Congratulations Phil Kesten: you have correctly explained here
how momentum is conserved, in my opinion. That isn’t so common. I thought I’d go into a bit more detail in my own explanation.
First watch this video from the two minute mark to the two minute forty seconds mark. It shows clearly how angular momentum is conserved in the astronaut’s body:
I figured out the same thing before coming to your site while watching the first falling cat (the second cat does not show it so clearly — and it’s a pity it was included) in slow motion in the Smarter Every Day video called Slow Motion Flipping Cat Physics.
You can see in that video that the cat’s flexible body is in a U shape with each of the two vertical parts of the U rotating in opposite directions so that there is no net angular momentum. The parts are not perfectly vertical, and there is the short horizontal part of the the U that is also rotating and as you point out the angular velocities are not exactly the same and the tail helps out with some fine tuning by rotating in a great circle but these details can be ignored in a simple explanation. Once the cat has completed its twist while maintaining a concave upward U shape, all that’s left for the cat is to straighten out its spine from U shaped to dash shaped, i.e. to a horizontal line (actually it will bend a little bit past straight and become concave downward but that’s just a detail).
It is hard for us humans with our relatively inflexible spinal columns to understand what the cat is doing because no one but a contortionist could do it. A cat can easily lick its own spine. Think for a moment how much more flexible than the human spine the feline spine must be for a cat to be able to do that.
What the cat is doing in mid-air in order to land on its feet is *twisting* its own spine through about one hundred eighty degrees while keeping it *bent* in a U, i.e. while keeping it bent through one hundred eighty degrees.
One way to understand what the cat is doing is to consider a flexible soft rubber torus (‘donut’ shape) that you can get your thumbs inside and twist so that the surface of the donut facing the center of the hole rotates until it is facing directly away from the centre of the hole, and instead faces outwards. It’s the same motion that happens when you roll a rubber band up your arm, or a smoke ring (vortex) twists quickly as it moves forward. Thus to understand and visualize the twisting the cat’s body, and especially of it’s backbone, think of the cat as being the lower half of a smoke ring.
There’s no mystery how the cat is able to get itself rotating either. The muscles and tendons inside the cat are quite easily able to cause the two vertical donut section to rotate in opposite directions. It just has to quickly shorten the muscles on middle of the far side of its body while relaxing those on the near side. Of course, I not saying it does it this way, only that there is no mystery regarding how it is *possible* for the cat to do it. The key is that its body is U shaped. Or as Phil Kesten put it, when talking about alligators, C shaped. In terms of forces it’s the equivalent of getting a spring with a fish hook on each end and and stretching it until it reaches across a rubber donut, or half of one, and letting the spring twist the donut or half donut so that it twist like half a smoke ring.
It is as if a man first formed a U shape by lying on his or her back with his legs and arms sticking up and then and got hold of his toes, and then without letting go of his toes, twisted around so that he was on his belly. It’s probably extremely dangerous to the human spine. Don’t try it unless you are a cat.
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