268. assignment (rotational inertia - energy)

How much accounting for the rotational energy matter? Consider allowing a hollow cylinder to roll down a ramp that flattens out at the end, landing to a ledge that is some height above the ground. Suppose you start the cylinder off from rest at the top of the ramp. The rotational inertia of a cylinder rotating around its central axis is MR^2. Compare how far you would predict the cylinder lands horizontally from the ledge when you take into account that it rolls without slipping versus if you just treat it as though it slides down the ramp without rolling. Give your answer as a ratio of the case where rolling is considered over the case where it is neglected.   

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