# Q: Can we consider Inertia a dimensionless vector?

1. Dec 20, 2008

### zd1899

I know that we do not measure or quantify Inertia , but it always acts in a direction opposing the cause for which a change in a bodies configuration or motion occurs , so it has a defined direction everytime a , let us say , force acts on the body.
But it is dimensionless and to my knowledge i dont think a dimensionless vector exists.

2. Dec 20, 2008

### Staff: Mentor

Can you give a specific example of what you mean by "inertia"?

(I would say that mass is a measure of a body's inertia--its resistance to acceleration.)

3. Dec 20, 2008

### Renge Ishyo

Mass is a measure of inertia, and I would also say energy is as well (because energy is equivalent to mass). Both measurements are considered scalers (a scaler is a "dimensionless vector" as far as I am understanding the term) even though they are defined by equations containing vectors. For example, the definition for inertia/mass is:

m = F/a where F and a are both vectors and mass is a scaler

The force is the vector quantity that takes into account both the quantity of inertia and its direction...not sure what you mean about inertia having an intrinsic direction all by itself (it doesn't matter what "side" that an object of mass m is pushed on, it will exert a force in the direction opposite...inertia in and of itself doesn't have a specific direction).

4. Dec 20, 2008

### Hootenanny

Staff Emeritus
This is simply not true. All unit vectors are "dimensionless" by definition, i.e. they have no physical units associated with them.

5. Dec 20, 2008

### HallsofIvy

I presume Renge Ishyo interpreted zd1899 to mean a "vector of dimension 0" although "tensor of order 0" would be better. zd1899, I would consider "inertia" to be a concept rather than any kind of quantity.

6. Dec 20, 2008

### Renge Ishyo

I think that might be what the original post was trying to get at, but I also think the original post was confusing the ideas of force and inertia which leads to all sorts of problems.

7. Dec 20, 2008

### zd1899

Thankyou , well yes , tensor quantities are there but i dont get to study them in the 11th grade , what i meant was , If inertia is just a property , and we have a measure of it , mass , then why cant we study it in terms of mass??
I mean , is it just a hypothetical concept ? we study about the rotational analogue of Inertia <moment of inertia> and we can assign direction of rotation to it , but then we are not able to do this with inertia of any other body.
And also , am i correct in saying that Inertia isnt even a scalar?
I must say Inertia has got my head rolling

8. Dec 20, 2008

### Renge Ishyo

Inertia just means an objects "resistance to motion." It is something that can easily be observed even if its not exactly known what it is. For instance, take an empty waste paper basket and push it forward noting its speed as you push it. Now, put some reasonably heavy trash in the waste paper basket and push it forward with the exact same strength as you did before. You can "feel" that it is resisting your push more this time, and the trash can doesn't move as quickly when you push it. You now need to come up with a word for this experience so you can talk about it with others and so you call it "inertia" because inert means unmoving and this is a phenomenon that causes the waste basket to resist moving the more stuff you put in it. That's all inertia is; its a word to describe an observable phenomenon.

You can now toss a bunch of your science textbooks in there and pretty soon you won't be able to move the waste paper basket at all! As you add "stuff" to the trash basket you observe that you increase its inertia and its ability to resist your attempt to move it. While you can't measure the "resistance to move" directly, you can measure the amount of stuff you have added to the waste basket by the amount of mass it has. So knowing how much mass an object has gives you an idea of how difficult that object is going to be to move.

9. Dec 20, 2008

### ThomasT

Your questions about the meaning of the term, inertia, have been answered. Were you just interested in sorting out the semantics, or are you worrying over the physical cause of inertia (ie., the question regarding some fundamental physical force that underlies physical objects' resistance to changes in their velocities)?

10. Dec 21, 2008

### zd1899

No , no;
Id taken up this question as i thought that Inertia acts in a direction, though it never acts but is observed, as i came to know now. Thats all , thankyou.

11. Dec 21, 2008

### rcgldr

Angular inertia depends on the axis of rotation, and in that sense, it's a vector with dimensions.

12. Dec 22, 2008

### zd1899

Yes , moment of inertia is a vector with dimensions , but then we have it as a vector when a rigid body rotates , why not for a translating object?

13. Dec 24, 2008

### Georgepowell

Sorry to be pedantic, but I think that is wrong. A photon has energy, but has no inertia. Energy is not equivalent to mass, In fact I don't have this topic completely clear myself...

Everything that has mass/inertia has energy, and everything that has energy has a gravitational pull, but not everything with energy has mass/inertia.

Am I right?

14. Dec 24, 2008

### zd1899

Mass are like bundles of trapped energy , run at the speed of light and it will disintegrate into the pure light energy.
Thats the concept i guess , rest since inertia is measured through , inertia should be measured through energy aswell , but yes , what about a photon?
So what can we conclude from this , about inertia , energy and mass?

15. Dec 24, 2008

### Renge Ishyo

That might be right. A photon is an interesting case in that it doesn't behave like a classical particle in all ways so it is hard to characterize it using old terminology.

16. Dec 24, 2008

### zd1899

But then photon can be considered the purest particle since it has all laws valid on it , except this one..??

17. Dec 25, 2008

### Renge Ishyo

I'm not sure if I'd call the photon the "purest" particle per say; it is special in the sense that it is the force carrier particle (boson) of the electromagnetic interaction whereas protons, neutrons, and electrons (all fermions) are the things we usually add up to measure the "mass" of something. The photon behavior is different in some ways from those other "particles" too (its spin is integer as opposed to fractional for one example). However, there are other bosons (and other fermions) to consider down the road...

Digressing a bit: I'm not sure if there is a "purest particle" that everything else is built out of. I know string theory and various other theories have attempted to uncover such things, but as far as I know these theories have gone nowhere. The next great hope is just to wait and see what happens with the LHC next year.

For studying inertia and forces I would just stick to large bodies anyways. I don't think too many classical ideas can survive for very long in the quantum world without serious modification...

18. Dec 25, 2008

Staff Emeritus
I don't think the "purity" of a particle is a scientific concept until you can quantify it. I also suspect that counting the number of laws that apply to a given system is not a well-defined quantity. Different people will give different counts.

19. Dec 25, 2008

### Georgepowell

A photon isn't the only massless particle is it? Are there other massless particles which also have energy, but no inertia?

I thought that neutrinos where massless, but a quick look on Wikipedia tells me otherwise.

20. Dec 25, 2008

### GetPhysical

If you think about it. Inertia acts in all directions. Wherever there is an applied force inertia is resisting at 180 degrees in the opposite direction. So inertia can act in any possible direction based on the applied force.