Instead of having the cars static, or keyframed to animate a certain way, I figured it wouldn't be too hard to write a quick and dirty physics simulation to make the cars swing as the wheel accelerates.
Here's how it turned out.
(Note: The mechanism for spinning the wheel was created in a very slapdash manner. The movie just looks at the position of the mouse cursor. The final site will have something much more elegant and intuitute. The purpose of this demo was just to get the pendulums to swing in a somewhat believable fashion.)
Oh, and thanks to Ryan for helping me with some of the maths.