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My book says friction is non dissipative for a cylinder rolling down an inclined plane,so is it conserved?

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    $\begingroup$ friction here plays the role of force of constraint. $\endgroup$ – wcc Jun 25 at 3:43
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No, you cannot view friction as a conservative force in this situation. Here is why:

We know that for a conservative force $F$ we can define a potential energy function $U$ such that $$F=-\frac{\text d U}{\text d x}$$

and a consequence of this is that the work done by this force is given by $$W=-\Delta U$$

However, static friction does no net work on the cylinder. Therefore for all instances of rolling here $W=0$. This means we must have a constant potential energy, which means that $F=0$. This is a contradiction, since we assumed we had a static friction force. Therefore static friction cannot be conservative.

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