Violating the law of conservation of energy

AI Thread Summary
The discussion revolves around the conservation of energy during a change in the radius of a rotating body. It explains that while the angular momentum remains constant, the moment of inertia changes, leading to a new angular velocity. The calculations suggest that the new energy can be either greater or less than the initial energy, depending on the factor k. However, it is clarified that work is required to change the radius, which affects energy conservation. The conversation concludes with an acknowledgment that asking questions is important for understanding complex concepts.
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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 Iw2.
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?
 
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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.
 
ok...got it... so silly of me to even ask this.
 
The only silly question is the one you don't ask.
 
hmm... who said that?
 

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