# Mass: Matter or Inertia?

by Gib Z
Tags: inertia, mass, matter
 HW Helper P: 3,353 Well my trouble stems from that I learned Inertia to be a property of all masses, the property that all masses will not accelerate unless a force is applied. To me, this was always just a property, like a square having adjacent sides at right angles. Today in my Physics class I was told : Mass is a measure how much inertia as object has, when previously I had replaced Inertia with Matter. I was somewhat confused and even right now, I think that was wrong - its like having 2 cubes with one with edges 2 units and the other 5 units, and then asking which cubes edges were "more equal" to each other. I asked my teacher and he said just because it was a property didn't mean it wasn't quantifiable, like density. But his example of density doesn't seem to do it for me, the fact that an object has a density merely states all objects that have mass take up a finite volume. So my question is: Is inertia quantifiable? If so, what are its SI Units? I asked my teacher that as well and he seemed to ignore that question =[ Thanks for any replies guys, greatly appreciated.
 PF Patron Sci Advisor Emeritus P: 9,789 I agree with what you were told today: mass in a measure of inertia. In other words, mass is how me quantify inertia. Mass also 'happens' to be how we quantify the amount of matter that a particular object has. I must admit that I don't follow your cube analogy, but if density doesn't do it for you, perhaps a different analogy will. Consider electric charge, now you agree that electric charge is a property of matter, yes? It is the property that two 'like' charges will repel and two 'unlike' charges attract. Hopefully you will also agree that we can definitely quantify the 'amount' of charge an object has.
P: 1,503
 Quote by Gib Z Well my trouble stems from that I learned Inertia to be a property of all masses, the property that all masses will not accelerate unless a force is applied. To me, this was always just a property, like a square having adjacent sides at right angles. Today in my Physics class I was told : Mass is a measure how much inertia as object has, when previously I had replaced Inertia with Matter. I was somewhat confused and even right now, I think that was wrong - its like having 2 cubes with one with edges 2 units and the other 5 units, and then asking which cubes edges were "more equal" to each other. I asked my teacher and he said just because it was a property didn't mean it wasn't quantifiable, like density. But his example of density doesn't seem to do it for me, the fact that an object has a density merely states all objects that have mass take up a finite volume. So my question is: Is inertia quantifiable? If so, what are its SI Units? I asked my teacher that as well and he seemed to ignore that question =[ Thanks for any replies guys, greatly appreciated.
Inertia = mass.

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P: 3,353

## Mass: Matter or Inertia?

Ok well that definitely is a good example Hoot, I guess this resolves itself out if I change my definition of Inertia? Because saying Inertia is a property of Masses when Inertia = mass is a bit weird lol.
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 Quote by Gib Z Ok well that definitely is a good example Hoot, I guess this resolves itself out if I change my definition of Inertia? Because saying Inertia is a property of Masses when Inertia = mass is a bit weird lol.
How do you define mass? Just think about it.
 P: 72 I think your initial ideas regarding inertia are correct, although I don’t think your analogies with geometric figures help out. You mentioned SI units…No, inertia is not an SI unit or any other unit for that matter, it is the property of matter which resists acceleration as expressed in Newtons first law. But let’s look at some SI units.. Length(meter), mass(kilogram) and Time(second) are base units in the SI system, and force(newton) is a derived unit . 1 newton is the force required to accelerate a mass of 1 kilogram 1 meter per second squared). This relationship is expressed in Newtons first law as F=m a, or as Newton expressed it “Every body persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it” Since mass is an SI base unit defined by a cylinder of platinum, mass represents a quantity of matter. Inertia on the other hand is the property of matter which resists acceleration as expressed in Newtons first law. This is how I see it, and I can see how your instructors view could be confusing. On the other hand, I might be the confused one.
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 Quote by lightarrow How do you define mass? Just think about it.
I don't know how to, thats the problem lol! Defining it as mass or inertia still doesn't do justice to my mathematically reliant brain :( If anyone has some nice mathematical definition, please show!
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 Quote by Gib Z I don't know how to, thats the problem lol! Defining it as mass or inertia still doesn't do justice to my mathematically reliant brain :( If anyone has some nice mathematical definition, please show!
Personally I find the definition,

$$m = \frac{|\mathbf{a}|}{|\mathbf{F}|}\hspace{2cm}|\mathbf{F}|\neq0$$

rather intuitive
 HW Helper P: 3,353 I was thinking of that, but then my definition of Force must be completely non reliant on mass, and I define a newton as the force required to accelerate a mass of 1kg by 1ms^-2 :(
 P: 72 Mass is a base unit in the SI system of units. It is not a derived unit. Here is what a kilogram of mass is *: The kilogram (kg) is the unit of mass: It is equal to the mass of the international prototype of the kilogram. The internal prototype is made of platitum-iridium (90% platinum, 10% iridium) and is preserve in a vault at Serves France, by the International Bureau of Weights and Measures . There are no units of force or acceleration mentioned in this definition because mass is not defined that way. In particular, the equation mass=force/acceleration does not define mass. *Metric Units and Conversion Charts", Theordore Wildi
P: 63
 Quote by Gib Z Well my trouble stems from that I learned Inertia to be a property of all masses [...] So my question is: Is inertia quantifiable?
Gib Z: Maybe your definition is that of a purist so to speak. Perhaps the history-based definition has meaning exactly in the case where external force is not present while others use it in the complementary case where force is present.

One definition ends up using inertia as a yes-or-no proposition: does the body behave in a certain way in the absence of force or not? Period. Others end up extending the inertia question to become: what happens when a force IS present and end up using quantifiable numbers for this usage of inertia which then relates to mass.

My suspiscion is that much of the confusion in physics is due to the fact that we use old terms in new ways.
 HW Helper P: 3,353 Yes kwestion! Your second paragraph is exactly it =] So I'm guessing I'm meant to change from the first to the second now?
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 Quote by jimvoit Mass is a base unit in the SI system of units. It is not a derived unit. Here is what a kilogram of mass is *: The kilogram (kg) is the unit of mass: It is equal to the mass of the international prototype of the kilogram. The internal prototype is made of platitum-iridium (90% platinum, 10% iridium) and is preserve in a vault at Serves France, by the International Bureau of Weights and Measures . There are no units of force or acceleration mentioned in this definition because mass is not defined that way. In particular, the equation mass=force/acceleration does not define mass. *Metric Units and Conversion Charts", Theordore Wildi

That doesn't answer the question. It is perfectly valid to choose other quantities as base units and derive, say, length and mass from them.

In what is called the "universal" system, you take universal constants, such as the speed of light c, the gravitational constant G, and Planks constant, h, as the "base" units, then derive units for length, time, mass, etc. from them.
P: 63
 Quote by Gib Z So I'm guessing I'm meant to change from the first [usage] to the second now?
Gib Z: I'm not completely convinced. My take is that inertia or inertness is an important building block for the terms mass and momentum, but not necessarily the other way around. After all, doesn't a photon demonstrate the principle of inertia without demonstrating mass? (Ugh, I don't intend for this to branch into a discussion about refraction--yet :-) )

It may be that we're meant to accept cross-over terminology sometimes and figure it out by context. Fortunately, I think you'll agree that people seem to usually change to the word mass when they mean the second usage (responsiveness to force).
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 Quote by kwestion Gib Z: After all, doesn't a photon demonstrate the principle of inertia without demonstrating mass?
Hmm, I guess I'd like to retract that as an assertion and leave it as a question because of pathway concerns. Also, if a massless photon has inertia due to its momentum (a question), then that usage of the term inertia would necessarily mean that inertia is not a synonym for mass.
 P: 72 I'm new here and havn't learned how to use the Quote/original post feature yet...that's why i've used the Title to direct this response. The original question posted by Gib Z was “Is inertia quantifiable? If so, what are its SI Units?” I believe I have answered this original question. This question came about as a result of information he acquired in his physics class which contradicted his understanding of inertia. I became interested in this post in part because I thought Gib Z’s understanding was accurate. To clarify this issue it is necessary to explore how mass, force, and acceleration are defined under the SI system. This has been at the heart of all my posts and I think it is the proper path to “answering” his original question. As to the choice of base units, yes, other base units could have been chosen by the General Conference of Weights and Measures.
 P: 87 Mass = inertia = quantity of matter They're the same thing. It's like a triangle: A triangle may be defined as a polygon with 3 sides, or it may be defined as a polygon with 3 angles. This is not an inconsistency because the definitions are equivalent. Physics can be derived from more than one axiomatic system. There is no point in arguing over which is correct. You just use whichever one is most practical. As a student, of course, it is most practical to use the system your instructor is using. :)
 P: 13 Ok, I'm confused now. I thought inertia was the energy of a mass in motion. If the mass is not in motion its only energy is that of the mass itself. If a force is applied to the mass then the inertia is the mass plus the energy that was applied to it. Am I missing something?

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