When a spinning coin falls on its side, it rattles with increasing speed until it stops abruptly. The final few seconds of motion are accompanied by a shudder and a whirling sound of increasing frequency. A similar effect is seen in Euler's disk, a toy that would spin for ever in the absence of friction and vibration. Now Keith Moffatt from the University of Cambridge in the UK has analyzed the motion of these systems in detail (Nature 404 833).
Moffatt became interested in the problem while looking for Christmas presents for his grandchildren. “I came across the toy in a mail order catalogue and thought it sounded interesting,” he says. After playing with the toy he became intrigued with the physics behind Euler’s disk. “The disk is continually losing energy throughout the process,” he says, “but the rattling movement goes faster.” Indeed, according to the equations describing the disk, its angular velocity should approach a ‘finite time singularity’. What, Moffatt wanted to know, stopped the angular velocity becoming infinite?
It turned out that the theory broke down when the vertical acceleration of the disk exceeded the acceleration due to gravity. Moffatt calculated that this happened when the coin was rotating at about 100 times per second. He also calculated that a commercially available Euler’s disk should spin for about 100 seconds before it stopped – which agreed with observations to within about 20%.
