According to Newton, Angular momentum is conserved when no external force is acting,that is, angular speed remains constant throughout the motion, but when we release a cat from height facing upward,it can rotate itself in between it's motion to land on its feet. As initially the angular speed was 0 then how does cat generates angular speed in between it's motion?
Answers
In rotational motion, we use moment of inertia instead of mass. The moment of inertia of an object is determined by the distance it's mass is distributed from the rotational axis. Imagine a ball tied to a string and swing it. Greater the length of string (i.e distance from rotational axis is greater), higher will be its moment of inertia.
So when a cat is dropped from a certain height, if the cat stretches out its legs and tail, it can significantly increase its moment of inertia, and at the same time can decrease the moment of inertia by curling up.
Now, when the cat is in the air, no net external torque acts on it about its centre of mass, so the angular momentum about the cat's centre of mass is not changing. But if it pulls its legs back, the cat can considerably reduce it rotational inertia about the same axis and thus considerably increase its angular speed. And by stretching out its legs, it can increase its rotational inertia and slow down its angular speed. The conservation of angular momentum allows the cat to rotate its body and slow its rate of rotation enough so that it lands on its feet safely.