# Violating the law of conservation of energy

1. Feb 24, 2013

### deep838

Let there be a body rotating about its axis, with a moment of inertia I and an angular velcity w.
The angular momentum of the system is L = Iw.
Now, if the radius of the body change, its moment of inertia will also change. Let the new moment of inertia be I, such that, I= kI.
But the angular momentum of the system will remain constant.
So, the angular velcity must change. So, w=w/k.
But, initially, the energy of the system was purely kinetic and was given by
E=1/2 Iw2.
The new energy is given by, I= 1/2 Iw2 = 1/2 kI (w/k)2
So, E`= E/k.

So the new energy of the system is either more {0<k<1} of less {k>1} than the previous energy!

What am I doing wrong?

2. Feb 24, 2013

### ModusPwnd

You need to do work to change the radius. Imagine whirling a ball on a string around. If takes work to pull in the ball.

3. Feb 24, 2013

### deep838

ok...got it... so silly of me to even ask this.

4. Feb 26, 2013

### CWatters

The only silly question is the one you don't ask.

5. Feb 26, 2013

### deep838

hmm... who said that?