# Is there a common misunderstanding of inertia?

1. Sep 8, 2011

### johann1301

According to wikipedia, «inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion.»
To explain what i think the common misunderstanding of inertia is, one finds it helpfull to talk about matter without inertia.

Mass with- and without inertia:
If I were to talk about matter without the property of inertia, I would be talking about an unobserved object. In other words; Matter without inertia does not really exist(or very unknown). Yet it is important to stress that a hypothetical object without inertia, would also keep its original state of motion when not-forced-upon, just as an object with inertia would. At least hypothetically.
The difference lies in the amount of force needed to move the objects. An object without inertia - no matter how big or small it is - would need a force of zero Newton(no force) to change its state of motion. In the case where the object has inertia(wich is the realistic case), the amount of force would vary proporsional with the objects mass. (this is a known fact). If the mass is bigger, the inertia is bigger. (and vica versa)
If this hypothetical presumtion is true, it would imply that inertia (not matter) is the reason why a force is needed to move an object.
For example: You get shot by a pistol. If the bullet has no inertia, you would not feel the bullet hitting you.
To explain even further; the period where an object goes from beeing in one state of motion A to another state of motion B, is the timeframe where inertia plays its role. This is the period were one observes resistance. In the case were inertia does not exist, there would be no resistance in this period. In any other time then between A and B, no-inertia and inertia would be the same thing.

1. An object at rest tends to stay at rest.
2. An object in motion tends to stay in motion.
Source: http://www.qrg.northwestern.edu/projects/vss/docs/Propulsion/2-what-is-inertia.html

These are well known statements about inertia, but they do not mention anything about resistance.(at least not directly) These statements imply that objects stay in motion and rest becouse of inertia. As described earlier, this shouldnt be the true. They stay at rest and in-motion becouse nothing is acting on it. This leeds to another question...

What makes objects move?
In the example where the non-inertial bullet hits you without you feeling it, the bullet also stops!
Inertia shouldent stop objects, in fact it is known to resist any change of motion. There is no logic then, in that a non-inertial bullet should act any different. Inertia has therefore nothing to do with why objects change their state of motion or change shape. That must be explained by something else.
There are probably many explenations why an object can change its shape or state of motion. The Pauli exclusion principle is perhaps one of the explenations or our general idea of friction.

anyway...

Are there other people who agree with me?
Is saying «An object at rest tends to stay at rest» the same as saying that «An object tends to resist any change in its motion»?

i think not...

2. Sep 8, 2011

### Freye

I'm really not quite sure what you're trying to get at here, but to answer your last question "Is saying <an object at rest tends to stay at rest> the same as saying that <an object tends to resist any change in its motion>?", the former statement does not imply the latter, it is merely a specific application of it, whereas the latter (which is essentially Newton's first law) implies the former. Hopefully this at least partially answers what you're asking.

3. Sep 8, 2011

### Andrew Mason

You have put some thought into the nature of inertia. It is one of the real mysteries of the physical world. Good luck in trying to figure it out.

You are right that inertia alone does not explain why objects speed up or slow down when they interact with other objects.

For example, neutrons, which have significant inertia, will go through matter quite easily without slowing down (unless they hit an atomic nucleus). So if you could make a bullet out of neutrons, the bullet could go through you without leaving a hole and without slowing down (much). That has nothing to do with inertia. It has to do with its ability of neutrons to interact with the molecules in your body. (Since you can't make a bullet out of neutrons for other reasons, we don't observe this).

Neutrinos are particles that have inertia. They are emitted during nuclear reactions such as occur in the sun. Huge numbers pass through the sun and through the earth every second without slowing down at all. Very few get stopped. Again, it has nothing to do with inertial. It has to do with the ability to interact with other matter.

The reason a normal matter bullet slows down when it strikes something has to do with the electromagnetic forces between atoms. A bullet slows down because there is an interaction - a mutually repulsive force - between the atoms in the bullet and the atoms in the target. These are electromagnetic forces.

When, however, two particles do interact, inertia does matter. It determines how the particles will behave in the interaction and what the momentum will be after the interaction.

So, you are right. Inertia does not explain why particles are subject to forces. But inertia does determine how two bodies will move if they are subject to forces.

AM

4. Sep 8, 2011

### 256bits

Just consider what the situation was before the concept of inertia and that was that it was incorectly believed that a body in motion needed a continious force to keep it in motion.

There is also the debate of whether or not gravitational mass is the same as inertial mass. So far the two seem to be equal and the question then is why? No one has come up with a complete explantion to explain the equality if I am not mistaken.

Last edited: Sep 8, 2011
5. Sep 9, 2011

### johann1301

What is the difference between gravitational mass and inertial mass?

6. Sep 9, 2011

### johann1301

I guess you are talking about velocity here??(after the interaction)

I didn't think of that, of course inertia plays a role after! But i guess i was thinking of the acceleration, not the velocity when i said:

If i could re-express myself:
In any other time then between A and B, no-inertia and inertia would give the same acceleration. 0 m/s2 to be accurate.

I totally agree that both velocity, position(at a specific time) AND acceleration would be influenced by inertia IN the interaction, but after; the acceleration has nothing to do with inertia.

right?

Last edited: Sep 9, 2011
7. Sep 9, 2011

### Samshorn

Aren't those two statements mutually contradictory? Or do you claim "no force" is different from "not-forced-upon"?

It's questionable whether postulating attributes for non-existent things (e.g., objects without inertia) has any rational content, but postulating mutually contradictory attributes surely has none.

8. Sep 9, 2011

### Dickfore

For me, the principle of inertia simply follows from the Lagrangian formulation of Mechanics. Namely, for a free point particle, the Lagrangian can not depend on position and time due to homogeneity of space and time, and it cannot depend on the direction of its velocity due to isotropy of space. Therefore, it can only depend on the square of the magnitude of velocity:
$$L = L(v^{2})$$
But, when we try to insert the derivatives:
$$\frac{\partial L}{\partial \mathbf{v}} = 2 \mathbf{v} L'(v^{2})$$
and
$$\frac{\partial L}{\partial \mathbf{r}} = 0$$
into the Euler-Lagrange equations of motion:
$$\frac{d}{d t} \frac{\partial L}{\partial \mathbf{v}} - \frac{\partial L}{\partial \mathbf{r}} = 0$$
we get:
$$L'(v^{2}) \mathbf{v} = \mathbf{\mathrm{const.}}$$
This vector equation implies that:
$$\mathbf{v} = \mathbf{\mathrm{const.}}$$
which is a mathematical expression of the principle of inertia: That a free point particle tends to move with a constant velocity, i.e. uniformly along a straight line.

9. Sep 9, 2011

### Dickfore

Notice, however, that this only applies to a point particle. A free rigid body, for example, can continue to rotate along a any of its principal axes of inertia with a uniform angular velocity.

10. Sep 9, 2011

### johann1301

Yes it is contradictory, sorry about that! usually when an object changes momentum there has been some force involved. thats why i wrote "not-FORCED-upon".

An object without inertia would also keep its original state of motion when not-being in contact with any other object.(just as an object with inertia).

This shouldn't be a problem; because inertia does not explain why particles are subject to forces. (as concluded earlier).

Last edited: Sep 9, 2011
11. Sep 9, 2011

### johann1301

true.

12. Sep 9, 2011

### chrisbaird

The word "inertia" can be misleading because it historically can refer to two different things. So you always need to be clear with you mean. It can mean "the amount of resistance an object has to a change in velocity" which is the same thing as inertial mass, or it can mean "the amount of powerful movement contained in a moving body" which is the same thing as momentum. These are different concepts. When you speak of a speeding bullet having more inertia because it is harder to stop than, say, a large shopping cart, you mean momentum. In the sense of accelerating from 0 to 60 mph, the bullet actually has less inertia (less mass). Some of the confusion in the OP may lie with these two meanings.

If you mean inertia in the sense of mass, than to speculate about an object that has mass but no inertia is meaningless. It is like talking about an orange carrot that is colorless.

13. Sep 9, 2011

### Andrew Mason

Inertia and force determines the accelerations resulting from an interaction. a = f/m

After the interaction, there is no force and no acceleration.

AM

14. Sep 9, 2011

### johann1301

When newton says in his first law of motion:
The velocity of a body remains constant unless the body is acted upon by an external force.
-http://en.wikipedia.org/wiki/Newton's_laws_of_motion

He could just have said:
The acceleration of a body remains zero unless the body is acted upon by an external force.

This is becouse the derivative of a constant always have a value of zero.(ofcourse)

If the accelleration remains zero, inertia plays no crucial role. This is what i belive we have established erliar.

In other words Newtons first law has nothng to do with inertia. Or; Newtons first law is valid with- and without the existence of inertia?

(i know this is stretching it far) When people use newtons first law as an illustration of inertia, i believe that it is wrong to do so. This is what i believe is the common misunderstanding of inertia.

Feel free to disagree, honestly;)

15. Sep 9, 2011

### Dickfore

Newton's First Law holds only in Refrence Frames that are called 'inertial'. It should be treated as a criterion of whether or not a particular frame is inertial and not as a consequence of Second Newton's Law:
$$\mathbf{F} = \mathbf{0} \Rightarrow \mathbf{a} = \mathbf{0} \Rightarrow \mathbf{v} = \mathbf{\mathrm{const.}}$$
This is not the essence of it, because it is supposed to be a logically independent statement from the other two Laws. And, in the context that I mentioned, it is. Newton's Laws strictly hold only in Inertial Reference Frames.

16. Sep 9, 2011

### Ken G

One way to look at all this is to imagine we have a series of questions that first deal with understanding our reference frame, and later with understanding the forces present. We might define an inertial reference frame as one that exhibits the symmetries that Dickfore mentioned, and invoke the dynamical laws to then assert, as he showed, that in such a frame, velocity will stay constant. We are then not using the constant velocity as our definition of an inertial frame, we are using the fact that we will observe the laws to hold good in that frame. In that program, Newton's first law is indeed contained in the second law-- the law that must hold good is the second law, if we are in a frame with those symmetries. We call that an inertial frame.

Seen this way, the point of culling out the first law for special attention, even though it is contained in the second, is expressly because the first law does not make reference to inertia. There is no requirement to have a concept of inertia to have the first law, we only need a concept of an inertial frame (an unfortunate overlap in terms). So I think the issue raised in the OP is a valid one-- the term "inertia" really does get used in two quite different ways, one around the lines of "what will not happen when there are no forces on a body" (which relates only to the issue of what the observer is doing, i.e., whether the observer frame exhibits symmetry in space, time, and orientation), and the other around the lines of "how much will happen when there are forces" (which relates to the concept of mass, often used as a synonym for inertia).

17. Sep 9, 2011

### Andrew Mason

To determine whether Newton's first law is valid with or without inertia, you would have to find a physical entity that has no inertia and see if Newtons' first law applies. (There are such particles eg. a photon).

It can be shown by experiment that a photon will impart momentum to an atom when an atom emits or absorbs the photon. So the photon carries momentum ($p = h/\lambda$). In this respect, it behaves like a matter particle. But does it follow the first law? In these interactions with atoms, does its state of motion change? No. It doesn't. It always travels at c.

So I would say that Newton's first law does not apply to bodies that have no inertia. You are quite right that it is not about inertia (the second law is about inertia). But it certainly has something to do with inertia. It describes the motion of inertial objects that are not subjected to forces.

AM

18. Sep 9, 2011

### zoobyshoe

To the contrary. Newton, very directly, defined inertia as a resistance:

"Definition III.

The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, endeavors to persevere in its present state, whether it be of rest, or of moving forward in a right line.

This force is ever proportional to the body whose force it is; and differs nothing from the inactivity of the mass, but in our manner of conceiving it. A body, from the inactivity of matter, is not without difficulty put out of its state of rest or motion. Upon which account, this vis insita may, by a most significant name, be called vis inertiae, or force of inactivity. But a body exerts this force only, when another force, impressed upon it, endeavors to change its condition; and the exercise of this force may be considered both as resistance and impulse; it is resistance, in so far as the body, for maintaining its present state, withstands the force impressed; it is impulse, in so far as the body, by not easily giving way to the impressed force of another, endeavors to change the state of that other. Resistance is usually ascribed to bodies at rest, and impulse to those in motion; but motion and rest, as commonly conceived, are only relatively distinguished; nor are those bodies always truly at rest, which are commonly taken to be so."

-Newton
Principia Mathematica

Newton's three Laws are much clearer if you make the effort to penetrate the somewhat archaic language and read the definitions that preceed them in Principia Mathematica:

http://www.archive.org/stream/newtonspmathema00newtrich#page/n77/mode/2up

A body without inertia would, by definition, offer no resistance to being moved. And, since it offers no resistance, it would deliver no impulse to the body that moved it, effecting no change in the state of rest or motion of that other body. Matter like this would be useless, undetectable, ignorable.

19. Sep 9, 2011

### Ken G

If we imagine a sequence of objects with less and less inertia, it would be odd to expect something different to happen to a zero-inertia object than happens in the limit as the inertia goes to zero. Therefore, if Newton's first law applies throughout that sequence, as is the claim in that law, then it would also apply to a zero-inertia object. Ergo, the first law does not refer to inertia in any way. In other words, a law that does not care what the inertia is, does not refer to inertia.

20. Sep 9, 2011

### johann1301

Someone finally sees my point!