Gently balance a coin edge-down on a flat surface and give it a sharp flick on the side to set it spinning. You’ll observe that the coin’s initial pure rotation turns into a mix of spinning and rolling before dissipative forces bring the coin to a stop. That behavior, like almost all other classical dynamics phenomena, was explained in the 18th and 19th centuries, beginning with the work of Leonhard Euler (1707–83). You might expect that repeating the disk game with a ring would yield essentially the same results. But to the best of our knowledge, until recently the ring game was not carefully observed and rolling-ring dynamics was not carefully studied.

On a chilly afternoon, one of us (Jalali) was deeply frustrated by a science problem that seemed to defy any reasonable approach. To cope, he took off his wedding ring, spun it on his glass-covered desk, and began...

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