A wheel with a mass, $m$ and radius rolls down a rough surface incline CW with an initial velocity $v_0.$ The final velocity of the wheel is $0.$ Using "THE PRINCIPLE OF LINEAR AND ANGULAR IMPULSE AND MOMENTUM", Express

a$)$ Draw the $"3$ part" FBD$.$

b$)$ Express the required magnitude of ${}_0$ in terms of $v_0$ and $r_{.}$

c$)$ Express the time required for the wheel to come to rest in terms of $v_0$ and the coefficient of kinetic friction ${}_k.$