PhysicsLAB AP Free Response Question
2000 C3

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A pulley of radius R1 and rotational inertia I1 is mounted on an axle with negligible friction. A light cord passing over the pulley has two blocks of mass m attached to either end, as shown above. Assume that the cord does not slip on the pulley. Determine the answers to parts (a) and (b) in terms of m, R1, I1, and fundamental constants.

 (a) Determine the tension T in the cord.

(b) One block is now removed from the right and hung on the left. When the system is released from rest, the three blocks on the left accelerate downward with an acceleration g/3. Determine the following.
i. The tension T3 in the section of cord supporting the three blocks on the left

 ii. The tension T1 in the section of cord supporting the single block on the right

 iii. The rotational inertia I 1 of the pulley

(c) The blocks are now removed and the cord is tied into a loop, which is passed around the original pulley and a second pulley of radius 2R1 and rotational inertia 16I1. The axis of the original pulley is attached to a motor that rotates it at angular speed ω1, which in turn causes the larger pulley to rotate. The loop does not slip on the pulleys. Determine the following in terms of I1, R1, and ω1.
 i. The angular speed ω2 of the larger pulley.

 ii. The angular momentum L2 of the larger pulley

iii. The total kinetic energy of the system

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