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

Explanation

Using law of conservation of angular momentum,
I_(1) omega_(1)=I_(2)omega_(2)`
`I_(1)^(2)omega_(1)^(2)=I_(2)^(2)omega_(2)^(2)`
`I_(1)((1)/(2)I_(1) omega_(1)^(2))=I_(2)((1)/(2)I_(2)omega_(2)^(2))`
`I_(1)K_(1)=I_(2)K_(2)`
If `I_(1) gt I_(2)`
Then `K_(2) gt K_(1)`