Violating the law of conservation of energy

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Discussion Overview

The discussion revolves around the implications of changing the radius of a rotating body on its moment of inertia, angular momentum, and kinetic energy, with a focus on the law of conservation of energy. Participants explore the relationships between these quantities and the work required to alter the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant presents a scenario involving a rotating body, expressing confusion about how changing the radius affects energy and angular velocity, leading to a potential violation of energy conservation.
  • Another participant points out that work must be done to change the radius of the body, implying that this work affects the energy considerations.
  • A later reply acknowledges the initial confusion and reflects on the nature of asking questions in the learning process.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of changing the radius on energy conservation, as the initial confusion remains unaddressed beyond the acknowledgment of the need for work.

Contextual Notes

The discussion does not resolve the mathematical relationships or assumptions regarding the conservation of energy in the context of changing moment of inertia and angular velocity.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of physics, particularly those exploring concepts of rotational dynamics and energy conservation.

deep838
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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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