“If I have ever made any valuable discoveries, it has been due more to patient attention, than to any other talent.” -

Isaac Newton

Born the year Galileo died, Isaac Newton is one of the most revered figures in all of physics.

In addition to the work he did on optics, planetary motion and gravitation, Newton is also famous for his three laws of motion, which — *even today* — apply very well to every particle in the Universe. They are:

**Law #1:** An object at rest will remain at rest, and an object in motion will remain in motion, *unless* acted upon by an outside force.

What does this mean? It means that, whatever *velocity* something starts out with, that velocity — both *speed* and *direction* — will not change unless something *else* in the Universe exerts a force on it. In other words, any object can’t change its motion *on its own*; it needs something else to push, pull, or otherwise exert a force on it.

**Law #2:** The **time rate of change of momentum** of any object is equal to the **net external force** acting upon it.

This law is *often* — including on wikipedia — misstated as force equals mass times acceleration, or **F = ma**. This is often, but not universally true, as we’ll see below. But this is very important, because it tells us not just that something *changes its motion* if something pushes, pulls, or otherwise exerts a force on it, but it tells us *how* that motion changes!

And finally…

**Law #3:** For every *action*, there is an *equal and opposite reaction*.

What did Newton mean when he said **action**? He meant — at any instant — **force**, or, over time, a **change in momentum**. So if you punch your enemy in the face…

…your fist exerts a force on his face, and his face exerts an *equal and opposite force* on you fist. And in the prior example, if you use a small gunpowder explosion to change the momentum of a bullet, the equal and opposite reaction is the equal and opposite change in momentum of *you holding the gun*, known commonly as recoil.

*It pays to be aware of this.*

*you can’t exert a net force on yourself*, and you can’t

*change your own momentum*without also changing something else’s momentum by an equal and opposite amount!

So do we really need all *three* of Newton’s Laws? Think about that first one for a minute. You can be at rest and stay at rest, or you can be in motion and stay in motion. But in either case, there’s **no external force** on you.

You might realize that **Newton’s 1st Law is a special case of Newton’s 2nd Law**! So we can combine those two and simply say that the net external force, which *can* be zero, is the time rate of change of momentum.

But remember, there’s that third law, too.

That external force that changes your momentum *is coming from somewhere*. And there’s an equal and opposite force on whatever thing pushes you, and therefore — by the *second* law again — **it gets an equal and opposite change in momentum**!

So what do we learn from this? *Momentum, if you look at all the objects exerting forces on each other, is *conserved* overall.*

So there’s this one concept, the conservation of momentum, that when you combine it with the definition of momentum, gives you all of Newton’s Laws.

And one last thing: why do I say that **F=ma** isn’t quite right?

Because when you get close to the speed of light, you can’t *accelerate* up to it, no matter how much force you have!

But you *can* still increase your momentum, and the time rate of change of momentum is *still* equal to the net force on you! Does that mean Newton anticipated Einstein’s theory of special relativity?

We’ll never know, but of all the ways for Newton to phrase his second law, he sure did pick an interesting one!