When an object is spinning, it has something called angular momentum. Angular momentum remains constant while that object is spinning, unless an outside force (such as friction) comes in. If nothing else changes, the speed and direction of the spin will remain constant.

Angular momentum is made up of the speed of the spin (v), the radius of the spinning object (r) and the mass of the spinning object (m). We can show angular momentum in this equation:

ang. mom. = v × m × r.

Since angular momentum is constant, if any one of those things changes, then the others must also change to make up for it. So if the radius gets smaller, the speed must get faster to make up for it.

This is what happens in the Spinning Chair. As you spin with your arms and legs out to the side, your radius is large. When you tuck your arms and legs in, this decreases your radius, so you speed up to keep yopur angular momentum the same.

Figure skaters take advantage of this when performing spins. Often they begin a spin with their arms and other leg out to the side, and spin relatively slowly. Then, they bring their arms and leg in so that they spin incredibly fast. They decrease their radii so that they spin faster to maintain their angular momentum. When they stop, they throw their arms and leg out again, to increase their radii and slow down, so they can stop safely. Not only is this a nifty use of physics, it’s also very impressive to watch.

Click for larger image

Falling cats (see opposite) also use conservation of angular momentum, and the fact that they are very flexible. If a cat falls from above one metre it will always land on its feet, because it is able to right itself as it falls. It does this by twisting its body (cats have very bendy backbones) so that both sets of legs turn to the ground, but in different directions.

It is able to turn its front half further than its back half because it tucks its front legs in and stretches its back legs out. Since its front and back halves must have the same angular momentum, its smaller front half goes faster.

It then tucks in its back legs, and stretches out its front legs, and twists its body back. Now its back half moves faster than its front half. This means that its whole body has now turned. It repeats this movement over and over, until it is the right way up. At falls of less than one metre, cats don’t have time to do this, but falls that small are not likely to damage them anyway.

Click here for an explanation, or here for a Wikipedia article on the cat-righting reflex.