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Test your knowledge of inertial forces

  1. Sep 18, 2011 #1
    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
    Last edited: Sep 18, 2011
  2. jcsd
  3. Sep 18, 2011 #2

    Ken G

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    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).

    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.
  4. Sep 18, 2011 #3


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    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".
  5. Sep 18, 2011 #4


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    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.
  6. Sep 18, 2011 #5
    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?
  7. Sep 18, 2011 #6

    Ken G

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    We both know what inertial forces mean, yes. I can't vouch for your potentially mistaken understanding of some professor.
    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.
    Last edited: Sep 18, 2011
  8. Sep 19, 2011 #7
    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.

    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
  9. Sep 19, 2011 #8


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    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.

    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.
  10. Sep 19, 2011 #9
    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'.
  11. Sep 19, 2011 #10

    Ken G

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    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.
    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.
    Yes, and note that everything you just said is a force on the mass, not 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.
    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.
  12. Sep 19, 2011 #11
    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?)
  13. Sep 19, 2011 #12
    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.
  14. Sep 19, 2011 #13
    Are you seriously suggesting that force is the same as stress?
  15. Sep 19, 2011 #14

    Ken G

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    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?
    None of the forces on the bar are inertial. No massless object ever has any inertial forces on it.
    As long as you refer to any inertial forces on the bar, you have not made that separation.
  16. Sep 19, 2011 #15

    Ken G

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    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.
  17. Sep 19, 2011 #16
    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.
  18. Sep 19, 2011 #17
    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.

    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)
  19. Sep 19, 2011 #18
    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?
  20. Sep 20, 2011 #19


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    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.
  21. Sep 20, 2011 #20
    Introducing electromagnetic and rotational systems only serves to confuse the issue further.

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

    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?
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