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This question already has an answer here:

Can anybody share some ideas as to how to treat the dynamics of a gymnast's body when they're in air? As in, dynamics of a system consisting of mechanically coupled rigid bodies in a torque free system? My aim is to find out how a gymnast initiates a mid-air twist without any apparent torque.

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marked as duplicate by John Rennie, user36790, Community Sep 20 '16 at 10:57

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Here's how cats do it

After determining down from up visually or with their vestibular apparatus (in the inner ear), cats manage to twist themselves to face downward without ever changing their net angular momentum. They are able to accomplish this with these key steps:

Bend in the middle so that the front half of their body rotates about a different axis from the rear half. Tuck their front legs in to reduce the moment of inertia of the front half of their body and extend their rear legs to increase the moment of inertia of the rear half of their body so that they can rotate their front further (as much as 90°) while the rear half rotates in the opposite direction less (as little as 10°). Extend their front legs and tuck their rear legs so that they can rotate their rear half further while their front half rotates in the opposite direction less. Depending on the cat's flexibility and initial angular momentum, if any, the cat may need to perform steps two and three repeatedly in order to complete a full 180° rotation.

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