1. The problem statement, all variables and given/known data Hey guys. The other day I was doing some physics questions, studying for the finals, you know the story. Me and my friend came across this physics question where: There is a particle of mass 2kg (m) hanging by a mass-less string that went around a pulley with mass 4kg (M) and is attached to a vertical spring of spring constant 100Nm (k). The moment of inertia of the pulley is given as follows, I=(.5)(M)(R^2) We must find the maximum velocity of the mass assuming the system begins at rest, that is no movement and the spring at its natural length. NOTE: R is not given 2. Relevant equations F=ma v=ωR change of Potential Energy = Change in kinetic energy 3. The attempt at a solution Since energy is conserved: where d is distance dropped (traveled by a point on the string) Considering the string does not slide relative to the pulley: v=ωR Knowing the forces in action: mg-T=ma and t-kd=ma (T and t are tensions on different sides of the pulley) We look at the point in time where the acceleration is 0 (maximum velocity), thus mg=T and t=kd This is where I get stuck, conceptually. If I set t=T then I manage to get the answer simple enough. However, why is T=t if the pulley has moment of inertia?!