Combining Linear and Rotational Dynamics

Today we 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! Also, if a problem has a rope going over a pulley that has mass, the tensions are different for the pieces of rope "entering" and "leaving" the pulley. Double 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. We'll have a work day tomorrow, so if you have trouble don't take too much time struggling with it. I can help you tomorrow.