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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

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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)

 free body diagram 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).

Free body diagram for case2

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.

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

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