1. The problem statement, all variables and given/known data A pulley hangs of mass, m, and radius, R, hangs from the ceiling. Two blocks of masses, m1 and m2 are connected by a massless, non-stretchable rope on the pulley (assume no slipping). What is the angular acceleration of the pulley and what is the ratio of the tension forces on the vertical portions of the rope while the blocks are moving? 2. Relevant equations τ=Iα F=ma Icyl=0.5mR2 atan=αR 3. The attempt at a solution Because the pulley has a mass, the tension forces on each side of the rope are different (if the pulley were massless then the tensions on each side would be the same, to my knowledge). The torque determines the angular acceleration: τ=Iα Since the tension work in opposite directions, the tensions, T1 and T2, act in opposite directions (where T1 is on the side of block 1 and T2 is on the side of block 2). τ=Iα=T1-T2 I can use Newton's Second Law to try and find the two unknown tension forces: F1=m1a=m1g-T1 F2=m2a=T2-m2g Solving for T: T1=m1g-m1a T2=m2g+m2a Plugging this into Iα=T1-T2: m1g-m1a-m2g+m2a=Iα Here is where I start to get more unsure. I still have the unknown linear acceleration, a. I think I can relate it to α using a=αr since there is no slipping. Then my equation would be: m1g-m1αR-m2g+m2αR=0.5mR2α Then, I can isolate and solve for α. I like to try and see if my answers make intuitive sense, and I'm not sure this one does: α= g(m1-m2) / 0.5mR2+m1R-m2R It seems angular acceleration increases as the mass of block 1 increases. This makes sense because if the weight of block 1 is greater, the pulley will rotate faster. However, the denominator also increases as m1 increases and decreases as m2 increases, which seems counterintuitive to me. The ratio of tensions (T1/T2) is as simple as m1(g-a)/m2(g-a). I'm not sure how to think about this, but I'm confident in my work on this part. Thanks for checking over my work!