Q:

Rotation, cats landing on their feet, and conservation of angular momentum

Let θ be the orientation (angle) of a body (such as a cat), and let ω be its angular velocity.
It is well-known that θ can change even when the body is not rotating, using the conservation of angular momentum; that is, even when ω = d﻿θ/d﻿t = 0. That's how cats land on their feet so well.
But how can θ possibly ever change, when its derivative is zero?! What's wrong with the math?

A:

A rigid body can't change it's angle, but a cat is not rigid (it can move one
part in one direction and other parts in the opposite direction, and effectively
wiggle around the full circle).

A:

Good answer from bobuhito. Here's another explanation. Satellites have reaction wheels (which are not gyroscopes) to help them change orientation.
If you sit still on a rotating stool, and you want to change direction, and you are holding a long heavy rod, simply hold the rod over your head and rotate it horizontally a couple times.
Your total angular momentum at all times is zero, but that's because there's a positive angular momentum in the rod, balanced by a negative one in your body. When you stop turning it, both you and the rod have changed direction.

