The force of inertia is the property common to all bodies that remain in their state, either at rest or in motion, unless some external cause is introduced to make them alter this state.
That is the definition by Jean d'Alembert in the Encyclopedia (1757) he explains (this is lost in the bad translation from French) that he used 'property' and not 'power' because he believes that this word evokes a metaphysical being resident in the body. (sic: sort of poltergeist). And this is the original wording by Newton: (1726), in definition III
*Materiae vis insita [internal/resident/lit: implanted force] est potentia resistendi, qua corpus unumquodque, quantum in se est, perseverat in statu suo vel quiescendi vel movendi uniformiter in directum.*
The introduction in italics [the internal force of matter is the power to resist..] is prodromic to the first law (see below), but what is interesting is the explanation thereof given:
Haec semper proportionalis est suo corpori, neque differt quicquam ab inertia massae, nisi in modo concipiendi. Per inertiam materiae fit, ut corpus omne de statu suo vel quiescendi vel movendi difficulter deturbetur. Unde etiam vis insita nomine significantissimo vis inertiae dici possit.
This [internal force] is always proportional to its body and is not different in any way from the inertia of its mass but for [our] way of conceiving it. It is because of the inertia of matter that it is more difficult to alter the state of a body of being at rest or in motion. Therefore this internal force may also by called by the most significant name of force of inertia.
Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
Law I: Every body persists in its state of being at rest or of moving uniformly in a straight line unless it is compelled to change its state by forces impressed.
[motive] force impressed vi motrici impressae is also the denomination of the esternal force that produces [kinetic] energy in the second law.
As you can see from the original texts (by Newton and d'Alembert), there is no difference whatsoever between 'inertia' [= sloth] and 'force of inertia' this latter denomination is a sort of 'promotion' to a higher status of conception: the 'laziness' of mass/matter is (proportional to) mass and is the 'power' that opposes change, it is an internal 'force': the 'force of laziness/ inactivity' of all matter. In the original post I quoted verbatim this latter definition from the Principia and pointed out the amusing oxymoron, this was taken as 'hostile' [sic], 'unclear' by hasty, superficial or poorly-informed readers andas 'nonsensical babble'[sic] by Olin Lathrop.
All the arguments to criticize this question, to condemn it as 'unclear', to close it, eventually delete it altogether and differ its reopening seem rather unjustified hair-splitting and (themselves really) incomprehensible.
I am striving to reopen it as a matter of principle, because a distinguished member (Rod Vance) has repeatedly stated in comments, alas deleted, that he has a very interesting answer. I also want an opportunity to learn what exactly is my 'nonsensical babble' and to learn how to make this question 'clear' and comprehensible, hoping the worthy members who inexplicably ostracized this question (and btw the downvoters) to explain what is wrong with this question:
- Is the concept of [force of] inertia still useful and used?
- Is it now just one of the fictitious forces or what?
- Can you list a few situations in which, if we didn't use this tool we might be in difficulty?
It is possible that the two terms have acquired, in use, different meanings of which I am not aware, some might (wrongly) assume that moment of inertia is a different 'concept' from 'force of inertia', or other:
Are you asking about inertia in general, or just the term force of inertia? Please edit the question and title accordingly. Using parenthesis (force of) inertia is ambivalent. – Qmechanic
Is this a semantic/linguistic question about the term force of inertia (as opposed to e.g. the terms fictitious force, pseudo force, or inertial force)? – Qmechanic
I suppose that after these authoritative comments a fourth additional question is necessary:
- What is the (physics) difference between: 'inertia', 'force of inertia' and 'inertial force'?
It would be of great interest for everybody, I suppose, to learn when and how the to terms diverged and if they have a different fate. I left the parenthesis because I am enquiring about both terms.
Answer
The question of mass has arguably been one of the two most important issues in physics (the other being the electromagnetism). Physics has tried to uncover the true nature of mass for hundreds of years, to no avail so far. Not surprisingly, its description is somewhat circular:
where „the body's resistance to being accelerated” is, obviously, inertia, which is „one of the primary manifestations of mass”, while gravity „is the only force acting on all particles with mass”.
To answer bobby's question: the most successful (the only?) theory that has done away with inertia is the General Theory of Relativity. Einstein aimed at extending the Relativity Theory to gravitation, and while working on this problem, he found inertia to be the major obstacle, for rather obvious reasons. The equations of SR could not be used for non-inertial frames of reference, and gravity is all about acceleration. In his letter to Born, Einstein said: "the gravitational equations would still be convincing, because they avoid the inertial system (the phantom which affects everything but which is not itself affected)." Einstein was able to claim this, because he made two truly amazing insights: being at rest on the surface of Earth is equivalent to being in an elevator accelerating up, and also - perhaps more importantly in the context of inertia itself - when freefalling toward the source of gravitation, one feels no acceleration at all. As Einstein was looking for the equations for motion, and the movement under gravity turned out to show no proper acceleration (the acceleration is only coordinate), he was allowed to assign an inertial frame of reference to this movement. Consequently, gravity was called a fictitious force. Problem solved.
Well, was it? Aside from the fact that acceleration is still measurable on the surface of the source of gravity, there is also another question left. Apparently, Einstein missed one thing: the geometrical space-time curvature concept, which replaced the force of gravity in GR, quite well explains the movement along geodesics, but does not explain the very impulse to motion in this field. The curvature by itself cannot make things move. If there is no force “underneath” the curvature, there is no reason the body should move at all. The usual counter-argument at this moment is that this is not a problem in GR, because under the concept of space-time and velocity 4-vector, each body is always in motion along the time axis. Assuming time is really orthogonal to space, Newton's first law of motion still says that one needs a force not only to set a body in motion, but also to change the direction of its motion. A body that moves along the $t$ axis requires a force to change the direction of its motion toward any of the space axes. And this change without a force is unexplained. This omission is a really serious one, since the ability to make things move is by far the most important aspect of mass and gravity.
Now, all these considerations make the concept of force of gravity – or to be precise, acceleration – is still valid. This means that the force of inertia is also still in play. OK, so what is inertia then?
Yeah, we all know it. What we do not know, however, is how this "resistance to any change in motion" is produced.
Let's follow a simple line of logic then. What is a change in motion? Acceleration obviously. So inertia resists any acceleration. Now, what does it take to resist acceleration? Another acceleration. Would that suggest that inertia is acceleration itself? Well, each massive body generates gravitational field, and gravitation is acceleration. All seems to fit in.
How would that work in practice? If one is trying to move a material body, one must work against the body's own acceleration pointing outwards. It is a fact as long as Einstein's equivalence principle holds true. The more massive the body, the bigger the acceleration it produces, and the more external force it takes to work against this acceleration.
Seems very simple, although not intuitive. But hey! If there is a single most often repeated statement in contemporary physics, it would be probably this one: “Intuition is not the final argument in science; science is about models, equations and predictions”. True. Inertial mass has been proven to be equal to gravitational mass, and therefore the force required to move inertial mass must exceed its force of gravity at the surface.
To sum up, addressing the original questions by bobby:
1) What is the (physics) difference between: 'inertia', 'force of inertia' and 'inertial force'?
There is none. All these terms express the same property of mass - its innate resistance to external force (acceleration). What makes inertia special is that it resists acceleration (force), and it takes another acceleration (force) to do that.
Also, following the line of reasoning above, which is confirmed by the famous Eötvös experiment, we can say that there is yet another synonym to inertia - gravitation. And following the Ockham's razor principle, it would only be logical to assume twin properties - inertia and gravity - to be simply one and the same thing.
2) Is it now just one of the fictitious forces or what?
If understood correctly, no. Inertia is the fundamental reason why it requires a real force to change the motion of a body. It's real, because mass, and nothing else, really resists a change to its motion. Also, inertia, being a synonym of gravity, is - as shown by Einstein - a real acceleration when measured at the surface of the body (source).
3) Is the concept of [force of] inertia still useful and used?
4) Can you list a few situations in which, if we didn't use this tool we might be in difficulty?
I take these two questions as provocative, or intending to explicitly demonstrate that dismissing (force of) inertia is not so wise an idea, to say the least ...
Whenever there is mass influencing the mechanics and equations of motion, there is always the concept of inertia involved. Because mass could (and should) be understood just as another synonym for inertia.
As to the situations where inertia - and therefore mass - cannot be neglected as a concept. There were some examples given in the comments (by Jim) to the question. There is a plenitude of examples: road traffic (car safety belts, bumpers, road railings, safety helmets), planes, lifts/elevators, or even building designs. So, in all situations, where mass (understood as acceleration out and therefore exerting real force on other objects it is in contact with) affects the equations and reality they describe, inertia is included by definition, and therefore dismissing it would get us into trouble. Even relativity that is believed to do just fine without (force of) inertia does provide equation for relativistic mass. Why? Because inertia is a fundamental factor when dealing with motion, and even particle physics must accept that.
Winding it all up - unless we manage to get rid of the concept of mass, we also cannot get rid of its synonym, inertia (or another synonym, gravity) - as simple as that.
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