## Newton's Mass

Mass is a toughy and we'll see over and over how complicated it is --- to the current day. Here's how he defined it in the *Principia*:

"Mass is the quantity of matter arising from its density and bulk conjointly."

There you go. Useful? ...no?

> **Wait.** Doesn’t that seem circular?<br>
> **Glad you asked.** You might think so, yes. You know that density is an object’s mass divided by its volume and so to define mass…using mass…does seem so. I think it’s probably hard to invent your own science out of almost nothing! So word-explanations can seem a little strange. (There’s also some reason to think that “density” for Newton referred to specific gravity, but let’s not follow that.) You’re correct to be a little unsatisfied with this definition! But we can forgive him since “mass” becomes almost a theme in QS&BB. It’s really complicated!

In any case, you do perfectly well---at least in solving engineering homework or building bridges---to accept the idea that mass is the amount of the “stuff” in an object and that it's also the quantitative measure of an object's reluctance to be coaxed into changing its motion.

Here begins our love-hate relationship with mass. This much works:

> Inertia is an object's resistance to being accelerated and the measure of an object’s inertia is its mass.

This is the most profound and at the same time, the most mundane idea that Newton had! It's with us today as a primary focus of particle physics research:

>**What is the nature of Mass?**<br><br>
>At the deep level of elementary particles, mass confuses us, perhaps in a different way from how it confuses engineering freshmen. We think that mass may actually not be an actual property of object, but rather a result of an object's interaction with a spooky field that sprang into existence just after the birth of the Universe. Now, in the 21st century, we've got a whole new set of neuroses about this subject, as understanding it occupies almost the entire Particle Physics community. So, Mass has been a problematic subject since its beginning in Newton's hands.

And then, there are units. The MKS unit for mass is the kilogram, kg and we’ll use it almost universally. So remembering the bathroom scale discussion above, you can now see that US bathroom scales report a force while for everyone else in the world, their scales report people’s masses, kg. But their scales, like ours, are still measuring the earth's force on us but their readings are calibrated to report back mass, not force. Their scales will not work to Mars without difficulty. We’ll come back to this.

With this “feeling” for pushing on big and little things, we can state the impulse proportionality as a full-fledged model --- an equation.