## Why Do Cats Always Land on Their Feet?

A falling cat usually lands on her feet. This remarkable ability depends on two deeply fundamental aspects of physics. Let’s wonder a bit about falling cats.

In 1894, French physiologist Étienne-Jules Marey used a new photographic technique to take a series of photos that documented one of the animal kingdom’s wonders: a falling cat flipping over to land safely on its feet. The series of high speed photos, reproduced in Nature two years later, show the cat released with its legs pointing skyward and landing gently on all fours.

But while Marey’s photos documented the amazing trick, the bigger question remained: how do cats do it?

To start, let’s consider some physics that you’ve almost certainly observed. Watch any Olympic ice skater’s routine—I’ll pick Kristi Yamaguchi’s 1992 gold medal performance in Albertville, France—and you’re bound to see a skater execute a spin on the tip of one of her skates. As Kristi pulls her arms and hands in closer to her body, she spins faster and faster.

First, a rotating object spins faster when more of its mass is brought closer to the axis around which the rotation occurs. And second, for every rotating system there is a physics quantity that will always stay the same if no external agent acts on the system.

Here’s the physics: First, a rotating object spins faster when more of its mass is brought closer to the axis around which the rotation occurs. And second, for every rotating system there is a physics quantity that will always stay the same if no external agent acts on the system. This quantity—angular momentum—depends on rotation rate, mass, and where the mass is relative to the rotation axis.

Consider Yamaguchi. She spins at a certain rate with arms extended. As she pulls her arms in, the component of her angular momentum having to do with the distribution of her mass gets smaller. Her angular momentum cannot change, so something else has to get bigger. She spins faster.

Now back to Tabby. A careful look at Masey’s images (particularly the third, fourth, and fifth frames) reveals that the cat begins her fall by arching her back. This effectively breaks her body into two, separate, rotating parts. In frames five and six, she’s rotated her head toward the camera and extended her back legs. With her front legs in tight, her head and upper body rotate quickly. To keep her total angular momentum from changing, her lower body begins to rotate in the opposite direction. With back legs extended, that rotation is slow and controlled. In the next set of frames the cat extends her front legs to slow and eventually stop her upper body rotation.

Finally, she full extends her back legs to slow and stop the rotation of her lower body—ta-dah!

In about one and a half seconds, Tabby is upright, with all four legs extended and ready to cushion her fall. And it’s all physics.

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Question to ponder:

The configuration of an alligator’s jaws and teeth make these reptiles unable to bite off chunks of their prey that are small enough to swallow. Their legs are too short to hold the food, and worse, while they’re swimming they can’t push against the river bottom for leverage. Their solution is the alligator “death roll,” which involves bending its head, body, and tail into a “C” shape. Can you imagine how rotations come into play that enable the alligator to generate enormous forces that can rip apart its prey?

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