# Friction in Rolling Motion [duplicate]

My understanding of rolling motion:

When a body rolls, at every instant, there is just one point of contact between the body and the plane and this point has no motion relative to the plane.

Now if there is no motion relative to the plane, then how does the rolling friction came into being?

I researched a bit about the origin of rolling motion but could not understand what does the following paragraph means:

During rolling, the surfaces in contact get momentarily deformed a little (Why?), and this results in a finite area of the body being in contact with the surface.

Your first quote is correct for an idealised model. There is no rolling friction then. Both wheel and surface are considered completely rigid.

Ideal model - no rolling friction

Non-ideal/more realistic model - rolling friction comes into the picture

These pictures are from this link that gives a very good graphic view on this. Going away from an ideal model introduces rolling friction since the wheel touches more than just one point, and not all points press back directly through the center - forces from such points cause counteracting torques, which is perceived as the rolling friction.

• Thanks!! that was really helpful! Can I say that the normal forces in the non-ideal situation are providing a torque to the wheel in the direction opposite to that of rotation of wheel? Jun 20, 2015 at 7:04
• @Abdullah Yes, you keep in mind that it is not just one - there are many normal forces from many points. Jun 20, 2015 at 8:15

Firstly, friction is the resistance to lateral motion between two surfaces and so is required for there to be no motion at the point of contact.

There may be confusion between rolling friction and rolling resistance. The former being the friction between the rolling object and the rolling surface required for rolling motion to occur. The latter being the resistance due to inelastic deformations, of the rolling object and the surface, causing a freely rolling object on a horizontal surface to slow down and eventually stop.

For a wheel to roll, especially if being driven, friction is required between the wheel and the surface, otherwise the wheel would "slip" and the rotational motion would not be converted into linear motion.

In the first case you mention, both the wheel and surface are assumed to be rigid, no deformation, so only one point of a perfect circle can be in contact with the surface at any time. The point in contact with the surface can be thought of as a, temporarily static, pivot. The rest of the body pivots around this and shifts the mass onto the next point of the circle, repeating, producing continuous motion.

In the second case (the more realistic case) the wheel and the rolling surface will be deformed due to the pressure from the weight of the wheel and the "equal and opposite" force of the surface acting on the wheel. (The amount of deformation in most rolling objects in small and difficult to observe.) In a simple case, this deformation tends to flatten a small area of the wheel in contact with the surface, increasing contact area of the wheel and surface, with respect to the ideal case (previous paragraph), increasing the friction between the two. This increased friction allows a greater torque to be applied before the wheel would "slip", and is why air/rubber tires are used on cars.

Hopefully this helps.