conservation of angular momentum with energy

[suhagsindur]

Ice sketar rotates with open arms & her moment of inertia is I, rotational speed W. So, angular momentum is I*W. Energy is (1/2)I*W*W
she folds her arms & her moment of inertia decreases to I/2. From conservation of angular momentum rotational speed became double say W*2.
Energy became (1/2)*I/2*W*W*4 = I*W*W ( Energy is doubled, How?)

Please tell me in this caculation where I am wrong?

[Doc Al]

You're not wrong. The skater does work when she brings her arms in. She converts internal energy into rotational KE.

[atreusk]

Rotational kinetic energy isn't conserved

[suhagsindur]

OK, Very much Thanks for clearing my doubt.