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I have a physics test tomorrow on special relativity and one of the questions on the previous test was as follows: "A particle of mass m hits another particle of the same mass that was originally at rest. The collision is non-relativistic, totally elastic and non-central.

  1. Write down the conservation laws that hold for this problem."

Now I know that totally elastic means conservation of momentum and kinetic energy and non-central means that the centre of mass of the collision moves. But I can't find anywhere what it means for a collision to be non-relativistic. Can someone help me with this?

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    $\begingroup$ Doesn’t non relativistic simply mean not involving the theory of relativity? $\endgroup$
    – Bob D
    Commented Jun 27 at 21:25
  • $\begingroup$ Presumably, you had a course in intro physics before a course in relativity. What was an elastic collision in the intro course? $\endgroup$
    – robphy
    Commented Jun 27 at 21:58
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    $\begingroup$ Not sure if this is what you are looking for, but two implications of a collision being non-relativistic are: (1) mass is conserved, in addition to energy and momentum (although this might not be useful to solve the problem), (2) the non-relativistic formulas for energy and momentum in terms of mass and velocity are different from the relativistic ones. $\endgroup$
    – Andrew
    Commented Jun 27 at 22:09
  • $\begingroup$ Don't forget that angular momentum is separately conserved and that the conserved energy includes angular kinetic energy and potential energy. As Andrew mentioned, mass is not necessarily conserved in the relativistic case "Radioactive decay may be considered a sort of time-reversed inelastic collision" See en.wikipedia.org/wiki/Special_relativity#Relativistic_analysis, however, relativistic momentum and relativistic energy (which includes rest mass energy) are conserved in the relativistic case. The deflection angles after a collision are different in the relativistic case . $\endgroup$
    – KDP
    Commented Jun 28 at 3:08
  • $\begingroup$ The NR part means use $p^2/2m$ for kinetic energy. 3-Momentum is always conserved, but the "non central" part means consider transverse momentum as well as longitudinal. It really is that simple. Of course, there are 2 transverse dimensions, but you always chose in-plane coordinates, so OOP is trivially $0\rightarrow 0$. $\endgroup$
    – JEB
    Commented Jun 28 at 4:44

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