AP PROBLEM TWO LINKED DISKS

AP PROBLEM TWO LINKED DISKS

The two uniform disks shown have equal mass, and each can rotate on frictionless bearings about a fixed axis through its center. The smaller disk has a radius R and momentum of inertia I about its axis. The larger disk has a radius 2R.

A) Determine the moment of inertia of the larger disk about its axis in terms of I.

The two disks are then liked as shown by a light chain that cannot slip. They are at rest when, at time t = 0, a student applies a torque to the smaller disk, and it rotates counterclockwise with constant angular acceleration a. Assume that the mass of the chain and the tension in the lower part of the chain are negligible.

In terms of I, R, a., and t, determine each of the following.

B) The angular acceleration of the larger disk

C) The tension in the upper part of the chain

D) The torque that the student applied to the smaller disk

E) The rotational kinetic energy of the smaller disk as a function of time.