1+ 2+ 3
Two-Cent Wobbler By George W. Hart
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!
YOU WILL NEED
2 identical coins or other disk-shaped objects that
a slot can be cut into, such as a CD
Dremel tool or saw to cut slots
NOTE: In some countries it is illegal to damage coins.
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.
+ 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 3
“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.
Photography by George W. Hart
136 Make: Volume 15