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As the title above, why is the momentum always conserved in elastic collision (no loss of kinetic energy)?
Does it related to the conservation of kinetic energy? If so, how do we prove that?
Further more, can elastic collision release some energy but still obey the conservation of kinetic energy?
If so, where does the energy released come from? And what about the angular momentum?Why is it conserved?

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  • $\begingroup$ Don't think of the conservation rules of collisions as special or separate from those for other interactions. They are the same rules applied to a defined class of systems. The exception is "elastic collitions conserve bulk kinetic energy" which serve to define what we mean by "elastic" (there is afterall no general rule of conservatioj of kinetic energy). $\endgroup$ – dmckee Oct 11 at 19:13
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Momentum is conserved in collisions whether they are elastic or inelastic.

Momentum is conserved in a collision regardless of whether KE is conserved.

An elastic collision is defined as one in which the total KE of the colliding bodies is conserved, so any collision that 'releases' energy is by definition not elastic.

There is no requirement for KE to be conserved- there is only a requirement for total energy to be conserved, so KE can be converted to other forms of energy.

Angular momentum is also conserved, regardless of whether collisions are elastic.

The conservation of momentum is a general law- it does not just apply to collisions. It follows from Newtons third law.

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Momentum, energy and angular momentum are always conserved. In inelastic collisions macroscopic kinetic energy is not conserved.

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As the title above, why is the momentum always conserved in elastic collision (no loss of kinetic energy)?

If there are no external forces acting on a system then the momentum of the system is conserved.
Note that there is absolutely no mention of energy in this statement.

So the answer to your question

Does it related to the conservation of kinetic energy?

is, no.

Further more, can elastic collision release some energy but still obey the conservation of kinetic energy?

An elastic collision is one in which kinetic energy is conserved with no mention of any other forms of energy.

And what about the angular momentum? Why is it conserved?

Same sort of idea as for linear momentum but now one needs to have no external torques acting on the system.

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Whether it is elastic or inelastic collision momentum will always conserved, despite of k. E is conserved or not, momentum conservation and k. E conservation of system are two different things, momentum transfer can make a rest body accelerate where energy transfer can produce several affects like sound, velocity, heat, etc.

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why is the momentum always conserved in elastic collision (no loss of kinetic energy)?

Momentum is always conserved. Both in elastic and non-elastic collisions.

Of all the possible collisions that are possible, some happen to conserve mechanical energy (kinetic and potential). We give those collisions a name and call them elastic.

Does it related to the conservation of kinetic energy? If so, how do we prove that?

Momentum conservation is a result of Newton's 3rd law and is not a consequence of energy conservation.

Further more, can elastic collision release some energy but still obey the conservation of kinetic energy?

Unclear what you mean here. In elastic collisions kinetic energy is converted into potential elastic energy, which then in turn is converted 100 % back into kinetic energy. If there were energy losses along the way, we wouldn't call the collision elastic.

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