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Principle of conservation of angular momentum is followed by the cat.
When a cat is falling to ground from a height, it stretches its body alongwith the tail so that its moment of inertia becomes high and no net torque is acting , so total angular momentum is conserved.
Torque = 0
Hence L = constant
L = Iω
Since, Iω is to remain constant, and tretching out its legs increases its rotational inertia and thus the value of angular speed ω decreases and therefore the cat is able to land on the ground gently.