Clarification regarding rolling cylinder with CG slightly above

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SUMMARY

The discussion focuses on the mechanics of a rolling cylinder on an inclined plane, specifically addressing the work done by rolling friction and normal reaction forces when the center of gravity is positioned slightly above the center. The user proposes formulas for the work done: W1 = F * c * Sinθ for rolling friction and W2 = R * (c - c * Cosθ) for normal reaction. The inquiry seeks validation of these equations, highlighting the importance of understanding forces acting on non-standard configurations of rolling objects.

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seshikanth
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Hi

Can anyone please clarify the following?

Let there by a rolling cylinder on an inclined plane. Let the solid cylinder(with Center O) on the inclined plane has Center of gravity at a distance 'c' slightly above O. If the cylinder is displaced slightly through an angle θ then

[Let N = normal reaction; F= Rolling friction]

1. What is the work done by rolling friction F
I think, W1 = F. c Sinθ. ---- Can you tell am i correct here?

2. What is the work done by Normal Reaction?
I think it is W2 = R. (c - c Cosθ) ; --- Can you tell me if i am correct here? I know that the work done by normal reaction for a cylinder with center O as zero !



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