Re: [Phys-l] Pcons from N's Laws

[Carl Mungan <mungan@usna.edu>]

> My off-the-cuff quick-and-dirty shot at this (literally too lazy to  
> pick up Feynman down the hall) follows.  Ps and Fs below should have  
> vector symbols over them; read F_12 as "force of object one on object  
> two" etc.
>
> start with (only) two objects interacting
> N3:  F_12 = - F_21
>
> recall N2 and P defns:
> F_net = ma = d (mv) / dt = dP / dt
>
> assume net forces are the interacting forces (only)
> therefore F_12 = dP_2 / dt and F_21 = dP_1 / dt
>
> substitute back into N3 above:
> dP_2 / dt = - dP_1 / dt
>
> regroup, et voila:
> dP_1 / dt + dP_2 / dt = 0 = d(P total) / dt
>
> conservation of linear momentum for the two interacting objects
>
> ...so conservation of linear momentum seems a direct implication from  
> N2  and N3 (and definitions which probably ropes N1 into the game as  
> well).  That'd seem to me to make Newton's Laws a consequence of the  
> conservation of linear momentum (or vice versa).

Your summary is good. Now what happens if we have an object interacting with a field?

---
Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-5002 
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/