Violating the law of conservation of energy

[deep838]

I know that's impossible, so please help me!

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 Iw<sup>2</sup>.
The new energy is given by, I`= 1/2 I`w`² = 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?

 

[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.

 

[deep838]

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

 

[CWatters]

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

 

[deep838]

hmm... who said that?