• # What do tumbling Olympic Snowboarders and cats have in common?

Credit: Wikimedia
Date:28 February 2018 Tags:

If you want to understand how snowboarders, skiers and whirling Winter Olympians perform twists, turns and complex tricks while zooming through the air, you need to understand cats, according to Rafi Letzter, a writer for Live Science.

A we know cats usually land on their feet. If a cat tumbles off a 4m high ledge upside down, it will twist in the air and land on its feet. The result will be the same from half or double the distance.

Cats are remarkable in that they don’t need any initial momentum to start to turn their feet toward the earth. “Like an Olympic snowboarder suddenly twisting their board around after leaving the ramp, cats pull off their turns even when they don’t have any rotational or angular momentum (think, spin energy) at all at the start of their fall,” writes Letzter.

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Cats (and skiers and snowboarders) can seem to generate momentum mid-air, without having anything to push off of or any leverage, and they use it to turn themselves.

“A simple model for how a cat flips over is if you picture it as being a front half of a cat and a back half of a cat, so that the torso is two parts. It can bend its body sort of counterrotate the front and back half of the body,” said Greg Gbur, a physicist at the University of North Carolina Charlotte.

Gbur continued to explain that if you drop a rigid object, like a pencil or even a couch, they way that it moves through the air and spins is entirely dependant on the way that it’s dropped. If it starts its fall spinning, it will keep spinning. If it starts its fall without any angular momentum — rotational energy of an object — it won’t turn.

And the total angular momentum of a flexible object, like a cat or an Olympian, can’t change either without a push. That’s Isaac Newton’s first law of motion: An object in motion stays in motion, and an object at rest stays at rest.

When a cat twists in the air, the average angular momentum of its whole body never changes. Its front and rear bend toward one another, then twist in opposite directions around a central point. The internal forces exerted — the muscles pulling against bone and other muscles — cancel one another out. The orientation changes, but from the perspective of the universe, the cat’s angular momentum stays the same.

That’s the same thing that happens when a skier suddenly turns one part of their body that had previously been still. For every bit of mass in their body that starts to spin one way, another bit of mass in another part of their body has to turn the opposite way.

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But what about Olympians who start their tricks turning slow, but suddenly turn faster or slower? Don’t they gain or lose angular momentum?

Nope.

“Unlike a cat, which tends to fall without any initial angular momentum, a snowboarder will deliberately push off of the edge of the track to give themselves some initial rotation,” Gbur said.

The angular momentum of that rotation is a product of the “moment of inertia” or the radius of the mass spinning through the air — the distances between a skier’s outstretched arms and the central axis of their rotation.

A big radius means more angular momentum; it takes a lot more energy to spin around 10 times with your legs and arms outstretched than if you tuck into a little ball. (This is one reason a very lightweight bicycle wheel spins with so much more force than the wheels attached to your rollerblades.)

So to speed up during a trick, an athlete will start with their body outstretched as much as possible, then tuck their arms and legs to shrink their total radius, Gbur said. With a smaller moment of intertia, the same angular momentum will make them spin much faster.

Want to slow down? Just stretch out, and the same angular momentum will slow your twist.

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