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

where ,

L is angular momentum.

I is moment of Inertia

w is angular momentum.

I

_{1}w

_{1}= I

_{2}w2

or I1w1/I2w2 = 1 ............(1)

Now lets check for Rotaional Kinetic energy

1/2 I1w12 / 1/2 I2 w22

=$\frac{{I}_{1}{{w}_{1}}^{2}}{{I}_{2}{{w}_{2}}^{2}}=\raisebox{1ex}{${w}_{1}$}\!\left/ \!\raisebox{-1ex}{${w}_{2}$}\right.\ne 1$

so rotational kinetic energy not conserved

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