I have two problems, they are labeled in the attached picture. Here is the first question: A rope is fastened to the ceiling and passes under a wheel and then back up again. If the mass of the wheel is 2 kg, its moment of inertia is .04 kg m^2 and the radius of the wheel is .3m, find the upward acceleration if a force of 50N is applied to the rope. (ANS 33 m/sec^2) Here is what I have. Since the pulley is supported by the ceiling, this means that half of the weight is supported by the upward force. So I subtract half of the weight from the total force F = 50 N - .5(2)(9.8) = 40.2 N I then figure out the torque caused by the moment of inertia and the rotational acceleration. Torque = I alpha a = F / m, a = 40.2 / 2, a = 20.1 alpha = a / r, alpha = 20.1 / .3m, alpha = 67 Torque(wheel) = .04 * 67 = 2.68 T = rF Torque (caused by force) = .3 * 40.2 = 12.06 Torque (net) = 12.06 - 2.68 = 9.38 9.38 = .3 F, F = 31.27, F = ma, a = 31.27 / 2 = 15.63 Obviously Incorrect Here is the second question: Find the rotational acceleration of the pulley. (ANS 88.35 rad / sec^2) So I start by figuring out the moment of inertia of the pulley, since this is a combination pulley, the moment of inertia is the sum of the individual pulleys. SO, (Inertia of a disk, I = 1/2MR^2) I = 1/2(1)(.02m)^2 + 1/2(4)(.06)^2 = .0002 + .0072 = .0074 T1 =3 * 9.8 * .02 = .588 T2 = 5 * 9.8 * .06 = 2.94 T(net) = 2.94 - .588 = 2.352 2.352 = .0074 (alpha) alpha = 317.83 Which isn't correct either. Thanks, Any help would be appreciated.