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.

 

[PJC01]

Your calculation is correct. The increase in energy can be explained by the fact that the skater's rotational speed has doubled, meaning she is now moving faster and therefore has more kinetic energy. This increase in kinetic energy is equal to the decrease in moment of inertia, as predicted by the conservation of angular momentum. So, while the skater's moment of inertia may have decreased, her increase in speed compensates for it and results in an overall doubling of energy. This is a common phenomenon in rotational motion, where changes in moment of inertia can result in changes in speed and energy, but the total angular momentum remains constant.