Violating the law of conservation of energy

In summary, the conversation discusses the relationship between angular momentum, moment of inertia, and angular velocity of a rotating body. It is stated that if the radius of the body changes, its moment of inertia and angular velocity will also change, but the angular momentum will remain constant. The new energy of the system is also calculated and it is determined that work must be done to change the radius. The conversation ends with the acknowledgement that there are no silly questions.
  • #1
117
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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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  • #2
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
ok...got it... so silly of me to even ask this.
 
  • #4
The only silly question is the one you don't ask.
 
  • #5
hmm... who said that?
 

1. What is the law of conservation of energy?

The law of conservation of energy is a fundamental principle in physics that states energy cannot be created or destroyed, only transformed from one form to another.

2. How can the law of conservation of energy be violated?

The law of conservation of energy can be violated if energy is created or destroyed, or if the amount of energy in a closed system changes without any external work being done.

3. What are some examples of violating the law of conservation of energy?

Some examples of violating the law of conservation of energy include perpetual motion machines, where energy is claimed to be created without any external input, and nuclear reactions which release more energy than was originally present.

4. What are the consequences of violating the law of conservation of energy?

If the law of conservation of energy is violated, it would mean that our understanding of the fundamental laws of physics is incorrect. This could have far-reaching consequences and could potentially lead to a complete overhaul of our scientific theories.

5. Has the law of conservation of energy been proven to be true?

The law of conservation of energy has been extensively tested and has been found to hold true in all observed physical phenomena. However, it is still a fundamental principle that is constantly being tested and refined by scientists.

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