Specific situation : A ring of mass M and radius R is rotating about its axis with angular velocity w. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be?

I can find out the KE loss by finding final w by conservation of angular momentum.

But my query is why is angular momentum conserved and KE not conserved? I don't see any work done by an external torque. Will we consider friction between the two bodies of mass m and the ring?


Angular momentum is conserved because there are no external torques acting on the system of ring and two bodies.
However when the bodies are dropped there are internal forces acting.
Since the blocks cannot suffer an infinite acceleration there must be a time when the blocks and the ring are moving relative to one another.
There must be a kinetic frictional force acting to accelerate the blocks (and decelerate the ring).
Due to this kinetic frictional force the kinetic energy decreases and as a result heat is generated.
So that is the reason for the decrease in the kinetic energy.
Since the frictional forces are internal to the ring and two bodies system (form Newton;s third law pairs of forces) they do not affect the angular momentum of the system.

  • $\begingroup$ Mechanical energy changes when work is done by an external force. Right? But as the friction is internal why does ME change? $\endgroup$ – Utkarsh Barsaiyan Apr 1 '16 at 10:31
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    $\begingroup$ Internal forces are allowed to do work you just have to change the system. Consider two equal masses travelling at the same speed towards one another. After collision those masses stick together. The final kinetic energy of the joined masses is zero. Where has the kinetic energy gone? In this case the internal forces produced by the collision have done work in permanently breaking bonds and producing heat. Mass 1 exerts a force on mass 2 and that force does work on mass 2 and changes the mechanical energy of mass 2. The same thing happens when mass 2 exerts a force on mass 1. $\endgroup$ – Farcher Apr 1 '16 at 10:58
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    $\begingroup$ "But as the friction is internal why does ME change? " @UtkarshBarsaiyan There are lots of kinds of energy. There is no law of conservation of mechanical energy (or indeed of any particular kind of energy), just a law of conservation of energy that encompasses all kinds at once. Friction is notorious for converting mechanical energy into thermal energy. We do a lot of problems in physics class where mechanical energy is assumed to be conserved, but those are approximations to reality and not an indication of how you should expect things to be. $\endgroup$ – dmckee Apr 2 '16 at 2:42

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