Drop a cat upside down and, somehow, it lands on its feet. The puzzle is deeper than it looks. When a cat is let go it isn't spinning at all, and falling can't give it a spin — there's nothing to push against in mid-air. So how does it turn over? The trick is that a cat isn't stiff like a board; it bends in the middle. It twists the front half of its body one way while twisting the back half the opposite way. The genius is in the legs: it tucks its front legs in so the front spins easily and far, while stretching its back legs out so the back barely turns — then it swaps, tucking the back and stretching the front. Each twist cancels the other, so the cat never "cheats" any spin into being, yet it ends up the right way up. In the simulator, scrub the sequence and watch the spin ledger stay at zero.
Most people think a falling cat pushes off the air or somehow spins itself round. In fact it starts and stays at zero spin: it bends and counter-rotates its two halves, finding a loophole in the law of angular momentum rather than breaking it.
What's actually happening
It looks like cheating. Hold a cat upside down a little way above a cushion, let go, and before it lands it has flipped over and touched down on its paws. Photographers in the nineteenth century captured it frame by frame and it only deepened the mystery, because the cat clearly twists itself round in mid-air with nothing to push against. That's the part that bothered physicists. There's a rock-solid law that says a spinning thing keeps spinning and a still thing stays still unless something outside gives it a twist. A falling cat starts perfectly still, and gravity, pulling evenly on every part of it, supplies no twist at all. By that law the cat should land exactly as it was dropped — on its back. It doesn't.
The escape from the paradox is that the law forbids a rigid object from turning itself, and a cat is anything but rigid. Its flexible spine lets it bend in the middle and treat its front and back as two separate spinning sections. Here is the move. The cat folds at the waist and starts to rotate its front half in the direction it wants to face. By the law of spin, the back half must rotate the opposite way to keep the total at zero — and ordinarily that would simply undo the turn. So the cat plays its trump card: how fast each half spins depends on how spread out it is. By pulling its front legs in tight, it makes the front compact and easy to twist, so it whips round a long way. By flinging its back legs out wide, it makes the back ungainly and hard to twist, so it barely creeps backward. A big forward turn of the front is paid for by only a tiny backward turn of the back.
Then the cat swaps the roles. Now it splays the front and tucks the back, and repeats the move with the halves reversed, advancing the rear while the front hardly gives ground. Stitch the two strokes together and both halves have come round to face the same new way: the whole cat has flipped a full 180 degrees, belly-up to feet-down — and at no single moment did its total spin rise above zero. It never broke the law; it found a loophole in it, the same loophole that lets an astronaut floating free in a capsule turn to face the other way with nothing to grab, just by waving their limbs in the right sequence. A cat does it in a fraction of a second and a fall of about thirty centimetres, which is also why a very short drop can be the dangerous one: there isn't enough air-time to finish the trick.
A cat rights itself by bending and counter-rotating its halves, netting a 180° flip while its total spin stays zero — a conservation trick, not a push-off.
- 1Sit on a swivel office chair with your feet off the floor so it can spin freely, and hold still — you have zero spin, like the cat.
- 2Hold your arms out wide and swing them horizontally in one direction; the chair turns the other way. Now pull your arms in and swing them back. The chair does not fully unturn.
- 3Repeat the wide-swing, tuck, swing-back cycle and you slowly rotate the chair from rest — turning yourself with no push-off, exactly the trick a falling cat uses.
Common questions
By changing shape. A rigid body could not turn itself, but a cat bends at the waist and counter-rotates its front and back halves. Each twist cancels the other, so its total spin stays zero while the body still flips.
How fast each half spins depends on how spread out it is. Tucking a half makes it turn easily and far; splaying a half makes it turn slowly. So a big turn of the tucked half costs only a tiny opposite turn of the splayed half.
The righting move takes a little time and roughly 30 cm of fall to complete. From a very low drop the cat may not have enough air-time to finish turning before it lands.