The Wobbler

Here’s an odd little animal: Get two rigid disks, cut a notch in each one, fit them together as shown, and try to send them rolling across a table. If the notches are too deep, marrying the discs too closely together, then the object will pretty quickly slow to a stop with each disc standing at a 45° angle to the table. If the notches are too shallow, it will stop with one disc standing up at right angles to the table. But if the notches are about the right length, ideally 29.2893 percent of the radius, then the contraption will roll along quite happily for a surprisingly long distance.

The reason is that in that configuration the object’s center of mass remains level as it rolls along. (It does move from side to side, which is why it’s called the wobbler.)

Apparently this was originally discovered by A.T. Stewart, who dubbed his creation the “two-circle roller” in a 1966 note in the American Journal of Physics. I found it described in Matt Parker’s 2014 book Things to Make and Do in the Fourth Dimension, which includes a simple proof of the principle involved. There’s a more rigorous discussion here.