Is energy conserved in this case?

[Stereo_Chemist]

I recently had a question presented to me, and I am wondering if I got it right.

The question stated that a figure skater with a moment of inertia was rotating at an angular speed of 4 rad/s. Then the figure skater reduced her moment of inertia by bringing her arms in, and her speed increased to 12 rad/s. How much did her moment of inertia increase by.

For this part I know that angular momentum is conserved, so if the angular speed increased by a factor of 3, her moment of inertia must decrease by a factor of 3 also.

The next question then asked if energy was conserved in this case.

I figured that the only type of energy in this case was rotational energy and there is no translational energy, so you could simply use the formula

R.E. = 1/2Iw^2

So if you plug in the initial moment of inertia and angular speed and then the final one, you will get two different values, so energy is not conserved, correct?

 

[Doc Al]

Correct. Mechanical energy is not conserved. The skater has to do work to pull in her arms; she adds mechanical energy. (Of course total energy is conserved. She transformed chemical energy into mechanical energy.)