# Calculating the coefficient of rolling friction

I am unsure as to how I calculate the coefficient of rolling friction. Is there a particular formula I should use? I am having difficulty locating it online, as all that shows up is how to calculate rolling friction, which involves the coefficient, but not the coefficient formula itself. Thanks

The coefficient of rolling friction may vary with different conditions.

I am finding it for a cylinder of mass M and radius R in 2 cases. g is acceleration due to gravity and a is the acceleration in each case. ( Representing it with u, As in my keyboard i dont have mu)

Case1:

Normal reaction force N= Mg.

Resultant force Ma= F - uN.

Torque due to friction = RuN.

Also Torque due to friction = Ia/R.
( a/R is the angular acceleration and I is the moment of inertia.)

Thus uN = Ia/R^2.

I= MR^2/2 for a cylinder.

uN= Ma/2.

Thus Ma = F - Ma/2

a=2 F /(3M).

uMg= Ma/2.

Thus u= a/2g = F/(3Mg).

Case 2:

Normal reaction force N= Mg cos o. ( I am using o in place of theta in the diagram for the angle of inclined plane)

Torque due to friction = RuN.

Again uN = Ia/R^2= Ma/2.

Resultant force Ma= Mg sin o - uN.

Thus a= 2/3 × g sin o.

Thus u Mg cos o=Mgsin o/ 3.

Thus u = tan o /3.

• In the figure i have shown the cross section of the cylinder – Suprabha Apr 21 '17 at 5:28