Conservation of angular momentum problem

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Discussion Overview

The discussion revolves around a problem related to the conservation of angular momentum and energy in the context of a clay mass colliding with a rod. Participants explore the implications of inelastic collisions and the transformation of energy during such events.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions the apparent violation of the conservation of energy, noting a discrepancy between calculated kinetic energy and the stated total energy of the system.
  • Another participant explains that mechanical energy is not conserved in inelastic collisions, indicating that the clay sticks to the rod.
  • There is a query about the fate of the lost energy, with suggestions that it transforms into internal energy or heat due to deformation during the collision.
  • Participants discuss the analogy of dropping clay onto the floor to illustrate energy transformation during collisions.
  • One participant raises a hypothetical scenario involving a sticky ball colliding with a rod, questioning whether energy loss would occur similarly.
  • Responses suggest that energy loss during collisions manifests as heat and other forms of random energy, reinforcing the idea that mechanical energy is lost in inelastic interactions.
  • A reference to the ballistic pendulum problem is made, highlighting the conservation of momentum in such scenarios while noting that energy can change forms.
  • Another participant confirms that angular momentum is conserved in the absence of external torque, emphasizing the distinction between momentum and energy conservation.

Areas of Agreement / Disagreement

Participants generally agree that angular momentum is conserved in the discussed scenario, but there is no consensus on the specifics of energy transformation and the implications of energy loss during inelastic collisions.

Contextual Notes

The discussion includes assumptions about the nature of collisions and energy transformation, but these assumptions are not universally accepted or resolved among participants.

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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