When body is rolling without sliding friction force is called rolling friction. It is denoted by $f_{r}$ Laws of rolling friction :

$(1)$ Magnitude of frictional force do not depend on area of contact.

$(2)$ Magnitude of rolling friction is proportional to normal force.

$f_{s} \propto \mathrm{N}$

$\therefore f_{s}=\mu_{r} \mathrm{~N}$

$u_{r}=\text { co-effil }$

$\mu_{r}=$ co-efficient of rolling friction.

It is unitless,

$\mu_{r}=\frac{f_{r}}{\mathrm{~N}}$

When a ring or a sphere rolling without slipping over a horizontal plane, 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.

In this ideal situation kinetic or static friction is zero and body should move with constant velocity.

But in practise there is some resistance to motion in form of rolling friction hence motion is retarded.

To keep body rolling some applied force is needed.

For, object of given mass rolling friction is $\frac{1}{100}$ or $\frac{1}{1000}$ times static or kinetic friction. Because of this reason discovery of wheel has major milestone in human history. Origin of rolling friction is different than static friction and kinetic friction.

During rolling the surfaces in contact get momentarily deformed a little and small part of body remain in contact with surface.

As a result there is component of the contact force parallel to surface which opposes motion. $\mu_{r}<\mu_{k}<\mu_{s}$