Falling cat problem

The falling cat problem is a problem that consists of explaining the underlying physics behind the observation of the cat righting reflex: that is, how a free-falling body (cat) can change its orientation such that it is able to right itself as it falls to land on its feet, irrespective of its initial orientation, and without violating the law of conservation of angular momentum.

Although amusing and trivial to pose, the solution of the problem is not as straightforward as its statement would suggest. The apparent contradiction with the law of conservation of angular momentum is resolved because the cat is not a rigid body, but instead is permitted to change its shape during the fall owing to the cat's flexible backbone and non-functional collar-bone. The behavior of the cat is thus typical of the mechanics of deformable bodies.

The falling cat problem has elicited interest from famous scientists including George Gabriel Stokes, James Clerk Maxwell, and Étienne-Jules Marey. In a letter to his wife, Katherine Mary Clerk Maxwell, Maxwell wrote, "There is a tradition in Trinity that when I was here I discovered a method of throwing a cat so as not to light on its feet, and that I used to throw cats out of windows. I had to explain that the proper object of research was to find how quick the cat would turn round, and that the proper method was to let the cat drop on a table or bed from about two inches, and that even then the cat lights on her feet." Maxwell's and other scientists interest with so-called "cat turning" was reputed to have caused the death of many cats after being dropped from windows of multi-storied buildings. Maxwell in particular was interested in discovering the precise height that a cat needed to be dropped from so that the cat would be incapable of using its righting reflex to land on its feet, an endeavor in which he eventually succeeded.

Whereas the cat-falling problem was regarded as a mere curiosity by Maxwell, Stokes, and others, a more rigorous study of the problem was conducted by Étienne-Jules Marey who applied chronophotography to capture the cat's descent on film using a chronophotographic gun. The gun, capable of capturing 12 frames per second, produced images from which Marey deduced that as the cat had no rotational motion at the start of its descent the cat was not "cheating" by using the cat handler's hand as a fulcrum. This in itself posed a problem as it implied that it was possible for a body in free fall to acquire angular momentum. Marey also showed that air resistance played no role in facilitating the righting of the cat's body.

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