Mathematical Sciences Research Institute

Home > Videos > MSRI Xiralback

MSRI χiralback

This one-of-kind math toy was conceived by Tadashi Tokieda and produced by the Elwyn and Jenny Berlekamp Foundation.

The χiralback is a variation of a rattleback, it has a strong preference for which direction it spins. If spun in the reverse direction, it converts its energy into a rattle, and then spins back in the preferred direction. This behavior seems to defy the physical law requiring the conservation of angular momentum. The strength of the effect varies on the surface on which it is spun.

Older explanations of rattlebacks have focussed on surface asymmetries near the place where the bottom of the rattleback rests. But the surface of this one is a symmetrical ellipsoid given by the equation x^2/a^2 + y^2/b^2 + z^2/c^2 = 1.

It also has the property that if it is turned upside down, then the preferred direction of spin is reversed!  So we call it a χiralback.

Chiralback Demonstration (0:45) and Production (5:38)

Mathematics of Chiralbacks and Other Toys (52:42)

Lecture by Tadashi Tokieda at MSRI on April 15, 2014