The problem consists of having 2 masses m_1 and m_2 attached to a pulley by a string (negligible mass I assume) where m_1 hangs under the gravitational force and m_2 sits on a frictionless surface. The pulley has mass M and radius R. It asks to find the acceleration. In my book it used the angular momentum approach to solve the problem as follows: Total angular momentum: L = m_1vR + m_2vR + MvR = (m_1 + m_2 + M)vR Net Torque: Ʃτ = m_1gR = dL/dt = d[(m_1 + m_2 + M)vR]/dt m_1g = (m_1 + m_2 + M)dv/dt a = dv/dt = m_1g/(m_1 + m_2 + M) When I solve this problem using Newtons laws and the fact that Ʃτ = Iα (assuming I = 1/2MR^2); I get: a = m_1g/(m_1 + m_2 + M/2) EDIT: This always happens. I found out the problem. I reread it and it says the pulley has mass M at the RIM. The spokes are of negligible mass. That makes sense!