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Member advised to use the homework template for posts in the homework sections of PF.

This isn't about a specific physics problem, but rather a question:

Given I have a ball or cylinder rolling

I.e. if ##E_mech = K+U = K_{trans} + K_{rot} + U##, then ##\Delta E_mech = 0##?

I have been able to formulate a proof for a cylinder rolling down an inclined plane, with a change in height ##\Delta h##. I've been able to show that, at the bottom, ##K_{rot}+K_{trans} = mgh##.

But I just wanted to check that this is generally true along any path (e.g. curved paths), given that the rolling is always smooth? And also, are there any caveats here where this assertion doesn't work?

Thanks!

Given I have a ball or cylinder rolling

*smoothly*along some path, is it generally true that mechanical energy is conserved?I.e. if ##E_mech = K+U = K_{trans} + K_{rot} + U##, then ##\Delta E_mech = 0##?

I have been able to formulate a proof for a cylinder rolling down an inclined plane, with a change in height ##\Delta h##. I've been able to show that, at the bottom, ##K_{rot}+K_{trans} = mgh##.

But I just wanted to check that this is generally true along any path (e.g. curved paths), given that the rolling is always smooth? And also, are there any caveats here where this assertion doesn't work?

Thanks!