19.5 Role of friction in rolling  (Page 5/5)

We can accelerate rolling by applying force through its center of mass. As discussed earlier, friction in such case acts in the backward direction to counteract sliding in the forward direction. However, it is difficult to visualize a mechanical force that can be applied through center of mass of a rolling body. Incidentally, gravity provides a ready made arrangement in which force acts through center of mass.

A ball rolling along an incline is one such example, in which external force is gravity. Its component along the plane “mgsinθ” acts through COM of the rolling body.

The friction, in this case, acts in the backward direction as shown in the figure above.

Another way to accelerate rolling is to impart a force such that its line of action does not pass through center of mass. In this case, force constitutes a torque that imparts angular acceleration in addition to translational acceleration.

Such is the case with all transporting vehicles having wheels. The internal drive rotates the shaft, which in turn tends to rotate the wheel. We can visualize the situation better for the case of bicycle. When a bicycle is peddled, torque is imparted to the wheel. The chain – socket arrangement rotates the wheel. As discussed earlier, the friction, in this case, is in the direction of the acceleration of COM.

What if we apply the brake? The sole purpose of applying the brake is to apply a torque in the opposite direction to the direction of rotation. The brake pad jams on the rim. The tangential friction force constitutes the torque opposing the rotation. There is a corresponding linear deceleration of the wheel. A linear deceleration is equivalent to an acceleration in the backward direction. The friction between the wheel and surface, therefore, also acts backward along the backward direction of acceleration (i.e. deceleration) as shown in the right figure above.

Summary

1: The friction between surface and rolling body is self adjusting static friction for accelerated rolling.

2: The friction between surface and rolling body is less than that in the case of sliding.

3: Friction facilitates simultaneous occurrence of two types of acceleration as a response to external stimuli (force or torque or both).

4: Direction of friction :

(i) If the force passes through center of mass, then there is sliding tendency in the forward direction of applied force. In turn, friction acts in backward direction of the external force.

(ii) If the force does not pass through center of mass, then it constitutes torque. There is sliding tendency due to torque in the backward direction of applied force. The net result is that there is either no net friction (in special circumstance) or there is friction in the forward direction.