Question $6(20\%)$

Referring to Fig. Q$6,$ a wheel of radius r and mass $m$ is released from rest on the incline and rolls without slipping.

$($a$)$ Assume the mass per unit area of the wheel is uniform, find the moment of inertia of the wheel about its centre.

$($b$)$ Derive the expression for the linear acceleration of the centre of the wheel down the incline in terms of $m,r,,$ and $g.$

$($c$)$ What is the static coefficient of friction between the wheel and the incline when it is pure rolling down the incline?