# What came first ?

1. Mar 8, 2005

### Imo

What came first....?

This question has been bugging me for about three years now. It has to do with the similarities of Newton's third law (Niii)and Conservation of Momentum (CofP).

Just to re-itterate for those unclear (or unable to remember) the two laws:
Niii: For each action, there is an equal and opposite reaction.
CofP: in any action, momentum (the product of mass and velosity) is conserved within the system.

In my mind, these are just saying the same thing. For example, if an astronaut throws their shoe into space, then from Niii, the astronaut will have an opposite and equal reaction, pushing in the opposite direction of the thrown shoe. So the harder the astronaut throws the shoe, the greater the force pushing backwards.

For momentum, the faster the astronaut throws the shoe, the faster the astronaut will move backwards. And then of course, if you get into impulse, you realize they say the same thing.

My question, is which came first? I remember hearing once that Newton came up with momentum. But then why do we use two laws? I mean, really, Newton's Third Law is just the same as Conservation of Momentum (right?). So which law came first?

Thanks for anyone who takes the time to read this and answer.

Imo
~Dirac Notation: The closest most male physicists get to bras

2. Mar 8, 2005

### dextercioby

Are u asking a purely historical question,or some "deep" conceptual one...?To the first,i'll invite you to do some research work.It might help for future situations.
To the second,i'd that an axiomatical approach to CM in Newton's formulation would derive the conservation of total momentum for the isolated systems starting with the 3 axioms.

It is the way i learnt it in school.

Daniel.

P.S.I prefer the real thing,taken off...

3. Mar 10, 2005

### Crosson

Yes, all three of Newton's laws are summarized in the statement:

$$\Sigma \vec{F} = \vec{\dot{p}}$$

That is, F = 0 implies p is constant. If mass is constant, F = ma.

For the third law, we must prove that the sum of the forces on a system is equal to the change in momentum on the system. Then , we know that if two bodies interact such that there are no outside forces on them, there momentum is a constant (meaning they individualy move with equal and opposite changes in momentum, i.e. force.

4. Mar 10, 2005

### Andrew Mason

Newton's three laws are really three slightly different statements of the same principle. The first law came first, because it is really Galileo's. The second and third were Newton's. The second law is arguably the most important because it expresses the mathematical relationship between force and momentum change. They all imply conservation of momentum where there are no external forces.

The first law - an object will remain in uniform motion unless acted on by a force - means that if there is no force, $dp/dt = 0$ and if there is a force $dp/dt \ne 0$. But $dp/dt = 0$ means that momentum, p, is constant, so it is really a law about conservation of momentum.

The second law, $F = dp/dt$ is just another way of expressing the principle of the first law, except that it provides a quantitative relationship between F and dp/dt (ie. F = dp/dt). If F = 0 then dp/dt = 0 so momentum does not change (ie. p is conserved).

The third law states that forces always come in equal and opposite pairs: $F_a = -F_r$ or $dp_a/dt = -dp_r/dt$. This means that $dp_a/dt + dp_r/dt = 0$ which is just another way of saying that (absent external forces) the forces between masses add to 0 so total momentum change is 0. Again, this means that momentum is conserved.

AM