# Is energy conserved in this case?

1. Dec 14, 2007

### 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?

2. Dec 14, 2007

### Staff: Mentor

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.)