1. The problem statement, all variables and given/known data My ENTIRE AP physics class is stumped on the way to correctly write the formula to find acceleration for a falling block (mass of "m") attached by a string (tension of "t") to a fixed, rotating pulley (mass of "M", radius of "r"). Our teacher told us that for a block attached on the left side of a pulley (rotating counterclockwise) the tangential acceleration ("a") of the pulley should be positive (+) and for one on the right side (pulley rotating clockwise) a should be negative (-). We cannot come to a decisive conclusion as to what the final equation to find a for each side should be. m = block mass M = pulley mass r = radius of pulley t = tension of string a = tangential acceleration (acceleration of the block) I = Inertia of pulley A = angular acceleration of pulley g = Gravity (assume g=10 if needed) 2. Relevant equations Positive "a" Formula Set: (+)Formula One: Pulley Rotating CCW T = rt, T = IA , I = 1/2M(r^2), and A = a/r therefore... rt = 1/2 M(r^2)(a/r) (r^2)t = 1/2M(r^2)a t = 1/2Ma (+)Formula Two: Block Falling to the Left t = sum of all forces t = mg + ma Negative "a" Formula Set: (-)Formula One: Pulley Rotating CW T = rt, T = IA , I = 1/2M(r^2), and A = -a/r therefore... rt = 1/2 M(r^2)(-a/r) (r^2)t = 1/2M(r^2)(-a) t = -(1/2Ma) (-)Formula Two: Block Falling to the Right t = sum of all forces t = mg + [m(-a)] or t = mg - ma (This part is where we some of the confusion begins. We assume t = mg "-" ma since the block is falling to the right and "a" should be negative) 3. The attempt at a solution Positive, CCW, Left t = mg + ma and t = 1/2Ma so 1/2Ma = mg + ma both sides x 2 Ma = 2mg + 2ma both sides -2ma Ma - 2ma = 2mg factor out a a(M - 2m) = 2mg both sides / (M-2m) a = 2mg / (M - 2m) Negative, CW, Right t= mg - ma and t = -(1/2Ma) so -(1/2Ma) = mg - ma both sides x-(2) Ma = -2mg + 2ma both sides -2ma Ma - 2ma = -2mg actor out a a(M - 2m) = -2mg both sides / (M - 2m) a = -2mg / (M - 2m) I've worked these out to the best of my ability and I believe that they are correct. Can someone please either confirm this or correct me ASAP? Thanks!