Rolling Friction

Theory:
Rolling friction is the resistance that occurs when a round object such as a ball or tyre rolls on a flat surface.

It is caused by
Deformation of the object
Deformation of the surface, or both.
Surface adhesion
Relative micro-sliding between the surface of contact.

It depends on
Material of the wheel or tire
Sort of ground
Wheel radius (smaller wheel has higher rolling resistance)
Forward speed.

The coefficient of rolling friction is generally much smaller than the coefficient of kinetic friction.

Donot confuse it with the friction that we use to solve the problems of rolling ball, where the ball is hit by a cue or where a ball changes its direction and starts to return due to resistance! The friction coefficient we use there is the normal friction coefficient!

Aside (You may ignore these.. but these are concepts!)
1. There are two different coefficient of Rolling friction (One is dimensionless, the other has a unit of length)
2. Rolling friction also acts on sliding bodies, we neglect it since its value is very less compared to sliding friction

The force of rolling resistance can be calculated as:
F=C_rrN_f
where
F is the resistant force,
C_rr is the dimensionless rolling resistance coefficient or coefficient of rolling friction (CRF), and
N_f is the normal reaction force

The force of rolling resistance can also be calculated as:
F = Wa/r
where
F is the resistant force,
a is the rolling resistance coefficient or coefficient of rolling friction with dimension of length,
W is the weight, and
r is radius of rolling body