Tutor (me) needs help on pulley angular accel question

[Ground State]

I am a high school teacher tutoring a family member in an introductory university class. I have good knowledge of typical pulley questions and semi-decent knowledge of angular acceleration (it is no longer in the high school curriculum here and I am out of practice). Can anyone give me a solution to the following so I can construct the best way to teach it to someone? Solution WILL NOT be simply handed over. The question is asking to solve for the angular acceleration of the cylinders (frictionless).

http://img838.imageshack.us/img838/70/pulley.jpg

 

[Doc Al]

Apply Newton's 2nd law for rotation and for translation. Give it a shot and you'll get plenty of feedback.

As always, start with free body diagrams for each object. You'll need three.

 

[Ground State]

I have no trouble doing a calculation for the angular acceleration of the "big disc" with the 2.5 kg rope hanging off the side, and a calculation for the angular acceleration of the "small disc" with the 4.0 kg mass hanging off the side. But I just can't seem to understand the connection of how this all goes together if the two discs are mounted together as one mass.

 

[Doc Al]

I have no trouble doing a calculation for the angular acceleration of the "big disc" with the 2.5 kg rope hanging off the side, and a calculation for the angular acceleration of the "small disc" with the 4.0 kg mass hanging off the side. But I just can't seem to understand the connection of how this all goes together if the two discs are mounted together as one mass.

It's really the same basic idea. One difference, of course, is that the rotational inertia of the combined mass is the sum of the separate rotational inertias. A second difference is that the ropes attach at different radii.

How would you draw the free body diagrams?