Explain why friction is necessary to make the disc in Fig. 7.41 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 ?

Explanation

It is the force of friction `(vecf)` which produces the torque required for rolling.
(a) The frictional force `(vecf)` at B is to oppose the velocity at B. Since the velocity of B (i.e., `omega_(0)R`) is in a direction opposite to the arrow, the frictional force is in the direction of the arrow. Applying right hnd rule for the direction of rotational vector, `vecomega_(0)` is perpendicular to the plane and directed inwards whereas the frictional torque `vectau`, though perpendicular to the plane is directed outwards
(b) The force of friction decreases the velocity of the point of contact at B (note that velocity of B, i.e., `omega_(0)R` and `vecf` are oppsitely (directed) . For perfect rolling, the velocity of the point B is zero . At this instant, f also becomes zero