Mass is a measure of inertia (inertial mass). And mass is also the amount of stuff something contains, independent of volume (gravitational mass).

The inertial definition for mass stems more from what an object does rather than what an object specifically is. In order to fully appreciate this concept for mass, let’s briefly discuss how an object behaves when pushed. The behavior is called inertia. Inertia is matter’s natural resistance to acceleration. Or in other words, it is matter’s intrinsic ability to resist changes in motion. An object tends to stay at rest, or to stay in motion or in a particular direction.

There are a couple of ways to state a quantity for inertia: There is "mass" and there is "moment of inertia". These are both specific amounts of inertia, basically. (For our purposes, we will focus on mass rather than moment of inertia.)

So "inertia" is resistance to acceleration while "mass" is a specific quantity of such inertia. How can we remember that mass is different from weight? One way to do this is to think of mass as an amount on inertia. I suppose one could think of mass as a sort of tablespoon of inertia. With regard to inertial mass itself, a bowling ball has greater resistance to acceleration than an equal-sized volleyball when pushed. Since the bowling ball has more stuff in it, it resists changes in movement more so than the volleyball. Therefore, the bowling ball has more inertia. The idea of stuff being present is the gravitational slant on mass. Since gravitational and inertial aspects of mass exist simultaneously, they can cause confusion.

The bowling ball’s inertial mass would be some sort of specific measure of inertia. For instance, the bowling ball, having a mass of six kilograms, say, might be twenty times more massive than the volleyball. Since both balls are basically the same size, we might further conclude that volume has little to do with inertial mass.

For a classical physics discussion about mass and gravitation, however, having mass does imply a certain amount of volume. It’s the amount of stuff something has. During college physics lectures, whenever a professor draws a picture of a car on a chalkboard to reference a car’s mass, it would be quite reasonable to assume that the mass of the car has some sort of size and shape. After all, it’s true that a certain amount of mass is contained within the volume of the car. And when such a car is sufficiently close to Earth, there is a mutually-attractive pull known as gravity. But the mass of the car itself is not the volume specifically. These are two separate properties of the object.

Failing to make this distinction, we might end up improperly assuming that one could always visualize mass as a kind of volume, or that mass always indicates some amount of space. It’s true that an item such as a car has mass, and that it has volume too in order to occupy space. But these really are two separate aspects not to be confused.

With regard to fully appreciating how inertial mass, gravitational mass and volume are related, it might be helpful to know that when a single force acts upon an object, it places you in a position where you can calculate the object’s volume and mass. You can do this by measuring the volume of the object while also measuring the object’s acceleration by timing the object’s changing velocity. Once you’ve done that, you can divide the force by the acceleration, mathematically-providing a quantity for the mass of the object.

Otherwise, if the object has no force acting upon it at all, you are only able to determine its volume. You are free to think about the object’s mass if you’d like, but you aren’t likely to calculate it, or maybe even imagine it. With regard to inertial mass specifically, you aren’t really able to imagine the object’s inertial mass as a picture in your mind. Because making a picture involves visualizing some sort of three dimensional shape. And three dimensional shapes are examples of volume. As stated before, inertial mass has no volume (all inertial mass is, is a measure of inertia).

But, by visualizing mass in terms of its gravitational point of view we can start making a mental picture. Looking at mass by way of how much stuff there is, we can use a three-dimensional picture of the object to mentally store all the stuff inside. However, the place is not the stuff. That can be confusing.

Therefore, mass in general should be viewed as a measurement that is always independent of volume, such that an item’s mass is never enough to tell you how much space the item utilizes. But since there is some sort of item there to begin with, we can expect a certain amount of volume to be present. For this discussion, the gram is the unit of measure for mass. Within a given size category, the mass of each particle may differ depending upon gold purity. So we need both mass and volume in order to tell the difference between purities.

When using the calculator, QuickGoldTally, notice how medium sand-sized (35 mesh) 24 karat gold has a mass of .002410250 grams while the same-sized 23 karat gold has a lower mass of .002329083 grams. This is due to the fact that one particle is solid gold, while the other is a gold alloy. This means that even though the particles are the same size, the mass is less when the particle is not entirely pure gold.

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