Does Conservation of Momentum & Energy Hold in the C.O.M. Reference Frame?

In summary: That is, the total momentum of all particles is zero. So in the CM frame, conservation of momentum does not hold. However, the kinetic energy of the particles is still conserved.
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ruivocanadense
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Do classical conservation laws apply to center of mass frame at speeds close to the speed of light?
We know classical equations fail to follow conservation of momentum and energy when we are dealing with speeds closer to the speed of light. But does it fail in the center of mass reference frame of a system?
 
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The conservation laws work just fine (energy is neither created nor destroyed - tuis is true in relativity just as it is in Newtonian physics). It's the non-relativistic expressions for the energy and momentum that are not correct, and are not a good approximation at high speeds.
 
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  • #3
ruivocanadense said:
We know classical equations fail to follow conservation of momentum and energy when we are dealing with speeds closer to the speed of light. But does it fail in the center of mass reference frame of a system?
Yes, the classical formulas for momentum kinetic energy fail in the center of mass frame as well.
 
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ruivocanadense said:
Summary:: Do classical conservation laws apply to center of mass frame at speeds close to the speed of light?

We know classical equations fail to follow conservation of momentum and energy when we are dealing with speeds closer to the speed of light. But does it fail in the center of mass reference frame of a system?

From context, I assume that you don't regard special relativity as a "classical theory". It seems that it's a bit ambiguous, I am used to regarding it as a classical theory (as it's not quantum), but after looking at the definition, I suspect the term may be ambiguous. In any event - if two relativistic particles collide, correct predictions of the energy require special relativity, not Newtonian physics. Which I believe would be a "yes", if we assume that by classical physics you mean only Newtonian physics.
 
  • #5
In relativity it's more accurate to speak about a center-of-momentum frame rather than a center-of-mass frame. By definition the CM frame is defined such that the total three-momentum of the particles involved in the scattering vanishes.
 
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1. What is the conservation of momentum and energy?

The conservation of momentum and energy is a fundamental principle in physics that states that in a closed system, the total momentum and energy remain constant over time. This means that the total amount of momentum and energy before an interaction or event is equal to the total amount after the interaction or event.

2. How does the conservation of momentum and energy hold in the center of mass (C.O.M.) reference frame?

In the C.O.M. reference frame, the total momentum and energy are calculated by taking into account the motion of the entire system as a whole. This means that the total momentum and energy of the system will remain constant in this frame, just as it would in any other reference frame.

3. Why is the C.O.M. reference frame useful in studying conservation of momentum and energy?

The C.O.M. reference frame allows us to simplify complex systems and focus on the overall motion of the system. By considering the motion of the system as a whole, we can more easily apply the principles of conservation of momentum and energy and make predictions about the outcome of interactions or events.

4. Are there any limitations to the conservation of momentum and energy in the C.O.M. reference frame?

The conservation of momentum and energy holds true in the C.O.M. reference frame as long as the system is isolated and there are no external forces acting on it. If there are external forces present, then the total momentum and energy may not remain constant in this frame.

5. How is the conservation of momentum and energy related to Newton's laws of motion?

The conservation of momentum and energy is a consequence of Newton's laws of motion, specifically the law of conservation of momentum and the law of conservation of energy. These laws state that in the absence of external forces, the total momentum and energy of a system will remain constant.

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