Combining Rotational + Linear Dynamics

I am sick again today. We would have walked through a problem that combines rotational and linear dynamics. The basic strategy goes like this:

1. Draw a free body diagram of the linear thing.
2. Write Newton's 2nd Law for the linear thing, fill in what you can.
3. Draw a free body diagram for the rotational thing with the forces drawn at the point they really are applied to the body.
4. Write Newton's 2nd Law (rotational version) for the rotational thing, fill in what you can.
5. Write (linear acceleration) = (radius)(angular acceleration) for the point where the linear and rational objects interact.
6. You should now have a system of three equations and three (or less) unknowns; solve!

Note: if there is more that one linear thing or rotational thing, you might end up with more than three equations and three unknowns. Fun!

Here is the problem we walked through:

Two years ago I was actually gone for this lecture, so here are some videos I made (thanks past me!):
Part 1: YouTube
Part 2: YouTube

Homework: p.269 #35, 40, 87. I hope to be back tomorrow, and we'll have a work day so I can help people.