A torque of $\backslash (36\mathrm{.}2\backslash$mathrm$\{$~N$\}\backslash$cdot $\backslash$mathrm$\{$~m$\}\backslash )$ is applied to an initially motionless wheel which rotates around a fixed axis. This torque is the result of a directed force combined with a friction force. As a result of the applied torque the angular speed of the wheel increases from $0$ to $\backslash (9\mathrm{.}5\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ).$ After $5\mathrm{.}80$ s the directed force is removed, and the wheel comes to rest $59\mathrm{.}8$ s later.

$($a$)$ What is the wheel's moment of inertia $($in $\backslash (\backslash$mathrm$\{$kg$\}\backslash$cdot $\backslash$mathrm$\{$m$\}^\{2\}\backslash ))?$

$\backslash (\backslash$times $\backslash$mathrm$\{$kg$\}\backslash$cdot $\backslash$mathrm$\{$m$\}^\{2\}\backslash )$

$($b$)$ What is the magnitude of the torque caused by friction $($in $\backslash (\backslash$mathrm$\{$N$\}\backslash$cdot $\backslash$mathrm$\{$m$\}\backslash ))?$

$\backslash (\backslash$times N $\backslash$cdot m $\backslash )$

$($c$)$ From the time the directed force is initially applied, how many revolutions does the wheel go through?

$\backslash ($ x $\backslash )$ revolutions