1. The problem statement, all variables and given/known data Two identical cylinders are released from the top of two identical inclined planes. If one rolls without slipping and the other slips without rolling then which one will reach the bottom first? How will their speeds compare when they reach bottom of incline? I am not sure if my attempt is correct, since this is a test question and I cannot verify my answer. 2. Relevant equations Apply Work Energy Theorem to both situations ΔKE + ΔPE = Worknet 3. The attempt at a solution Let θ be the angle of incline with horizontal and h it's height. Let v be the velocity at bottom of incline. for rolling, since force of friction does no work on rolling cylinder, ∴ Worknet = 0 ∴ (0.5 x m x v2 - 0 ) + (0 - mgh) = 0 0.5 x m x v2 = mgh for sliding, force of friction does work, ∴ Worknet ≠ 0 ∴(0.5 x m x v2 - 0 ) + (0 - mgh) = - f x hsinθ 0.5 x m x v2 = mgh - fhsinθ From above analysis, the velocity at bottom for rolling disk will be greater, which also means the rolling disk will reach bottom first.