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To explain why a falling cat can turn by 180 degree without external torque and without violation of the conservation of angular momentum, one usually models the cat as two cylinders as in

http://en.wikipedia.org/wiki/Falling_cat_problem

This may explain the turn. However I often heard contrary to this that she can rotate her body simply because she rotates her tail very fast into the opposite direction (and essentially keeps the rest of the body rigid).

So, what effect does the tail have in reality? Is there any detailed model, which takes the tail rotation into account and calculates how large its effect is?

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Actually I know experimentally that a cat can do this quite effectively without her tail. Our littler cat taunts our bigger one by sneaking up on him (often when he's relieving himself), whacking him on the rump and then making a swift getaway by springing up and backwards very strongly and doing the flipover in air manouevre whilst she does so, so that she lands a few metres away, right way up but headed in the opposite direction, whereupon she sprints off. When she was two years old, she got hit by a car and ended up needing her tail removed. After she got better, she took up taunting .... –  WetSavannaAnimal aka Rod Vance Jun 20 at 6:57
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... our bigger cat again, doing exactly the same trick and manouevre but without her tail. Her lack of tail does not noticeably hinder her ability to flip over and make her quick getaway! Moreover, she did this within a matter of days after recovering - i.e. she did not seem to need to train herself to compensate for her lack of tail. It kind of makes sense: although the tail has a high moment, it is very, very light. I suspect most of the relevant moment of inertia is in the powerful muscles of the hinder legs, well beneath the spine: these are quite amazingly big in our littler cat. –  WetSavannaAnimal aka Rod Vance Jun 20 at 7:00
    
Dear Julia: here is another relevant video: theatlantic.com/technology/archive/2011/09/… Thomas Kane, one of the early researchers was actually trying to teach astronauts to do the same thing, and they seem to be almost as good at it as cats with a bit of practice! Also of relevance (at an elegant, but more difficult level) is people.ucsc.edu/~rmont/papers/cat.PDF . "Das Umdrehen der Fallenden Katze in der Luft" by Rademaker and ter Braak (1935) is an early experimental study: unfortunately I don't have a copy anymore. –  WetSavannaAnimal aka Rod Vance Jun 23 at 7:22

1 Answer 1

The two answers are physically equivalent. If you watch the Wikipedia animation

enter image description here

you see that the fastest part of her body on the top animation is the tail. It makes a substantial contribution to the angular momentum. At any rate, the angular momentum of the tail is included in the angular momentum of the "back cylinder". The trick the cat needs to achieve the task is to perform a fast relative motion of the back of her body (including, importantly, the tail) and the front of her body.

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The video on video.nationalgeographic.com/video/animals/mammals-animals/cats/… shows that the tail is actively moved relative to the body during the rotation (in at least one cat :-), so the situation is a bit more complicated than the animation. I would guess that because the weight of the tail is small compared to the body it is just used for fine control. –  John Rennie Apr 30 '12 at 16:14
    
Sorry, John, but I don't follow your logic. The relative motion of the back of her body (especially the tail) with respect to the rest of the body (the front) is the only thing that the cat may be doing by controlling her muscles and it is also what this animation shows. All other aspects of the motion are dictated by the changing total momentum and conserved angular momentum. In what sense can the "situation" be more complicated than the animation? The precise motion may have a bit different shape but the animation captures 100% of the physics related to the change of the orientation. –  Luboš Motl Apr 30 '12 at 16:21
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If the tail were heavy enough the cat could hold it's body/legs rigid and just rotate its tail. Clearly this is not the case and the cat must flex its spine. I think the OP is asking how much rotation could be achieved by motion at the tail/body joint. –  John Rennie Apr 30 '12 at 16:30
    
OK but there isn't any universal number for all cats how independently they may turn their tail relatively to the spine, or how large a percentage of the change of the angular momentum is guaranteed by the tail. At least this isn't a question of physics because one would have to define what she exactly means by a cat. The tail is a non-negligible part of the effect because while it's light, its center-of-mass is further than the bulk of the body from the relevant horizontal axis. At any rate, if one knows the exact geometry and masses, she may use the Wikipedia model to calculate the numbers. –  Luboš Motl Apr 30 '12 at 18:24
    
@JohnRennie (and Luboš) For a light hearted look at the importance of the tail, see my comments to the OP's question, although this is a pretty solid observation, because I've seen my cat do as I describe many many times. I suspect the tail is more important for animals like snow leopards: the tail really is quite amazingly big and massive compared to the rest of the animal. Or check out the size of the tail on this one –  WetSavannaAnimal aka Rod Vance Jun 20 at 14:32

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