1+2+3 Two-Cent Wobbler
Mathematically rich thrills from a cheap toy.
I recently returned home from Japan with some leftover coins and decided to make them into “wobblers.” Two orthogonally interlocked disks will roll together with an amusing left-right wiggle. If the spacing between the disks is just right, the wobbler’s center of gravity remains at a fixed height so it will wobble down the slightest incline. It is surprisingly addictive to roll these and race them, and you can’t beat them as a cheap gift!
1. Cut slots in any 2 identical coins.
With a cutting wheel on a Dremel or other rotary shaft tool, cut a small radial slot in each coin, the same width as the coin’s thickness. Hold each coin in a vise while you cut, and wear a mask so you won’t breathe in any metal dust.
2. Press the 2 coins together.
Tap them gently with a hammer or apply gentle pressure with a vise. If the slots are not too wide, they’ll hold together without any solder or glue.
3. Wiggle your wobbler.
Put the wobbler on a smooth surface and watch it wiggle away.
Photography by George W. Hart
+ Going Further
After you make a few, you’ll want to make mathematically ideal wobblers, in which the center of gravity remains at a constant height as it rolls. For this, the center-to-center distance must be the square root of 2 times the radius (d=√2r), so the slot length should be 29% of the radius.
I’ve since learned of several earlier discoveries of this shape, going back to the mid-1900s, when the designer Paul Schatz used what he called the “Oloid” as part of a paint stirring machine.
Physicist A.T. Stewart first observed that the center of gravity stays at a constant height if the center separation is √2 times the radius; see his paper “Two Circle Roller” in American Journal of Physics, Volume 34, 1966, pages 166–167. Search the web for “two circle roller” to read more interesting papers about these toys.
George W. Hart is a sculptor and a professor at Stony Brook University. View examples of his work at georgehart.com.