Explain why friction is necessary to make the disc in the figure roll in the direction indicated.
$(a)$ Give the direction of frictional force at $B$,and the sense of frictional torque,before perfect rolling begins.
$(b)$ What is the force of friction after perfect rolling begins?

(N/A) To make the disc roll,an external torque is required to change its angular velocity. Friction provides this necessary torque.
$(a)$ The point of contact $B$ has a velocity relative to the surface due to the initial rotation $\omega_0$. Since the disc is rotating clockwise,the point $B$ has a linear velocity directed to the left. Friction acts in the direction opposite to the relative velocity,so the frictional force at $B$ acts tangentially to the right. The torque due to this friction about the center of the disc is directed outward,perpendicular to the plane of the disc,which acts to reduce the angular velocity.
$(b)$ Perfect rolling begins when the velocity of the point of contact $B$ becomes zero relative to the surface $(v = r\omega)$. Once perfect rolling is achieved,there is no relative motion between the point of contact and the surface. Therefore,the force of kinetic friction ceases to act,and the force of friction becomes zero.