# Direction of friction in pure rolling

Suppose a disc or a sphere with uniform mass density is purely rolling without any slipping/sliding on a ground having friction. Will there be friction acting on the disc/sphere? If yes, what will be it’s direction? What I think is there will be no friction acting, since friction plays no role in pure rolling, as a body that is initiated pure rolling continues to roll even if friction is absent (at least as far as I know) My high school professor says that there will indeed be friction acting on the body, however, there will be no direction, or rather the direction of friction would be ‘unknown’. Is he right?

• What other forces are present? And where are they applied? Commented Sep 22, 2019 at 18:58
• @AaronStevens other than friction, there is only gravity acting on the body. Commented Sep 22, 2019 at 19:08
• Then there will be no friction if the body is already rolling without slipping on a flat surface. However, if there was some other applied force, then you would need more information to discern in which direction friction would need to act. Commented Sep 22, 2019 at 19:14

Will there be friction acting on the disc/sphere? If yes, what will be it’s direction?

Technically its rolling resistance or rolling drag. Although the term rolling friction is used it is probably a misnomer. For a complete discussion of the subject see: https://en.wikipedia.org/wiki/Rolling_resistance

The rolling resistance force is given by

$$F_{r}=c_{rr}mg$$

Where $$c_{rr}$$ is the coefficient of rolling resistance. The following link give some values for the coefficient of rolling resistance:

https://www.engineeringtoolbox.com/rolling-friction-resistance-d_1303.html

These coefficients are typically an order of magnitude less that the coefficients of static and sliding friction.

The direction of rolling resistance or drag is the same as that for sliding friction, that is, rear ward in opposition to the direction of the pulling force or torque applied to the wheel, as illustrated in the introductory diagram in the second link. So like sliding friction, the rolling resistance opposes a force in the opposite direction.

But even without a pulling force or applied torque to the wheel axle, i.e., for the case of a coasting wheel, there is still energy dissipated due to the inelastic behavior of all real the materials at the area of contact. Wikipedia points out that the primary cause of pneumatic tire rolling resistance is hysteresis, that is, heating resulting from the inelastic behavior of materials such as rubber when it compresses and uncompresses during contact with the road.

The hysteresis increases with increased area of contact between the tire and the surface. So the loss is greater for under inflated pneumatic tires. If you ride a bicycle you will "coast" further with properly inflated tires than with under inflated tires, all other things being equal.

Hope this helps.