It is well-known that cats almost always land on their feet. Elementary
physics may suggest that this is impossible, due to the
conservation of angular momentum. A knowledge of intermediate physics reveals how the cat pulls it off.
The cat (suppose it is my cat, Fanny) starts off at some orientation other than right-side-up. She stretches her body out, increasing the moment of inertia of her rear legs and tail. By moving the extended parts of her body in the opposite direction from the direction she wants to twist, she alters the orientation of the rest of her body despite not having changed her angular momentum. However, she must still get her rear legs in place, since she will need them down in order to land safely. So she tucks them in towards her body again, decreasing their moment of inertia. Then she can twist them back into place without bringing herself out of line. There is a similar motion in the tail.
It may be necessary for her to repeat this procedure, though not more than once additional unless she has gotten extraordinarily fat (she's working on it). An amazing thing about this is how little space it actually takes up. A cat falling from rest can perform this maneuver while falling one meter, under earth gravity.
The elucidating thing about this is that angular position is not conserved, only angular momentum.