## Section6.11Rolling Friction

Friction of rolling bodies is a little different than the static and kinetic frictions we discussed above.

Suppose you roll a wheel on a foam. You will notice that the wheel deforms the foam at the surface of contact marked P in the figure. In rolling without slipping motion, speed of the center of the wheel $v\text{,}$ the radius of the wheel $R\text{,}$ and the angular speed of the rotation of the wheel $\omega$ (the Greek letter 'omega') are related by

$$v = \omega R.\tag{6.11.1}$$

You can see this by looking at the distance traveled by point on the rim and that traveled by the center of the wheel. The same type of momentary deformation happens between the wheel of a car and road.

For a rolling motion of a wheel, we demand that the wheel does not slide on the surface. The “non-sliding” condition means that the small part of the wheel that is in momentary contact with the surface must be static by a static friction. This static friction is called the rolling friction.

Since the surface of contact is small during the rolling process and is in contact for a moment only, the maximum rolling friction is usually considerably smaller than the maximum static friction for the same type of surfaces in contact because in rolling. The contact in rolling occurs over a small area and for a short period of time.

We will denote the rolling friction force by $\vec F_r$ and the magnitude by the same symbol without the arrow. Since, rolling friction is a static friction, we have a limiting value, which will be denoted by $F_r^{\text{max}}\text{.}$ A coefficient of rolling friction, $\mu_r \text{,}$ can be defined similarly to static and kinetic friction coefficients.

$$\mu_r = \dfrac{F_r^{\text{max}}}{F_N}.\tag{6.11.2}$$

We will study examples of rolling force when we study rolling motion in the chapter on rotation.