If angular momentum is conserved in a system whose moment of inertia is decreased, will its rotational kinetic energy be also conserved ? Explain.

Explanation

Let Ii and `omega_(i)` be the initial moment of inertia and initial angular velocity of the system and If and `omega_(f)` be the corresponding final values when the moment of inertia of the system is decreased. According to the law of conservation of angular momentum:
`I_(f) omega_(f)= I_(i) omega_(i)` or `I_(f)^(2) omega_(f)^(2) = I_(i)^(2).omega_(i)^(2)` or `I_(f)(I_(f)omega_(f)^(2)) = I_(i)(I_(i)omega_(i)^(2))`
As `I_(f) lt I_(i), I_(f)omega_(f)^(2) gt I_(i)omega_(i)^(2)` or `(1//2)I_(f)omega_(f)^(2) gt (1//2)I_(i)omega_(i)^(2)`
The rotational kinetic energy of the system thus increases on decreasing it moment of inertia.