# Newton's Third Law and Linear Momentum Conservation

1. May 13, 2014

I have always been under the impression that Newton's third law and the law of conservation of linear momentum are really the same thing; synonymous, so to speak. But then I was wondering if Newton's Third Law holds for a non-isolated system. I mean, I know for sure that momentum conservation is only applicable for an isolated system (At least, this is what I have been taught at A level). But, be it an isolated or non-isolated system, isn't it always the case that the force body A exerts on body B is equal and opposite to the force body B exerts on body A when they interact? The question here is, does Newton's Third Law apply for all systems, whether or not an external force is acting? Of course, my first stop was the internet, where I came across this:
http://physics.stackexchange.com/qu...on-of-momentum-really-imply-newtons-third-law
Now I have more questions really. For a system of more than two bodies, the forces between the bodies may not necessarily be equal and opposite?
Long story short, my questions are:
1) Does Newton's third law hold for non-isolated system? If it doesn't, why?
2) If there's a system of more than two bodies, does Newton's law hold?
3) Is the sum of internal forces in a system always zero?

I would be very grateful if someone would help me out with this.

2. May 13, 2014

### jbriggs444

Yes. Newton's law holds. Just because you can re-draw the lines around an isolated system so that it no longer includes both third-law partners does not change the force that they exert on one another.

Yes. It holds both pair-wise and in bulk. The force of each individual body on another is equal and opposite to the force of the other on the one. The total force of any collection of bodies on any other collection are also equal and opposite. The latter fact could be demonstrated by laboriously adding up all the individual pairwise forces.

If you make a huge spreadsheet of all of the pairwise forces, shuffle them around any way you want and add them all up the total has to come to zero. Each individual pair adds to zero. Shuffling makes no difference according to the associative and commutative rules for addition.

3. May 13, 2014

### A.T.

Newton's 3rd law implies conservation of linear momentum, but not the other way around. For more than two bodies there are other possible ways to conserve total momentum than Newtons 3rd law.

Last edited: May 13, 2014
4. May 13, 2014