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I know this is a scrap of thought, but the first law states that (from Wikipedia):

If an object experiences no net force, then its velocity is constant

Is it describing the conservation of momentum $p_{before} = p_{after}$? Where $p=mv$, so that in a regime of 'undisturbed motion' (although no such thing may actually exist) the momentum is conserved?

In case the answer to the first question is 'yes', then the second question is, how can I elaborate this idea a bit more?

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On which ground you've put -ve sign to right hand side using Newton's 1st Law? – Evil Angel Jan 10 '13 at 7:38
Yea, you are right. I used the third-law's logic in the equation. But the question is still similar. Sorry for that. – SHY.John Jan 10 '13 at 7:55
up vote 1 down vote accepted

The conservation of momentum originates from translational symmetry via Noether's theorem. See section III of this article for the application of this to a freely moving particle. Application of an external force destroys the translational symmetry because it matters where you are in relation to whatever is causing the force, and this is why momentum is not conserved in the presence of an external force.

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Newton's first law you mention applies to one body. Yes, the statement $v=const$ means $p=const$ for one particle. However for an isolated ensemble of interacting particles there is a total momentum that conserves too despite each individual momentum is not conserved due to interactions. The latter is derived from the second Newton's law, i.e., from the equations of motion.

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Well, momentum is basically "moving mass". This is because inertia is solely relating to mass, however $\mathbf{p} = m \mathbf{v}$, where $\mathbf{p}$ denotes momentum, $m$ denotes mass and $\mathbf{v}$ denotes velocity. This indicates that the difference between inertia and momentum is that momentum is just for moving objects. The Law of Conservation of Momentum has two conditions - it has to happen in a closed system and there cannot be any applied external force. I don't believe that it is actually for these conditions to be impossible, especially if you count the system as relatively large.

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