Conservation of angular momentum problem

AI Thread Summary
The discussion revolves around a problem involving the conservation of angular momentum and kinetic energy in a scenario where clay collides with a rod. The initial confusion stems from the calculation of kinetic energy, where the clay's energy is 5J, but the total initial rotational kinetic energy of the system is stated as 2J, suggesting a violation of energy conservation. It is clarified that during the inelastic collision, mechanical energy is not conserved, and the lost energy transforms into heat and other forms of internal energy. The conversation highlights that while angular momentum is conserved due to the absence of external torque, energy can change forms, leading to a loss in mechanical energy. Overall, the key takeaway is that angular momentum remains conserved, but energy can be dissipated in various ways during collisions.
abro
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I have been busy with rotating objects and I have a question which I don't understand. http://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_AngularMomentum.xml (last question of the page, about the clay on the rod)
What I don't understand is that the clay has a kinetic energy of KE=0,5*0,1*10^2=5J, but then one of the answers say the initial rotational kinetic energy, and thus the total energy of the system, is 2J. This is a violation of the law of conservation of energy. Please help?
 
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abro said:
This is a violation of the law of conservation of energy. Please help?
The clay makes an inelastic collision with the rod (they stick together). Mechanical energy is not conserved.
 
But where does the 3J go?
 
abro said:
But where does the 3J go?
Random internal energy, deformation... things like that. (Things get warm.)

Drop a lump of clay onto the floor. It goes splat. What happened to its kinetic energy? Same idea.
 
What about a solid ball that's sticky or something, will it suddenly get 3J of just because it hits a hanging rod with 5J?
 
abro said:
What about a solid ball that's sticky or something, will it suddenly get 3J of just because it hits a hanging rod with 5J?
* get 3J of heat
 
abro said:
What about a solid ball that's sticky or something, will it suddenly get 3J of just because it hits a hanging rod with 5J?
The collision takes some time. But yes, the system loses mechanical energy; that lost energy will show up as "heat" and other forms of "random" energy.
 
Doc Al said:
The collision takes some time. But yes, the system loses mechanical energy; that lost energy will show up as "heat" and other forms of "random" energy.

Aha, there is also a familiar example with the conservation of moment, called the ballistic pendulum problem.
In conclusion; (angular) momentum is always (!) conserved, but energy can be transformed into other forms of energy, but the sum is also conserved.?
 
abro said:
In conclusion; (angular) momentum is always (!) conserved, but energy can be transformed into other forms of energy, but the sum is also conserved.?
That's right. Angular momentum is conserved in such problems because there is no external torque acting. (The pivot is frictionless.)
 

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