19.4 Understanding rolling motion  (Page 2/4)

According to Newton’s first law for translation, if net external force is zero, then translation of the object i.e. linear velocity remains same. Similarly, according to Newton’s first law for rotation, if net external torque is zero, then rotation of the object i.e. angular velocity remains same. It means, then, that a body in uniform rolling motion shall roll with the same velocity.

Note here that when we say that a body is rolling with a constant velocity, then we implicitly mean that it is translating at constant linear velocity and rotating at constant angular velocity. It is so because two motions are tied to each other with the following relation,

We had difficulty to visualize a real time situation to verify Newton’s first law in translation or rotation, as it was difficult to realize a “force – free” environment. However, we reconciled to the Newton’s first law as we experienced that a body actually moved a longer distance on a smooth surface and a body rotated longer without any external aid about an axle having negligible friction and resistance. In the case of rolling also, we need to extend visualization for the condition of rolling when neither there is net force nor there is net torque.

One such possible set up could be a smooth horizontal plane. If a rolling body is transitioned (i.e. released) on a smooth plane with pure rolling at certain velocity, then the body will keep rolling with same velocity. This statement, if we agree, can be construed to be the statement of Newton’s first law for pure rolling motion.

Uniform rolling

The similarity of uniform rolling in the absence of external force and torque to its constituent motion ends in the real time situation. There is a surprising aspect of rolling motion on a surface (which is not friction-less) : “Friction for uniform rolling (i.e. at constant velocity) on a surface is zero”. This is a special or characterizing feature of uniform rolling motion. This feature distinguishes this motion from either translation or rotation. For, we know that surface friction decelerates translation and rotation of a body. The rolling is exceptional in this regard.

We explain the situation in two ways. First, we shall revert to the definition of pure rolling. The motion of pure rolling is characterized by absence of sliding. Friction, on the other hand, comes in the picture only when there is sliding i.e. there is relative displacement of two surfaces. Here, there is only a point (not a surface) in contact with the surface, which is continuously being replaced by neighboring particles on the rim of the rolling body. Thus, there is no friction as there is no sliding of surfaces over one another.

In yet another way, we can think opposite and analyze the situation. Let a force of friction (contrary to the situation) operates on the body in a direction opposite to the motion as shown in the figure below on the left. This friction decelerates translation. At the same time, friction constitutes a torque about center of mass. This torque accelerates rotation of the rigid body about the axis of rotation. This means that linear velocity decreases, whereas angular velocity increases. This contradicts the equation of rolling motion given by :