Newton's third law is...

"For every action there is an equal and opposite reaction."

This is probably the hardest law to really understand.

It really helps to understand this law if you understand that the law has its origin in the conservation of momentum principle.

The fact of the matter is, force can be most fundamentally understood to be the rate of change of momentum.

Let me explain why.

First momentum is..

P=mv

Now look at the equation for force.

F=ma

It is very similar except that in place of P we have F and in place of v we have a.

Looking at the force equation again..

f=ma

we note that acceleration is the rate of change of velocity so...

F=m dv/dt

Now since the mass, m, is constant we can put it directly beside the velocity like so..

F=d(mv)/dt

This is looking more like the below momentum equation...

P=mv

The only difference is that for the momentum equation, we have, mv, and for the force equation we have the rate of change of, mv, or, d(mv)/dt

Now in the force equation

F=d(mv)/dt

because P = mv, we can replace, mv with P...

F=dP/dt

As I said, force is the rate of change of momentum.

Now since the law of conservation of momentum states that momentum is neither created nor destroyed, if an object picks up momentum, another object to lose momentum. In Newton's third law the "action" force is the second body picking upmomentum and the "reaction" force is the first body losing that momentum.

As an example, imagine two people standing on a very slippery skating rink, because they are standing still, together, they have zero momentum. If one person pushes the second person, or "applies a force" on the second person, the second person has momentum delivered to them and that second person picks up speed/momentum in that direction. The first person however picks up speed/momentum in the other direction, which means that he also had momentum delivered to him. That second person picking up momentum was the "action force", and that first person picking up momentum in the other direction was the "reaction force".

The second person picked up momentum in one direction, and since there is the conservation of momentum law, the first picked up momentum in the opposite direction. Their momentum was zero before the event and since momentum has direction the sum of both momenta add up to zero after the event.

If both people had been moving, for example, to the right and the first person pushed the second person also to the right, the second person would have picked up momentum to the right and the first person would have only lost momentum to the right. There would have still been both an action and a reaction force however because momentum was only exchanged.

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