1. The problem statement, all variables and given/known data A uniform cylindrical spool of mass M and radius R unwinds an essentially massless rope under the weight of a mass m. If R = 12 cm, M = 400 gm and m = 50 gm, find the speed of m after it has descended 50 cm starting from rest. Solve the problem twice: once using Newton's laws for torques, and once by application of energy conservation principles. 2. Relevant equations I(spool) = (1/2)MR^2 τ = R * Fsin(90) (*it will be 90 degrees here due to the way the Gravitational Force pulls down) τ = Iά at = ά * R (tangential acceleration) vf = sqrt(vi2 + 2at*Δx) 3. The attempt at a solution So I used τ = R * Fsin(90) to come up with the torque (since I converted everything into meters and kilograms, my answer ended up being -5.88 x 10^-2 N-m) Then, I basically plugged in values for I: I = 0.5 * 0.4 kg * (0.12 m)^2 = 0.00288 kg m^2 After that, I thought about solving for ά. But ά is the angular acceleration, which is kind of useless in this case, since we're trying to find the velocity of mass m after is has fallen 50 cm. So I set ά = τ/I = at / R at = 0.12 m * -5.88 x 10^-2 N-m/0.00288 kg m^2 = -20.4 m/s^2, and from here I used the equation: vf = sqrt(vi2 + 2at*Δx) and got -4.52 m/s So, I honestly don't even know if I solved this problem right (more or less, where to even start if I was going to use conservation of energy principles to solve it again.) Any help would be greatly appreciated.