Problem $6(25$ points$)$

Consider the wheel with radius $r=0\mathrm{.}60m$ and mass $m_{\text{r}\text{i}\text{m}}=4\mathrm{.}00kg.$ The magnitude of the tire's angular speed is $=12\mathrm{.}00$rad$/$s$.$ A bug $($also with negligible mass$)$ is holding tight onto the tire.

$($a$.)$ What is the wheel's moment of inertia?

$($b$.)$ What is the bug's tangential speed?

$($c$.)$ What is the wheel's kinetic energy?

$($d$.)$ The wheel is decelerated at an angular rate of $0\mathrm{.}25$rad$/s^2.$ How long does it take to stop the wheel?

$($e$.)$ Given the angular acceleration from part $($d$),$ what torque was required to stop the wheel?