19.5 Role of friction in rolling  (Page 7/5)

The motion of a rolling body is altered due to external force/ torque. This can happen in following ways :

• The line of action of external force passes through center of mass.
• The line of action of external force does not pass through center of mass.

Depending on the line of action, a force causes linear or angular accelerations or both. The effect of external force or torque on rolling motion, however, is moderated by friction force between rolling body and surface.

In general, there is usually a bit of uncertainty with respect to the role and direction of friction in accelerated rolling. This module, therefore, aims to instill definite clarity with regard to the role and direction of friction. The friction in rolling is characteristically different and surprising in its manifestation with respect to the common negative perception (always negates motion) about it.

We have already learnt in the previous module that no friction is involved in uniform rolling. We shall find in this module that friction is actually the agent, which enforces the condition for accelerated rolling. In doing so, friction causes linear and angular accelerations or decelerations, depending on the requirement of rolling motion.

Role of friction

The line of action of external force passes through center of mass.

When the external force is passing through center of mass, it only produces linear acceleration as there is no moment arm and, thus, there is no torque on the body. Linear acceleration means linear velocity tends to increase. This, in turn, induces tendency of the rolling body to slide in the forward direction (i.e. in the direction of force/acceleration). Force of friction, therefore, appears in the backward direction of external force to check the sliding tendency.

We need to emphasize here that friction acts tangentially at the point of contact. Its direction is “backward” with respect to the component of external force parallel to this tangential direction. This clarification is required as the external force may not be parallel to the surface in contact.

So long the condition of pure rolling is met as given by the equation of rolling motion, there is no actual sliding – rather there is only a tendency to slide. As such the friction involved in accelerated rolling is static friction. We may recall our discussion of friction in translation. Friction is a self adjusting force. It adjusts with respect to external force. Importantly, the static friction is any intermediate value less than the maximum static friction ( ${\mu }_{s}N$ ).

The friction acts to balance the changes in a manner so that the condition as imposed by the equation of accelerated rolling is met. First, it reduces the net external force ( $F-f_S$ ) and hence the translational acceleration ( $a_C$ ). Second, it constitutes a torque in clockwise direction inducing angular acceleration(α). In the nutshell, an increase in linear acceleration due to net external force acting through center of mass is moderated by friction by a two pronged actions and the rolling is maintained even when the body is accelerated. Corresponding to linear acceleration, there is a corresponding angular acceleration such that :