r $\backslash )$ and mass $\backslash ($ m $\backslash )$ is placed with no initial velocity on a belt that moves to the right with a constant velocity $\backslash (\backslash$mathbf$\{$v$\}\_\{1\}\backslash ).$

Problem $16\mathrm{.}073.$b $-$ Linear and angular velocities of sphere on belt

Denoting by $\backslash (\backslash$mu$\_\{$k$\}\backslash )$ the coefficient of kinetic friction between the sphere and the belt, identify the linear and angular velocities of the sphere at time $\backslash ($ t$\_\{1\}\backslash ).$