What is rolling friction? Write the laws of rolling friction. Define the coefficient of rolling friction.

(A) Rolling friction is the resistive force that opposes the motion of a body when it rolls over a surface without sliding. It is denoted by $f_{r}$.
Laws of rolling friction:
$(1)$ The magnitude of rolling friction is independent of the area of contact.
$(2)$ The magnitude of rolling friction is directly proportional to the normal force $(N)$: $f_{r} \propto N$,which implies $f_{r} = \mu_{r} N$.
Coefficient of rolling friction $(\mu_{r})$:
It is defined as the ratio of the rolling friction force to the normal force,given by $\mu_{r} = \frac{f_{r}}{N}$. It is a dimensionless quantity.
Explanation:
When a rigid body rolls over a surface,the surfaces in contact undergo momentary deformation. This deformation prevents the body from moving with constant velocity,as there is a resistive component of the contact force parallel to the surface. Rolling friction is significantly smaller than static or kinetic friction (typically $\frac{1}{100}$ to $\frac{1}{1000}$ times),which is why wheels are efficient. The relationship between coefficients is $\mu_{r} < \mu_{k} < \mu_{s}$.