Math Cracks Egg Problem

Give 'em a spin. Researchers have cracked the physics of twirling eggs.

Put an Easter egg down on the table and give it a twirl, and you'll notice something strange: The egg will slowly rise on its end, seemingly defying the pull of gravity. Now, at long last, researchers have described the math behind this paradoxical behavior.

Normally, a rapidly spinning object will preserve its direction of spin--the reason a fast-moving bicycle doesn't topple over. But in the case of a hard-boiled egg, friction between the egg and the tabletop changes the direction of this angular momentum, says Keith Moffatt, of the École Normale Supérieure in Paris, who analyzed the motion of spinning eggs with Yutaka Shimomura, of Keio University in Yokohama, Japan.

Although the egg starts out spinning horizontally, this position isn't stable, so any tiny irregularity in the eggshell or table will tilt the egg slightly. This kicks off an escalating cycle: The change to a tilted spin makes the egg slip on the tabletop, creating a frictional force that pushes the end upward. That in turn makes the egg slip more, jacking up the frictional push. Eventually, this friction shoves the egg all the way to the vertical position. In the 28 March issue of Nature, Moffatt and Shimomura present a series of equations that describe the egg's ascent.

However, Moffatt cautions that Easter-weekend experimenters won't get the same rise out of a raw egg. The reason, he explains, is that when the egg spins, the yolk and white lag behind, gradually absorbing energy and slowing down the spin. The remaining speed is not enough to create the strong frictional forces that push the egg upright, so the egg simply slows down and stops.

Place a hard-boiled egg on a table,
And spin it as fast as you're able;
It will rise on one end
With vectorial blend
Of precession and spin that's quite stable.
--Keith Moffatt

"Their analysis is a very nice calculation," says Bernie Nickel, a physicist at the University of Guelph in Canada. "It's the simplest approach I could imagine, and the answer comes out almost immediately from the analysis."

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