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.)

 

[sir-pinski]

Based on the given information, it appears that energy is not conserved in this case. This is because there is a change in both the moment of inertia and the angular speed, resulting in a change in the rotational energy. In order for energy to be conserved, there would need to be no change in either the moment of inertia or the angular speed. However, it is important to note that this is only considering the rotational energy and there may be other forms of energy involved that could potentially make the total energy conserved. So, it is possible that energy is conserved in this case, but it cannot be determined based on the given information.