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

Explanation

(i) To roll a disc, a torque is required which in turn requires a tangential force to on it. As the force of friction is the only tangential force acting on the disc, so it is necessarily required for the rolling of a disc. (ii) Frictional force at `B` opposes the velocity of `B`. therefore, frictional force is in the same direction as the arrow. the sence of frictional torque is such as to oppose the angular motion. by right hand rule, `vec(omega)_(0)` act into the plane of paper and `vec(tau)` out of the paper. (iii) frictional force decreases the velocity of the point of constant `B`. perfect rolling begins when this velocity is zero at which the force of friction is zero.