1. The problem statement, all variables and given/known data A block of mass 2kg (mb) can slide down a frictionless 53 degree inclune, but it is connected to a pulley of mass 4kg (mp with a radius of 0.5m. The pulley may be treated as a disk. What is the angular acceleration of the pulley? 2. Relevant equations a = rα 3. The attempt at a solution I first expressed each object in terms of Newton's 2nd Law BLOCK: ΣFx = mbsinθ - T = mba ΣFy = N - mgsinθ = 0 PULLEY: ΣFx = T = mmpa ΣFy = N-mg = 0 Then, isolated for T (tension) for both the block and pulley and equated them to each other. Their tension would be the same because the pulley and block are connected by the same rope. (1) T = mbgsinθ - mba (2) T =mpa mpa = mbgsinθ - mba a = mbgsinθ / (mb + mp) a = 2.6m/s α = a/r = (2.6m/s/s) / 0.5m = 5.22rads/s/s CONCERNS: We weren't given the final answer, so I'm not sure if my approach is correct. But I have a feeling that my Newton's 2nd Law (N2L) expression for the pulley is incorrect. ΣFx = T = mpa Since the pulley is rotating, would the acceleration in N2L be CENTRIPETAL ACCELERATION? However, if this was the case, then the expression would turn into: ΣFx = T = mpv2/r This introduces another unknown -- velocity! If this were the case, I don't know how to solve the problem. Thank you!