Aha! I know this one.. Cats are able to always land on their feet by changing the relative “Moment of Inertia” between their front and back legs. Moment of Inertia is an object’s resistance to being rotated, it’s analagous to mass in linear motion, so something with a bigger moment of inertia is harder to rotate, just like something heavier is hard to push.
An example of this change in moment of inertia is if you sit in a computer chair and someone spins you round. If you stick your legs out straight, you spin slower but tuck them in and you spin faster. This effect is called the conservation of angular momentum. The cat turns itself round by holding in its front paws while its back legs are held out, and alternating between these two whilst twisting round provides a net rotation for the lucky cat.
I think they also have quite flexible spines which allows them to spread out very well. A cat terminal velocity, the fastest speed at which it falls (about 60mph), is much lower than a humans (about 130mph) giving it plenty of time to reorientate itself.
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