Test your knowledge of inertial forces

[Studiot]

We have had several threads lately discussing the nature of inertia and inertial forces.

Here is a practical exanmple for open discussion.

Take a flexible bar and closely thread several masses onto it.

Clamp both ends.

Arrange a disturbance to provide a flexing of the bar.
This will establish transverse vibrations of the system.

Now in flexing, the bar exerts a force on the masses accelerating them.
In turn the masses exerts an inertial force reaction on the bar.

Does gravity make any difference to this system, ie would the performance be the same in weightless conditions?

go well

 

[Ken G]

Now in flexing, the bar exerts a force on the masses accelerating them.
In turn the masses exerts an inertial force reaction on the bar.

I'd say we have a problem in the concept of inertial forces right here. The action/reaction pair force that the masses exert on the bar has nothing to do with inertia, it is simply the way forces come in action/reaction pairs. Inertial forces are generally taken to mean forces that pair with the forces on the masses, but they are also forces on the masses. They appear only if we adopt the mentality that all forces on the masses must balance, they are exerted on the masses not on the bars. There are no inertial forces on the bar, the bar obeys a different constraint that it must set up real forces on its surroundings such that the action/reaction pair forces on the bar add up to zero (since the bar has no mass).

Does gravity make any difference to this system, ie would the performance be the same in weightless conditions?

Gravity makes a difference, but not to the small-amplitude oscillations, only to the equilibrium configuration. Perhaps you are interested in the equivalence principle, such that gravity could be replaced by an external force that accelerates the bar and masses together. That will shift the equilibrium configuration, but not the normal modes.

 

[A.T.]

In turn the masses exerts an inertial force reaction on the bar.

I don't like the name "inertial forces" here at all. These are interaction forces. They obey Newtons 3rd Law, and are exerted by some object(masses) on some other object(bar), via an interaction. They are also known as "real forces"

The term "inertial forces" usually refers to forces that appear in non-inertial reference frames. Those inertial forces do not obey Newtons 3rd Law. They act directly on every mass, regardless any interactions with other objects. They are also known as "pseudo forces" or "fictitious forces".

 

[AlephZero]

I agree. There is no reason to call these forces "inertia forces" except to create confusion, IMO.

The term "inertia forces" does have a use if you are describing the motion of a system in a non-inertial reference frame (though personally I prefer to call them "d'Alembert forces"), but trying to model the structure described in the OP that way doesn't make much practical sense.

 

[Studiot]

So you guys would differ with the late Professor of Mechanical Engineering at MIT and author of many famous textbooks?

Since I specified the initial disturbance was to the bar, not the masses, what is the source of the reaction of the masses on the bar if not their inertia?

 

[Ken G]

So you guys would differ with the late Professor of Mechanical Engineering at MIT and author of many famous textbooks?

We both know what inertial forces mean, yes. I can't vouch for your potentially mistaken understanding of some professor.

Since I specified the initial disturbance was to the bar, not the masses, what is the source of the reaction of the masses on the bar if not their inertia?

Forces from the bar come from internal stresses in the bar, not from anything that has anything to do with the masses. That's why you could tell those forces from a photograph of the bar, and knowledge of the bar, without knowing squat about the masses. I'm sure the "late professor" knew that also.

ETA: The point is, inertial forces involving the masses are forces on the masses (in the mindset where all such forces must balance, that's the general philosophy of inertial forces), not forces on the bars, which are simple action/reaction pair forces as we both said above. All forces on the bars are real forces that relate directly to the configuration of the bar. Depending on the back story of the problem, there may certainly be situations where the inertial forces on the masses happen to be quantitatively equal to the real forces on the bar, and there may certainly be situations where they are not so equal. It depends on context, so there is no intrinsic or direct connection between inertial forces on masses and the stresses on the bar, but they will happen to be equal when the only forces on the masses (not counting inertial forces as forces) come from the bar. As this is the case here, this happens to be the situation where one can use the terms inaccurately, without making a quantitative error. Still, the word usage is inaccurate all the same, and since the whole thread is about inertial forces, getting the usage correct would seem to be important in general terms.

 

[Studiot]

Ken, with the greatest respect.

1) I didn't misunderstand the late Professor. I read something in one of his books and reproduced it here for discussion, not ridicule.

2) You didn't read or misunderstood what I wrote. I have not described the action between the bar and the masses as inertial.

Forces from the bar come from internal stresses in the bar, not from anything that has anything to do with the masses.

3) If one of the masses was quietly existing somewhere, continuing its state of motion as per the first law, and was acting upon by some force, I understand that the 'resistance to change of its motion' is called inertia. I understand the Professor to have meant this when he wrote his piece. He (correctly in my view) stated that this resistance is manifest in the reaction of the mass upon the bar.

4) This statement has undergone nearly a century of peer review through several editions and translations into many languages. I would certainly trust it over some respondents of PF in 2011 who can't even read it properly and seem to prefer to reduce any serious discussion to ridicule.

go well

 

[A.T.]

I have not described the action between the bar and the masses as inertial.

But you have described the reaction forces of the masses on the bar as "inertial". That is inconsistent with the currently common definition of "inertial force", where inertial forces are not part of action/reaction force pairs.

This statement has undergone nearly a century of ...

Maybe it's outdated terminology. Maybe he was a bit sloppy. No big deal, since you can guess what he means. But if you make a thread specifically about "inertial forces" and give this as an example, people will point it out.

 

[Studiot]

But you have described the reaction forces of the masses on the bar as "inertial".

Yes indeed.

But you are carefully avoiding the question posed originally and again more generally in (3) of my last post by redefining something as 'outdated'.

 

[Ken G]

1) I didn't misunderstand the late Professor. I read something in one of his books and reproduced it here for discussion, not ridicule.

The usage of "inertial force" is incorrect, that's just a statement not a ridicule. However, in the context you described, it just happens that the numerical value of the inertial force is the same as the numerical value of the stress on the bar. That doesn't mean the stress on the bar is of the "inertial" kind, it just means we can equate two forces in this situation, which happens all the time in physics (if I push on a block on sandpaper, and I can't move it, am I exerting a frictional force on the block?). Stress on a massless bar is not an inertial force.

2) You didn't read or misunderstood what I wrote. I have not described the action between the bar and the masses as inertial.

You characterized the forces on the bar as "inertial", in a thread based on understanding inertial forces. There are no inertial forces on the bar, the bar is massless. All inertial forces in this scenario are forces on the masses.

3) If one of the masses was quietly existing somewhere, continuing its state of motion as per the first law, and was acting upon by some force, I understand that the 'resistance to change of its motion' is called inertia. I understand the Professor to have meant this when he wrote his piece.

Yes, and note that everything you just said is a force on the mass, not the bar.

He (correctly in my view) stated that this resistance is manifest in the reaction of the mass upon the bar.

The forces are numerically equal, that is correct, but that does not make it an inertial force. Massless objects do not experience inertial forces, but they can have forces of other types exerted on them, which because of the backstory of the problem might numerically equal something that actually is well characterized as an inertial force. That depends on the backstory, and might normally not be a distinction worth making-- except in a thread specifically targeted at understanding what inertial forces are.

4) This statement has undergone nearly a century of peer review through several editions and translations into many languages. I would certainly trust it over some respondents of PF in 2011 who can't even read it properly and seem to prefer to reduce any serious discussion to ridicule.

And the statement was not the problem, it was your interpretation of its meaning, in regard to what inertial forces are. If you want to start a thread about inertial forces, I think it is natural for you to expect to be required to use the term correctly, and correcting your usage is hardly "ridicule." I agree with A.T. on this, if you think you are still asking a pertinent question you should probably try to clarify better just what problem you are posing.

 

[nonequilibrium]

I don't seem to get what the problem is, can somebody clarify shortly? (besides the semantics issue of what is meant by "inertial forces"; for the good of the thread it might be helpful to define and adopt a different name for whatever kind of force is meant?)

 

[Studiot]

Take a flexible bar and closely thread several masses onto it.

Clamp both ends.

Arrange a disturbance to provide a flexing of the bar.
This will establish transverse vibrations of the system.

Now in flexing, the bar exerts a force on the masses accelerating them.
In turn the masses exerts an inertial force reaction on the bar.

Now where exactly did I state that the disturbing forces are inertial or that the vibrational forces are inertial or that the force exerted by the bar on the masses is inertial?

So where exactly did I say that all the forces on the bar are inertial?

So by what chain of logic do you deduce that because I stated, and later agreed that I stated, that some of the forces on the bar are inertial that I am proposing that all the forces are inertial or at least, some which I have not claimed to be inertial, are in fact inertial?

I thought I had carefully separated inertial from non inertial forces.

 

[Studiot]

However, in the context you described, it just happens that the numerical value of the inertial force is the same as the numerical value of the stress on the bar. That doesn't mean the stress on the bar is of the "inertial" kind

Are you seriously suggesting that force is the same as stress?

 

[Ken G]

Now where exactly did I state that the disturbing forces are inertial or that the vibrational forces are inertial or that the force exerted by the bar on the masses is inertial?

Look at the line that both A.T. and I cited in our answers. To repeat:"In turn the masses exerts an inertial force reaction on the bar." If you are going to make this thread be about understanding inertial forces, the first thing you have to recognize is that there are no inertial forces, reaction or any other kind, exerted on the bar. It doesn't matter to us what you call the force exerted on the bar, what matters is that you seem to want this thread to be about inertial forces. There will never by any inertial forces exerted on that bar, no matter what the scenario, if the bar is massless, as it is here. So just exactly what question are you asking anyway, and why do you think it has something to do with inertial forces on the bar?

So where exactly did I say that all the forces on the bar are inertial?

None of the forces on the bar are inertial. No massless object ever has any inertial forces on it.

I thought I had carefully separated inertial from non inertial forces.

As long as you refer to any inertial forces on the bar, you have not made that separation.

 

[Ken G]

Are you seriously suggesting that force is the same as stress?

Stress is the force per unit area that the bar is subjected to. This would be simplest in the situation where we are interested in longitudinal oscillations of the masses, in which case the stress on each bar that separates masses is the tension in the bar divided by its cross sectional area. The transverse situation you described is a more general form of stress, more difficult but essentially similar. What actually matters is that the action/reaction pair to the stresses on the bar (the area of contact to the masses is staying constant, so we don't care about forces per unit area) is the force on the mass, which is what we would be analyzing. So yes, I am seriously suggesting that force on the mass is, in this context, the same as stress on the bar. The distinction to make is the inertial force on the mass, and the inertial force on the bar. The inertial force on the mass will balance whatever real forces are exterted on the mass by the bars. The inertial forces on the bars are all zero.

I don't really think you mean to reference forces on the bars at all, it's a complete red herring. I suspect that your question, when properly posed, will be entirely about forces on the masses, be they real forces from the bars, or gravity, or inertial forces on the masses. You only need the bars to tell you what forces the bars exert on the masses-- you never needed, or wanted, to refer to any forces on the bars, except to say that they are exerted at the ends and add to zero.

 

[Studiot]

I don't know whether to laugh or cry.

Ken this is not the first time in this thread I will have suggested you read more carefully what someone else has written, particularly since you seem unable to restrain the insults.

 

[Studiot]

I don't seem to get what the problem is, can somebody clarify shortly? (besides the semantics issue of what is meant by "inertial forces"; for the good of the thread it might be helpful to define and adopt a different name for whatever kind of force is meant?)

Good evening Mr Vodka, thank you for your interest.

This thread was not about resolution of a problem, it was meant to promote discussion about inertia as stated right at the beginning.

We have had several threads lately discussing the nature of inertia and inertial forces.

Here is a practical exanmple for open discussion.

I was trying to use a simple example to achieve this.

Here are some simple definitions taken from a text used to teach apprentices to Ordinary National Certificate or Diploma level under the auspices of the Technician Education Council.

Newton's third law states that to every action there is always an equal and opposite reaction.
A force applied to a mass with the purpose of accelerating it is referred to as the accelerating force.
Immediately this force is applied, an equal and opposite internal force, known as the inertial force, is produced in the mass and this force makes the mass resist any change of motion. The ultimate movement of the mass may be affected by frictional forces, which like the accelerating force acts external to the mass. Other external forces acting on the mass might be the gravitational force and the normal reaction by the support. Such external forces are called impressed forces.

Now to apply these definitions to my example. Let us remove gravity and friction for simplicity.

The bar and masses are existing quietly continuing in their state of motion or rest (first law)
In particular there are no forces acting between the bar and the masses.

The bar is then flexed by an external agent. The bar experiences elastic internal forces.

This causes the bar to move and thus exert an accelerating force on the masses (second law)

In plain English the bar presses against the masses.

In accordance with the definition above this in turn gives rise to an inertial force whereby the masses press back against the bar

That is they resist the change (third law)

 

[nonequilibrium]

Hello, thanks for trying to explain.

In one way I get everything you say, but on the other hand I still don't seem to understand the point: we're just giving specific names to forces? Or is the issue of a more physical nature? Is the matter perhaps whether these names can be given consistently?

And why would you call what you call an inertial force to be an internal force? It is my understanding that the action and reaction forces are the same kind of force, e.g. if something is pulled by an electric foce, then the reaction/inertial force is also electric; my point in this is that if you view the bar-to-mass force as external, then shouldn't you also view the mass-to-bar force, which you call the inertial force, also as external?

 

[A.T.]

It is my understanding that the action and reaction forces are the same kind of force, e.g. if something is pulled by an electric force, then the reaction/inertial force is also electric;

Exactly. And "inertial forces" are never part of 3rd Law force interaction pairs. "Inertial forces" are never exerted by one object on some other object. "Inertial forces" also appear only in non-inertial frames.

Replace space station with bar, and astronauts with masses here:

The space station is accelerating the astronauts, by exerting an electromagnetic interaction force on them (Fcp), and the 3rd Law reaction to this is an electromagnetic interaction force exerted by the astronauts on the station (Frcf). None of these two forces is an inertial force.

The inertial force (Ficf) appears only in the non-inertial rotating frame and acts on the astronaut directly, regardless of any interaction.

 

[Studiot]

Introducing electromagnetic and rotational systems only serves to confuse the issue further.

AT, you are still avoiding the issue now asked thrice of you.

But you have described the reaction forces of the masses on the bar as "inertial".

Yes indeed.

But you are carefully avoiding the question posed originally and again more generally in (3) of my last post by redefining something as 'outdated'.

I started from the premise that there is considerable confusion around about inertia, witness for instance the other threads here at PF on the subject.

I have certainly achievd my objective of stimulating discussion, it is just a pity that it is so ill natured especially as there seems to be more than one school of thought about the matter.

If academics cannot agree on a common format, what chance do students have and is it suprising that they end up confused?

 

[Doc Al]

Newton's third law states that to every action there is always an equal and opposite reaction.

OK. (The terminology of 'action' and 'reaction' is a bit old-fashioned.)

A force applied to a mass with the purpose of accelerating it is referred to as the accelerating force.

An odd term, but OK. Let's call the mass of interest mass A. Note that the force on mass A must be exerted by some other mass or object, which we can call mass B.

Immediately this force is applied, an equal and opposite internal force, known as the inertial force, is produced in the mass and this force makes the mass resist any change of motion.

Sure, if you switch to analyzing things from the non-inertial frame of the accelerating mass there will be an inertial force due to that change of reference frames. It's not a 'real' force and it's certainly not the 'reaction force' to the force on mass A. The Newton's 3rd law reaction to the force on A is a force on B.

 

[Studiot]

I'm sorry Doc Al, where did the change of reference frames come in, I certainly didn't open that door?

 

[Doc Al]

I'm sorry Doc Al, where did the change of reference frames come in, I certainly didn't open that door?

That's the only way you're going to get a second 'force' acting on mass A. (And that's the physics meaning of 'inertial forces'.)

If you stick to an inertial frame, then all you have is the 'accelerating force' on mass A. No other forces involved. (There will, of course, be the 'reaction force' on mass B, but that's a force on B not A.)

 

[A.T.]

I'm sorry Doc Al, where did the change of reference frames come in, I certainly didn't open that door?

Talking about inertial forces implies that you use a non-inertial reference frame.

AT, you are still avoiding the issue now asked thrice of you.

You mean the question if gravity affects the behavior of the system? If the ends of the bar are clamped and held against gravity, then yes. The equilibrium position around which the masses are oscillating would be different.

 

[Studiot]

If you stick to an inertial frame, then all you have is the 'accelerating force' on mass A. No other forces involved. (There will, of course, be the 'reaction force' on mass B, but that's a force on B not A.)

If A is the bar and B is one of the masses that is exactly what I said originally and subsequently.

As regards the frame, the example is essential one dimensional, at most two. I have 'assumed' a natural cartesian frame with one axis (say x) the unflexed axis of the bar and the second (say y) perpendicular to it. Since all the important action takes place in the y-axis we really only need consider this. I see no reason to introduce frames moving with the masses, nor did I ever expect anyone else to do so. Perhaps that was folly.

You mean the question if gravity affects the behavior of the system?

No I mean this one

But you are carefully avoiding the question posed originally and again more generally in (3) of my last post by redefining something as 'outdated'.

and

what is the source of the reaction of the masses on the bar if not their inertia?

 

[Dale]

Hi Studiot, my understanding agrees with Doc Al, A.T., and Ken G's understanding. Inertial forces are also known as fictitious forces. They are frame-variant and only arise in non-inertial reference frames, they are not part of any 3rd law interaction, and they are always proportional to the mass.

http://en.wikipedia.org/wiki/Fictitious_force
http://paul-a-heckert.suite101.com/understanding-physics-of-inertial-forces-a129313
http://www.thefreedictionary.com/inertial+force
http://www-istp.gsfc.nasa.gov/stargaze/Sframes2.htm

I have never heard a 3rd law pair described as an inertial force until your comments in this thread. I think you have misunderstood the passage quoted, which I would interpret as did Doc Al.

 

[Doc Al]

If you stick to an inertial frame, then all you have is the 'accelerating force' on mass A. No other forces involved. (There will, of course, be the 'reaction force' on mass B, but that's a force on B not A.)

If A is the bar and B is one of the masses that is exactly what I said originally and subsequently.

If so, then how do you explain this statement of yours:

Newton's third law states that to every action there is always an equal and opposite reaction.
A force applied to a mass with the purpose of accelerating it is referred to as the accelerating force.
Immediately this force is applied, an equal and opposite internal force, known as the inertial force, is produced in the mass and this force makes the mass resist any change of motion.

That sure sounds like the two 'forces' being discussed act on the same mass, and thus cannot be Newton's third law pairs.

 

[A.T.]

what is the source of the reaction of the masses on the bar if not their inertia?

The "sources" of interaction forces, are the interacting objects:
-The masses are the source of the forces on the bar.
-The bar is the source of the forces on the masses.

 

[Studiot]

AT

The "sources" of interaction forces, are the interacting objects:
-The masses are the source of the forces on the bar.
-The bar is the source of the forces on the masses.

So at least we are agreed on something. Progress.

But where does the reacting object (the mass) suddenly get the ability to exert a force?

The the acting object (bar) has the internal elastic forces to draw upon to exert the initial action.

I maintain that, although it is not always explicitly stated, the reacting object gains this ability from its inertia. An object with no inertia cannot participate in the third law.

To see what I mean look at the following extracts fro two different continents at two different levels.

The first is the original inspiration from Professor Den Hartog. I have ringed the paragraph where he clearly and explicitly states that the third law reaction is a result of inertia. However he does not elaborate as to how this might arise as he has other fish to fry.

Doc Al

If so, then how do you explain this statement of yours:

To see how this might arise the second extract is from Walker.
This makes the statement Doc Al thinks is in conflict with Den Hartog but to see that it is not, look at the diagram first.

No mention of how the horizontal "applied force" is made so let us suppose it is applied by a push rod and let us again suspend friction for simplicity.

Walker states that the inertial force is an internal force.
Quite so.
Just as the internal elastic forces in the bar generate the external action on the mass so the internal 'inertial force' generates the reaction of the block on the push rod.

Just as with free body diagrams it is important to take care noting which body which force acts on. Sometimes we take short cuts and forget the full chain.

go well

 

[Ken G]

Perhaps a concrete example could help Studiot see the problems with his terminology. Imagine we see a spring that stretches between a wall and a rocket. The rocket engine is on, but because of the stretched spring, the rocket is stationary. Ignore gravity. What are all the forces on the spring and the rocket, and what are their sources? I hope you will agree the answer is:
spring: tension at both ends, one from contact with wall, one from contact with rocket. These are equal and opposite (though not an action/reaction pair because they act on the same object and don't have to be the same type of force).
rocket: force from engine, force from spring. These are also equal and opposite (though not an action/reaction pair for the same reasons.)

OK, can we agree that exhausts all the forces in the rocket+spring system? In particular, please note there are no "inertial forces" anywhere. Of course, if the spring is massless, there will never be an inertial force on it, as I said above, because inertial forces are always proportional to mass. But of particular note here is that there aren't even any inertial forces on the rocket either, because the rocket is not accelerating.

Now imagine the instant that we shut off the rocket engine. All the above forces stay exactly the same, except that the force of the rocket engine is replaced by an "inertial force" of the same strength, which you can take to either mean a fictitious force in the accelerating frame of the rocket (as most people would mean), or you can just use "inertial force" as a placeholder for mass times acceleration (as was done by d'Alembert, which is just a kind of language that allows us to picture dynamics problems as statics problems). Either way you take the semantics, here is the key question for you:

What are the forces on the spring the instant after the rocket engine is shut off, and in particular, do any of their strengths, sources, or nature, change in the slightest way?

Given your answer to that (which hopefully is "no"), then ask: so where is this "inertial force reaction" on the spring that you were talking about in the OP?

 

[Studiot]

Good afternoon, Ken.

First I agree with all you say, up to the quote below.

What are the forces on the spring the instant after the rocket engine is shut off, and in particular, do any of their strengths, sources, or nature, change in the slightest way?

Now you have actually described the forces the instant the engine cuts using D'Alembert's Principle, which also appears in the second extract of my previous post.

I don't quite understand what you mean by the question however.

Change?

Change from what? Before and after the cut?,
You have already stated there was no inertial force before the cut, but there is after so there is a change there.

Clearly the effort from the rocket motor changes.

Or do you mean subsequent to the cut?

 

[Doc Al]

The first is the original inspiration from Professor Den Hartog. I have ringed the paragraph where he clearly and explicitly states that the third law reaction is a result of inertia. However he does not elaborate as to how this might arise as he has other fish to fry.

I'd say that despite the non-standard terminology, that first extract is clearly talking about 'reaction' forces. These are 'real' forces due to the interaction of two different bodies.

To see how this might arise the second extract is from Walker.
This makes the statement Doc Al thinks is in conflict with Den Hartog but to see that it is not, look at the diagram first.

That second extract, despite its failure to make explicit the fact that it is using a non-inertial frame of reference, seems clearly to be talking about inertial forces. Note that the applied force and the inertial force both act on the mass in question. (Not so in the first extract.)

Apples and oranges, I'm afraid.

 

[Studiot]

Apples and oranges, I'm afraid.

Respectfully you are again making my point for me.

Do you agree that a reactive force is applied to whatever pushes the block rightwards?

 

[Doc Al]

Respectfully you are again making my point for me.

And what point might that be?

Do you agree that a reactive force is applied to whatever pushes the block rightwards?

Of course. But that force is not an inertial force, at least as the term is used in standard physics.

 

[Studiot]

And what point might that be?

Just as the internal elastic forces in the bar generate the external action on the mass so the internal 'inertial force' generates the reaction of the block on the push rod.

But that force is not an inertial force, at least as the term is used in standard physics.

So where did it come from? and What do you call it?

Prof DH explicitly called it the "inertia reaction"

I was trying to show how this might arise and I think he is correct although I also think he left out a step or two.

I would be really helpful if folks would stop trying to 'prove me wrong' and just work through the logic with me - I am perfectly happy to say you are correct if it turns out that way, but so far it has not.