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@Damon You used moment of inertia about center of the ruler. But in your calcs you assume that it is rotating about its end. Shouldn't you use instead moment of inertia bout the end, when calculating KE of rotation?
@fima Did your conservation of E method worked for part a ?
did this work for you? are you sure that we shouldn't use parallel axis theorem to find I? Because rod is rotating about end. And you assume that it's a point mass in the rotational motion.

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