For athletes, the Winter Olympics mark the culmination of a grueling four-year pursuit of gold, silver or bronze that demands time commitments and physical sacrifices inconceivable to most.
For viewers, they’re a source of entertainment, national pride, and often-obscure stories thrust into a global spotlight that shines for two weeks.
But for the University of Nebraska–Lincoln’s Tim Gay and his fellow physicists, the Winter Olympics are a masterclass in classroom physics applied on ice and snow. Though he’s best known for explaining the Newtonian physics at play on the gridiron, Gay recently helped Nebraska Today understand a few of the phenomena behind (and underneath and around) the athletic feats of the 2022 Winter Games.
Spin it to win it
It’s among the most iconic imagery of any Winter Olympics: A figure skater goes into a slow spin with arms outstretched to the side. As she coils her arms to her chest or draws them together above her head, as so many skaters do to cap a performance, that rotation accelerates into a dizzying blur. But what exactly accounts for the transition from sleepy spin to whirling dervish?
“It turns out that the trick isn’t in the footwork, but in the physics,” said Gay, the Willa Cather Professor of physics and astronomy. “She’s using a principle called conservation of angular momentum.”
Linear momentum, the more-familiar sort that carries a skater across the ice, stems from a combination of the skater’s mass and velocity. Or, as math would put it: Momentum = Mass x Velocity. The greater the mass and/or velocity, the greater the linear momentum.
Its cousin, angular momentum — which describes the momentum of a rotating body, including a spinning skater — likewise depends on mass. It depends on velocity, too, just not of the straight-line variety. Instead, angular velocity describes how fast a skater rotates around her center axis. (It’s routinely measured in revolutions per minute, or RPM.) But a third factor also enters the fray: how the skater’s mass is distributed around her axis as she spins. With her arms extended to the side, she has greater so-called rotational mass; when drawing her arms inward, that rotational mass shrinks.
The resulting equation is just a spin on the original: Angular Momentum = Rotational Mass x Angular Velocity (RPM). Just like linear momentum, angular momentum is a conserved quantity, meaning that its value remains constant. To conserve her angular momentum, then, a skater’s rotational speed must change according to her rotational mass — that is, whether her arms are outstretched or withdrawn. When outstretched, her greater rotational mass means a slower rotation; when withdrawn, that rate of spin increases to compensate for the decrease in rotational mass. And so the sleepy spin becomes the whirling dervish.
As Gay pointed out, what applies to the arms also applies to the legs — and to the Summer Olympics, where gymnasts and divers employ the same principle.