I wanted to just make sure I was doing this right. The problem: A marble of mass M and radius R rolls without slipping down a track from height h1. The marble then goes up a frictionless track to a height h2. Find h2. I figure this has to be in terms of other variables, here is my work. initial mechanical energy = final mechanical energy Mgh1 = Mgh2 + (1/2)Mv^2 + (1/2)Iω^2 I for sphere = (2/5)MR^2 Plug in for I and cancel M's. Plug in v = ωR gh1 = gh2 + (1/2)v^2 + (1/5)v^2 g(h1 - h2) = (7/10)v^2 h2 = h1 - (7/10)(v^2 / g) Can the answer be expressed simpler?