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## Homework Statement

A cyllinder of radius rc starts a height h above a loop the loop on a track. If the radius of the loop is rl, how high does h need to be. The cyllinder does not slip. Express the answer in terms of the radius of the loop.

## Homework Equations

Conservation of energy

## The Attempt at a Solution

The cyllinder has potential energy mgh at the beginning and 2mgrl at the top of the loop. It also has kinetic energy 1/2mv^2 +1/2Iw^2 where v=[tex]\sqrt{rg}[/tex] is the critical velocity. The moment of inertia is I = 1/2mrc^2. I cant figure out how to get rid of rc in the answer.

I get h = rl/2 + rc^2/4rl + 2rl