If the angular momentum is conserved in a system whose MI is decreased, will its rotational KE be also conserved? Explain.

Explanation

According to law of conservation of angular momentum
`I_1 omega_1 = I_2omega_2`
`(omega_2)/(omega_1) = (I_1)/(I_2)`
Initial K. E. of rotation `E_1 = 1/2 I_1 omega_1^2`
Final K. E. of rotation `E_1 = 1/2 I_2 omega_2^2`
`therefore (E_2)/(E_1) = ((I_1)/(I_2)) ((omega_2)/(omega_1))^2 = (I_2)/(I_1) xx (I^2)/(I_2^2) = (I_1)/(I_2)`
Since `I_1 gt I_2 therefore E_2 gt E_1` .
Therefore, K. E. of rotation will increase and hence it is not conserved.