Rolling friction is the friction force acting on a body which is rolling on a surface.

in pure uniform rolling when V=RW (here W is angular speed) and acceleration is zero friction force will be also zero since body  does not have tendency to RUB the surface or in other word the relative velocity of lower most point will be zero w.r.t ground.





on the other hand if    V>RW then the lowermost surface will be rubbing surface in forward direction and hence friction will act backward.  

IF V<RW then body will exert force(rub) in backward direction on ground and hence friction will act in forward direction

I will describe this query to u by first telling you the theory behing rolling friction and then will come into how questions involving rolling friction are asked and solved.

Theory:

Rolling resistance, sometimes called rolling friction or rolling drag, is the resistance that occurs when a round object such as a ball or tyre rolls on a flat surface. It is caused by the deformation of the object, the deformation of the surface, or both. Additional contributing sources include surface adhesion and relative micro-sliding between the surface of contact. It depends very much on the material of the wheel or tire and the sort of ground. Additional factors include wheel radius, and forward speed.

The coefficient of rolling friction is generally much smaller for tires or balls than the coefficient of kinetic friction.

Several factors affect the magnitude of rolling resistance a tire generates:

• Material -


• Dimensions of rolling object -


• Smaller wheels, all else being equal, have higher rolling resistance than larger wheels.

Two imp things i would like to tell u here about rolling friction

1. Coefficient of rolling friction is of two types(mentioned below) .unlike coeff of static and dynamic friction, one type of RF is not a dimensionless quantity, it has a dimension of length and other is dimesnsionless.

2. The name rolling friciton suggests that i comes due to rolling motion, but accurately it also acts on the bodies which slides, we often neglect it since its value is very less compared to sliding friction(typically one percent of sliding friction)

Also I have found students have some misconceptions about the rolling friction

1. i have already mentioned in point 2.it is not caused by rolling motion

2. rolling friction makes the body roll-again a misconception- it is sliding friction that makes the body roll

rolling friction actually contributes to the eventual stopping of the body in perfect rolling motion, this u all must have noticed that every rolling finally comes to halt.

RF is generated due to deformation of the sufrace on which the body rolls, due to which the normal reactionshifts itself

The force of rolling resistance can be calculated as:

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:

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

Diagram showing deformation efffect on normal reaction which thus produces rolling friction