# Is Inertia Quantifiable and Measured by SI Units?

• Gib Z
In summary, during a conversation about the concept of inertia, it was discovered that mass is a measure of inertia and also the amount of matter an object has. The concept of inertia was compared to other properties like density and electric charge. There was some confusion about the relationship between mass and inertia, but ultimately it was agreed that mass is a base unit in the SI system, while inertia is a property of matter.
Gib Z
Homework Helper
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.

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.

Gib Z said:
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.

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.

Gib Z said:
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.

Gib Z seems to have the correct viewpoint

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.

lightarrow said:
How do you define mass? Just think about it.

I don't know how to, that's 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!

Gib Z said:
I don't know how to, that's 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

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 :(

Mass

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

Definitions can be moving targets

Gib Z said:
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.

Last edited:
Yes kwestion! Your second paragraph is exactly it =] So I'm guessing I'm meant to change from the first to the second now?

jimvoit said:
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.

Is inertia quantifiable?

Gib Z said:
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).

Retract assertion that photon displays inertia

kwestion said:
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.

To HallsofIvy and others

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.

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. :)

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?

dmt740 said:
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?

Inertia is the property whereby an object in motion tends to remain in motion and an object at rest tends to remain at rest. In other words, inertia = mass. See Newton's Laws of Motion.

The energy of motion is called "kinetic energy."

The relationship between force and energy depends on the properties of the force. Specifically, it depends on the potential energy corresponding to the force.

It is important to keep in mind that Newtonian physics and relativistic physics are different theories based on somewhat different assumptions.

In Newtonian physics, mass and energy are completely different things. They are not equivalent.

In relativity, mass and energy are equivalent. Mass is a form of energy, and energy possesses inertia.

inertia and fundamental ideas

I think Gib Z was onto something that is important at a fundamental level. The terms matter, inertia, mass, and momentum bring different things to the table, so I wouldn’t sweep the differences under the rug.

• The term matter helps us distinguish between physical objects and empty space or imaginary objects.

• The term inertia helps us understand that a physical object doesn’t spontaneously and independently change velocity (accelerate) without interaction with an outside force.

• The principle of inertia allows us to reliably credit 100% of acceleration to interaction with an outside force which we couldn’t very well do if the physical object were not 100% inert to self-acceleration.

• The reliable relationship between force on an object and the acceleration of an object is called mass and can be measured in kilograms.

In the very important fundamental sense above, inertia has no units. An object, regardless of size, mass, weight, etc., can either independently and spontaneously accelerate or it can’t. Real, physical objects (matter) can’t. I'm trying to draw out in the series of statements above, that these terms are building blocks for the next idea and not all the same idea.

After speaking of the fundamentals, we move to other more day-to-day usages of the term inertia which can cause confusion:
In another important sense of the word, inertia has been taken to mean resistance to acceleration which then correlates to mass and can be measured in kilograms.
In yet another more informal sense, inertia can informally mean momentum: the product of mass and velocity.

Last edited:
well for my two cents which don't really address the op question

i recall reading that mass can be thought of in two ways

1
inertial mass> defining the mass by its inertia, or resistance to acceleration

2
gravitational mass> defining mass by the amount of gravity it creates

and interestingly if you determine the mass of an object by method 1, it will not be the same as method 2. i don't remember which one is ever so slightly larger.

Gib Z said:
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 is quantified by the object's mass.

to post #21:

i think it was eotvos that showed gravitational and inertial mass are equivlent.

einstien used some of that info for the principle of equivlence.

in other news,

my prof once said "if you are ever having a hard time sleeping try to define mass and you'll pass right out"

Last edited:
The mass of an object is given by the total energy content (divided by c^2). So, an empty box with conducting walls has a mass that is slightly larger than the mass of walls alone due to the Casimir energy. If I remember correctly, the Casimir energy of a cube is positive unlike the case of two infinite plates.

So, it is not correct to say that mass is matter in the form of particles as the vacuum also contributes to mass.

Count Iblis said:
The mass of an object is given by the total energy content (divided by c^2). So, an empty box with conducting walls has a mass that is slightly larger than the mass of walls alone due to the Casimir energy. If I remember correctly, the Casimir energy of a cube is positive unlike the case of two infinite plates.

So, it is not correct to say that mass is matter in the form of particles as the vacuum also contributes to mass.

While I don't deny the truth of this statement, It doesn't quite cut it for me as a definition unless you can tell me a definition of energy that doesn't involve mass in any way.

energy is the ability to do work, if we let work be PdV instead of Fds you may be pleased. i don't have a problem with circular definitions

Gib Z, you're not alone. The confusion between inertia, mass, matter and momentum is still common today in textbooks and physics papers.
As kwestion said you are "onto something that is important at a fundamental level."
In quantifying one or the other we often negate or assume a certain relative quantity.
What is important, is to understand the fundamental conceptual differences first, so the math does not become ambiguous.

A body does not move of its own accord. This seems incredibly obvious from classical physics to today.
It essentially says, unless an external force is applied, a body will remain at "rest".
Why? Because in classical terms, inanimate bodies, are inert. (unable to move or act)
So matter is inert, force is the antithesis of matter, the two together are action. (not to be confused with motion)
The idea that a body in motion will remain in motion is just as obvious but is more easily understood as
a relative property of rest. A body at rest remains at rest even it that state of rest is "motion" with respect to another observer. So now a body is both at rest and in motion depending on the frame of reference taken.
But in either case, it still has inertia - it will not change of its own accord.
Now we want to quantify the force required to change the state of motion of this body.
When its at rest, with respect to one observer, no matter how fast it is moving with respect to any other, the force required is always the same. This force is a direct measure of the quantity of matter of the body and since motion does not change the total number of particles in a body, rest mass is constant.
As a measure of energy, that quantity of matter is called mass.
When the same body is measured by an other observer that measures the body to be in motion, the force required to bring it to rest depends on the speed of the body with respect to that observer. This force is called momentum. The momentum is a measure of the bodies mass and speed.
To recap:
Inertia is a property of Matter (the property that it remains inert, regardless its state of motion)
Mass is the constant, quantifiable energy of matter
Momentum is a relative measure of Mass.

Then along came Einstein and everyone started mixing metaphors.
As soon as E=mc^2 appeared everyone began to talk of mass as energy , which is fine as long as nobody
confuses a quantity of energy as a statement of a quantity of matter.
The most common confusion was energy expressed as relativistic mass.
This was analogous to saying: 2+2 = 4 unless you start with 3.
The remaining expressions are much less so, but still prone to confusion.
Gravitational mass, attractive gravitational mass, passive gravitational mass, "energy" of momentum, inertial "energy"...

Mass is a quantitative measure of inertia.

Apparently, a photon imparting momentum to a mass (or vice versa) allows inertia for the mass but not for the photon.

Loren Booda said:
Apparently, a photon imparting momentum to a mass (or vice versa) allows inertia for the mass but not for the photon.

Forgive me, but... what?

If the definition of inertia includes changes in momentum, by its definition how do interactions of photons (non-inertial) or masses (inertial) differ otherwise?

Photons and mass are two different subjects. They both 'obey' the geometric properties of spacetime though. That is, both will 'bend' to gravity. Photons have what's called an instant acceleration, relative or rest mass do not. Otherwise I agree in that it is a 'muddy' question :)

We can slow down light and even stop it, when we do that it disappear, as far as I understand, only to show itself when we accelerate it again. Then again, I might be wrong here. On the other hand, electrons are not defined particles either, they just have a probability focus, right:)

And inertia is a property of relative / rest mass which differs from photons instant acceleration. But I have problems with exchanging mass for inertia as inertia is a intangible property concurring from mass, whereas mass does not, as far as I know, create itself by experience inertia.

## 1. What is inertia?

Inertia is the tendency of an object to resist changes in its state of motion. It is a property of matter that describes an object's resistance to acceleration or deceleration.

## 2. How is inertia quantified?

Inertia is quantified by an object's mass, which is a measure of the amount of matter it contains. The greater an object's mass, the greater its inertia.

## 3. Can inertia be measured by SI units?

Yes, inertia can be measured by SI units. The SI unit for mass is kilograms (kg), which is used to measure an object's inertia.

## 4. What is the relationship between inertia and SI units?

The SI unit for mass, kilograms, is directly related to an object's inertia. The greater an object's mass, the greater its inertia, and therefore the greater its resistance to changes in its state of motion.

## 5. Why is it important to measure inertia using SI units?

Using SI units to measure inertia allows for consistency and accuracy in scientific measurements. It also allows for easy comparison and communication of results among scientists and researchers.

• Mechanics
Replies
1
Views
1K
• Mechanics
Replies
3
Views
1K
• Mechanics
Replies
19
Views
6K
• Mechanics
Replies
22
Views
2K
• Mechanics
Replies
2
Views
2K
• Mechanics
Replies
4
Views
2K
• Mechanical Engineering
Replies
10
Views
846
• Mechanics
Replies
10
Views
2K
• Mechanics
Replies
27
Views
7K
• Mechanics
Replies
14
Views
1K