c. As stated in the problem, the rope will slide around the pulley and rotate it without slipping. What this means is that the rate of rotational acceleration of the pulley is directly related to the rate at which the two hanging masses move. We already know that the two masses must move the same way (one up and the other down) due to the rope connecting them. In addition to that, the amount the pulley rotates will be equal to the length of rope that passes over and rotates the pulley, their motions are linked: @ = = R and a = R (these are the same conditions for any object that rolls without slipping). Use this knowledge to show that the acceleration of the masses, and the tensions in the left and right string are given by the following expressions: g M 2mi mag+ - m Mg Theft= my +m2+ = M 2mi mag+ - my Mg Tright = mi +m2+ = M