# When is rotational energy conserved?

1. Nov 3, 2009

### Jimmy25

1. The problem statement, all variables and given/known data

Four 60 kg skaters join hands and skate down an ice rink at 4.6 m/s. Side by side, they form a line 6 m long. The skater at one end stops abruptly, and the line proceeds to rotate rigidly about that skater. Find the linear speed of the outermost skater.

3. The attempt at a solution

What I did was equate the initial kinetic with the final rotational energy. This does not jive with the answer and the solutions say to use conservation of angular momentum.

Why isn't energy conserved?

2. Nov 3, 2009

### Phrak

I take this problem, and see it as a rigid rod partitioned into 4 parts; one for each skater.

A force is exerted at the center of the right-most partition. The force on the rod changes the kinetic energy of the rod. So energy is not conserved.

As this force is applied 3/8ths of the rod's length from its center of mass, angular momentum is not conserved.

Last edited: Nov 3, 2009
3. Nov 3, 2009

### Jimmy25

Another question involves a rod which is initially standing on end. It tips over with the bottom of the rod attached to the ground. In this case all the potential energy of the rod is converted to rotational kinetic energy.

How can I distinguish between these two types of problems? (ie how do I recognize when I can use conservation of energy). They both effectively involve a rotating rod about a fixed axis.

4. Nov 3, 2009

### Phrak

You seem to have gotten this one. Potential energy is converted to kinetic energy.

5. Nov 3, 2009

### Jimmy25

Yes, I did get that one. However I didn't get the first one because I don't understand how energy is conserved in one but not in the other.

What is the difference?