Is there a common misunderstanding of inertia?

[Ken G]

I have no idea what you're saying or where you're going with this.

The issue in the OP is, does Newton's first law reference the concept of inertia, or indeed even require such a concept, or does that only show up in the second law? The OPer was making the case, and I agree, that the first law does not reference inertia, which means there is a "common misconception" that inertia is the reason that objects that are in motion will stay in motion if no forces act on them. Instead, when an object has no force on it, then its inertia is irrelevant, since we can simply refer to the first law (even though the second law yields the same conclusion as the first-- that just means the laws are consistent). Inertia is the concept of how much objects accelerate when forces are exerted on them. The first law is merely the assertion of what happens when no forces are exerted, and that is true independently of the inertia or even if there is any inertia. To support that argument, I cite the first law.

The "law or axiom" is asserted as truth in the interest of getting traction on a problem. It provides a basis for a train of logic in analyzing something.

Yes, I use it in that same sense-- note especially the part about "in the interest of..."

The Laws or Axioms are not, therefore, "just" assertions.

I see the problem, you are reading something unintended into the word "just." I do not mean that any law is somehow equal, since they are all "just" assertions, I mean that a law is just an assertion. Which is just exactly what a law is-- the point is, if the law doesn't refer to inertia, then the assertion the law is making doesn't either, and it makes not the least bit of difference if the law doesn't apply in some situation (such as in quantum mechanics, or when there is no inertia-- even though this law does apply when there is no inertia, as long as we generalize "force" to "any influence or change in the environment"). I used "just" to stress that the law is what it is, so what it asserts is independent of when it holds, and so in analyzing what a law says, there is no need to wonder about when the law is actually true, or if the law is ever actually true. Note this is consistent with the definition you just gave.

 

[Drakkith]

From my understanding a scientific law is true whenever the conditions are the same as when the law was first observed to be true. However a law doesn't explain the underlying reasons on how it works or why, it simply states something that is true given the right conditions. Newtons laws don't care what makes them work, only that they do work. My opinion on this is that inertia is NOT the underlying reason why the laws work, but is a phenomona that we observe in objects that have mass.

 

[zoobyshoe]

The issue in the OP is, does Newton's first law reference the concept of inertia, or indeed even require such a concept, or does that only show up in the second law? The OPer was making the case, and I agree, that the first law does not reference inertia, which means there is a "common misconception" that inertia is the reason that objects that are in motion will stay in motion if no forces act on them. Instead, when an object has no force on it, then its inertia is irrelevant, since we can simply refer to the first law (even though the second law yields the same conclusion as the first-- that just means the laws are consistent). Inertia is the concept of how much objects accelerate when forces are exerted on them. The first law is merely the assertion of what happens when no forces are exerted, and that is true independently of the inertia or even if there is any inertia. To support that argument, I cite the first law.

Here is Newton I as he wrote it:

"LAW I.

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

"Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time."

http://www.archive.org/stream/Newtonspmathema00newtrich#page/n87/mode/2up

Here is his definition of inertia, as I quoted earlier:

"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."

Inertia is the concept of how much objects accelerate when forces are exerted on them.

Doesn't seem to be the case. Newton's definition simply asserts it's dual properties of resistance and impulse without quantifying them. (If inertia is "about" something I'd say it's about mass, not acceleration.)

Does the first Law "reference" those dual properties? I would say it does, but it depends on what you mean by "reference".

 

[Ken G]

Newton's definition of inertia is not completely clear, because much lies in the words "power of resisting." That might be taken to refer to a quantity, as it does in the modern meaning of the term. Now inertia is taken as a quantitative attribute, proportional to mass for an object in its rest frame. That is also the same thing as (the inverse of) its acceleration when subjected to unit force. So I would say Newton's first law does not reference the modern quantifiable concept of inertia. When zero force is exerted, no object accelerates, regardless of its inertia (in the modern sense), and that is the first law.

 

[zoobyshoe]

Newton's definition of inertia is not completely clear, because much lies in the words "power of resisting." That might be taken to refer to a quantity, as it does in the modern meaning of the term. Now inertia is taken as a quantitative attribute, proportional to mass for an object in its rest frame. That is also the same thing as (the inverse of) its acceleration when subjected to unit force. So I would say Newton's first law does not reference the modern quantifiable concept of inertia. When zero force is exerted, no object accelerates, regardless of its inertia (in the modern sense), and that is the first law.

Newton's Inertia is quantified by him to the extent he observes, "This force is ever proportional to the body whose force it is". What does that mean? Earlier, in the definitions, he makes it clear the word "body" will be used synonymously with "mass". In plain modern English, therefore, he's saying "inertia is directly proportional to mass", so that's no modern concept, but he says that without providing any units, hence, no way to plug it into an equation, which is what I meant when I said he didn't quantify it. (It's amazing to me how far he gets without ever offering any units of measure.)

That's neither here nor there, because the definition of inertia you offered: "Inertia is the concept of how much objects accelerate when forces are exerted on them," is still far from his. I have to say I think acceleration is the concept of how much objects accelerate when forces are exerted on them. In answer to the question: "How much do masses accelerate when forces are exerted on them?," you wouldn't simply present the measured inertia (mass) of the object as the answer. "How much acceleration, given this mass and this force?," is asking you to solve for acceleration: a =F/m.

The First Law and it's little expansion/discussion included underneath, describe objects whose observed motion is the result of resisting acceleration. It does not only mention objects on which no force is acting ("Every body perseveres in its state of rest, or of uniform motion in a right line,...") but also those resisting acceleration ("...unless it is compelled to change that state by forces impressed thereon."): "Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity." Since Inertia is a force that exerts itself to resist acceleration, I would characterize the First Law as one that "references" inertia, to be sure.

Earlier, in the first "scholium" Newton makes the point that he must define and explain certain things to dispel "vulgar" misconceptions. As 256bits pointed out earlier in this thread, one of the things he had to quash was the then common notion that it takes a continuous force to keep an object in motion (from Aristotle, I believe). That would be the reason the law might seem to emphasize the persistence of motion and rest in the absence of force as what's important, but it's abundantly clear from the definition he understands inertia to be a reactive force, and emphatically defines it as such. Newton wasn't confused.

 

[Ken G]

I have to say I think acceleration is the concept of how much objects accelerate when forces are exerted on them.

Acceleration is the rate of change of velocity. What you are talking about is not what acceleration is, but rather a dynamical principle about acceleration.

"How much acceleration, given this mass and this force?," is asking you to solve for acceleration: a =F/m.

I agree that the dynamical principle here is best thought of as a=F/m. But that's not the statement of what a is, it's the statement of how to calculate a. In other words, if I say "I am a physicist", that is not actually a statement of who I am, because "I" am a lot more than that, it is just attributing a property to "me." Similaly, a=F/m is attributing a property to a, that it will turn out to equal F/m, but the statement would mean nothing if we didn't already know what acceleration is. That's clear when you try to teach it to students who don't already know what acceleration is!

It does not only mention objects on which no force is acting ("Every body perseveres in its state of rest, or of uniform motion in a right line,...") but also those resisting acceleration ("...unless it is compelled to change that state by forces impressed thereon."): "Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity."

That all sounds like a rule about when forces are absent, not a rule about when forces are present.

Earlier, in the first "scholium" Newton makes the point that he must define and explain certain things to dispel "vulgar" misconceptions. As 256bits pointed out earlier in this thread, one of the things he had to quash was the then common notion that it takes a continuous force to keep an object in motion (from Aristotle, I believe). That would be the reason the law might seem to emphasize the persistence of motion and rest in the absence of force as what's important, but it's abundantly clear from the definition he understands inertia to be a reactive force, and emphatically defines it as such. Newton wasn't confused.

I certainly don't think Newton was confused, I think his first two laws had very specific objectives. The first law was to say what happens in the absence of forces, to dispell the Aristotelian notion that objects would come to rest in the absence of forces. The second law was to say what happens in the presence of forces, to be able to explain what it is that forces actually do (they create acceleration, subject to inertia). So the second law is the only one that refers to inertia, in the quantifiable way we use the word now, even though the first law is called the "principle of inertia." It's two very different meanings of the word-- if the "principle of inertia" is there to dispell the idea that objects come to rest in the absence of forces, then it is not actually necessary to know anything about the quantity we call inertia today.

 

[zoobyshoe]

Acceleration is the rate of change of velocity. What you are talking about is not what acceleration is, but rather a dynamical principle about acceleration.

I'll be happy to stipulate that the words "...is the concept of how much objects accelerate when forces are exerted on them," is a statement of a dynamical principle about acceleration, because it's still not a statement about inertia. (I wasn't trying to make any definitive statement about acceleration, of course, just pointing out your definition of inertia, which is where all those words come from, seemed, actually, to be about acceleration, if it was about anything.)

I agree that the dynamical principle here is best thought of as a=F/m. But that's not the statement of what a is, it's the statement of how to calculate a. In other words, if I say "I am a physicist", that is not actually a statement of who I am, because "I" am a lot more than that, it is just attributing a property to "me." Similaly, a=F/m is attributing a property to a, that it will turn out to equal F/m, but the statement would mean nothing if we didn't already know what acceleration is. That's clear when you try to teach it to students who don't already know what acceleration is!

This is an interesting read.

That all sounds like a rule about when forces are absent, not a rule about when forces are present.

OK: Since last posting, I went back and reread his definition of force, and found something interesting I missed the first time:

"Definition IV

An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of moving uniformly forward in a right line.
This force consists in the action only; and remains no longer in the body, when the action is over. For a body maintains every new state it acquires, by its vis inertiae only. Impressed forces are of different origins, as from percussion, from pressure, from centripetal force."

http://www.archive.org/stream/Newtonspmathema00newtrich#page/n79/mode/2up

Here we see that Newton ascribes to inertia the behavior of objects when no outside forces are acting on them: "For a body maintains every new state it acquires, by its vis inertiae only." He has directly stated that inertia (the force of inactivity) is what causes them to remain at rest or in motion, between accelerations.

Summing up it's 3 powers, inertia is responsible for resistance to acceleration, for the equal and opposite reaction of Newton III ("impulse"), AND for the fact objects do nothing in the absence of an outside force.

That last being the case, Law I can rightly be called "The Principle of Inertia."

I certainly don't think Newton was confused, I think his first two laws had very specific objectives. The first law was to say what happens in the absence of forces, to dispell the Aristotelian notion that objects would come to rest in the absence of forces. The second law was to say what happens in the presence of forces, to be able to explain what it is that forces actually do (they create acceleration, subject to inertia). So the second law is the only one that refers to inertia, in the quantifiable way we use the word now, even though the first law is called the "principle of inertia." It's two very different meanings of the word-- if the "principle of inertia" is there to dispell the idea that objects come to rest in the absence of forces, then it is not actually necessary to know anything about the quantity we call inertia today.

He had a specific objective, to be sure, but it didn't take the next step you suppose it did. The second law Newton actually wrote was a statement about momentum, not about acceleration or inertia.

Inertia, as defined by Newton (in the dedicated definition), has the dual powers of resistance and impulse. The latter power is explored in Newton III, and that law is, therefore, also a reference to inertia, it "cares" what inertia is, to use your odd word choice.

Inertia is a force. I wouldn't call a force a "quantity". I wouldn't speak of it as "...the quantity we call force today." "Quantity" is not something essential about what force is, such that we would be compelled to "refer to" quantity to define it. In other words, I don't think there's an modern understanding of inertia (as far as classical physics is concerned) that is any different than Newton's. (GR and the rest are outside the scope, here.)

 

[Ken G]

I'll be happy to stipulate that the words "...is the concept of how much objects accelerate when forces are exerted on them," is a statement of a dynamical principle about acceleration, because it's still not a statement about inertia.

Well I'm afraid I cannot follow your reasoning there, because that certainly sounds like a statement about the modern concept of inertia to me. In particular, the inverse of inertia is the amount objects accelerate per unit net force placed upon them. This is what "inertia" means today. In science, we don't look for truth by quoting century-old manuscripts, we recognize that concepts evolve.

That last being the case, Law I can rightly be called "The Principle of Inertia."

Even that isn't true, it should be called "The principle of what causes acceleration", or "the principle of when acceleration doesn't happen." Indeed, this entire thread is about the very true fact that the term "inertia" has come to have two meanings:
1) a vague general meaning that objects "resist" changes in motion, whatever that means, and
2) a crystal clear meaning given by what I said above. The fact of the matter is, Newton's first law in no way refers to this second precise meaning, and it really doesn't refer to the first vague meaning either, because an object receiving no force at all does not have anything to "resist". The term "resist" has no meaning in the context of Newton's first law, which is strictly a law about what happens in the absence of anything to resist. Really what the first law is, is a description of what it is that causes changes in motion, and nothing about resisting said changes. It is the second law that is all about resisting changes, once the first law has told us what causes changes in the first place.

 

[zoobyshoe]

Well I'm afraid I cannot follow your reasoning there, because that certainly sounds like a statement about the modern concept of inertia to me. In particular, the inverse of inertia is the amount objects accelerate per unit net force placed upon them. This is what "inertia" means today. In science, we don't look for truth by quoting century-old manuscripts, we recognize that concepts evolve.Even that isn't true, it should be called "The principle of what causes acceleration", or "the principle of when acceleration doesn't happen." Indeed, this entire thread is about the very true fact that the term "inertia" has come to have two meanings:
1) a vague general meaning that objects "resist" changes in motion, whatever that means, and
2) a crystal clear meaning given by what I said above. The fact of the matter is, Newton's first law in no way refers to this second precise meaning, and it really doesn't refer to the first vague meaning either, because an object receiving no force at all does not have anything to "resist". The term "resist" has no meaning in the context of Newton's first law, which is strictly a law about what happens in the absence of anything to resist. Really what the first law is, is a description of what it is that causes changes in motion, and nothing about resisting said changes. It is the second law that is all about resisting changes, once the first law has told us what causes changes in the first place.

Link me to a site that defines inertia as you do. I have about 10 physics texts, old and new, and I googled and read 3 different sites, and they all define it more or less as Newton did.

 

[Ken G]

Link me to a site that defines inertia as you do. I have about 10 physics texts, old and new, and I googled and read 3 different sites, and they all define it more or less as Newton did.

Easy. Google "inertia." In the first hit: (http://en.wikipedia.org/wiki/Inertia)
"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. It is proportional to an object's mass."

Second hit (http://www.physicsclassroom.com/class/newtlaws/u2l1b.cfm):
"All objects resist changes in their state of motion. All objects have this tendency - they have inertia. But do some objects have more of a tendency to resist changes than others? Absolutely yes! The tendency of an object to resist changes in its state of motion varies with mass. Mass is that quantity that is solely dependent upon the inertia of an object. The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion."

So, both of these hits have it perfectly correct-- inertia is the tendency to resist changes in motion, quantified as the inverse of the acceleration you get per unit force applied, and it depends only on mass (and is generally taken to equal mass). At first look, it might seem like Newton's first law is talking about that, but as I said, it's not. The first law, instead, tells us when we have nothing to resist-- when there is no force. So the first law is a description of what things do when they have no reason to do anything else-- and that is, they keep doing what they were doing. Note there is nothing to "resist" if all that is being stated is what happens when there is no reason for anything else to happen, the "default mode" has nothing to do with "resistance". The second law, on the other hand, has everything to do with resistance. So any time "resistance" is mentioned in the same breath as inertia, the second law is being referenced, not the first.

 

[Studiot]

At first look, it might seem like Newton's first law is talking about that, but as I said, it's not. The first law, instead, tells us when we have nothing to resist-- when there is no force. So the first law is a description of what things do when they have no reason to do anything else-- and that is, they keep doing what they were doing. Note there is nothing to "resist" if all that is being stated is what happens when there is no reason for anything else to happen, the "default mode" has nothing to do with "resistance". The second law, on the other hand, has everything to do with resistance. So any time "resistance" is mentioned in the same breath as inertia, the second law is being referenced, not the first.

I find this a perverse refutation of the proposal that 'inertia is to do with the first law' since the first law is a special case of the second law!

 

[D H]

I find this a perverse refutation of the proposal that 'inertia is to do with the first law' since the first law is a special case of the second law!

Not at all! A better way to look at it is that the second law is consistent with the first law in the case of a null net force.

The modern view (Ken G: "In science, we don't look for truth by quoting century-old manuscripts, we recognize that concepts evolve.") is that the first law establishes the framework in which the other two laws are valid. This framework is that of an inertial frame of reference.

 

[zoobyshoe]

Easy. Google "inertia." In the first hit: (http://en.wikipedia.org/wiki/Inertia)
"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. It is proportional to an object's mass."

Second hit (http://www.physicsclassroom.com/class/newtlaws/u2l1b.cfm):
"All objects resist changes in their state of motion. All objects have this tendency - they have inertia. But do some objects have more of a tendency to resist changes than others? Absolutely yes! The tendency of an object to resist changes in its state of motion varies with mass. Mass is that quantity that is solely dependent upon the inertia of an object. The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion."

So, both of these hits have it perfectly correct-- inertia is the tendency to resist changes in motion, quantified as the inverse of the acceleration you get per unit force applied, and it depends only on mass (and is generally taken to equal mass). At first look, it might seem like Newton's first law is talking about that, but as I said, it's not.

What I requested was a link to a site that defines it as you did :"Inertia is the concept of how much objects accelerate when forces are exerted on them". Instead you have linked to two sites which are saying, in effect, "Inertia is the concept of how much objects DON'T accelerate when forces are exerted on them, how much they RESIST acceleration." The concept of inertia as a resistance is the one your definition does not have.

I understand that concepts evolve, of course, but in this case there is no difference between the "centuries old text" and the links you provided. Neither sets out to define inertia by its inverse.

Earlier you said, "Well I'm afraid I cannot follow your reasoning there, because that certainly sounds like a statement about the modern concept of inertia to me. In particular, the inverse of inertia is the amount objects accelerate per unit net force placed upon them. This is what "inertia" means today." It could well be, but physics texts and google hits aren't introducing people to inertia this way. Just sayin': it's my observation they don't.

The first law, instead, tells us when we have nothing to resist-- when there is no force. So the first law is a description of what things do when they have no reason to do anything else-- and that is, they keep doing what they were doing. Note there is nothing to "resist" if all that is being stated is what happens when there is no reason for anything else to happen, the "default mode" has nothing to do with "resistance". The second law, on the other hand, has everything to do with resistance. So any time "resistance" is mentioned in the same breath as inertia, the second law is being referenced, not the first.

I completely understand what you're saying. I think you may think I don't get, or don't believe, your points in this paragraph because I suddenly updated my understanding of what the first law asserts based on new information. That update was exclusively in the interest of representing what Newton actually said. I felt it encumbent on me to inform you I ran across the information that Newton did actually assert that inertia was responsible for what objects do when no forces are acting on them. You are reacting to that by trying to explain how it isn't true. I actually thought your reaction would be something like, "Hmmm, interesting," in light of what you also said earlier: "...laws are just assertions, they are never responsible for when they are true...it is irrelevant when the law is true, if you are simply trying to understand what the law asserts." It's extremely interesting to me that Newton would assert this. It's like someone saying, "YES, a tree makes a sound when it falls over in the woods and there's no one there to hear it."

The appeal of reading and understanding his actual words to me is that it reveals Newton's manner of thinking, which is of interest because the way he thought allowed him to get traction on the problem he set out to tackle: describing the motion of the heavenly bodies. I'm not too concerned whether the law he called a law shouldn't have been called a law. The fact he characterized it as a law was part of the way of thinking that somehow allowed him to get traction on the problem.

 

[Ken G]

The modern view (Ken G: "In science, we don't look for truth by quoting century-old manuscripts, we recognize that concepts evolve.") is that the first law establishes the framework in which the other two laws are valid. This framework is that of an inertial frame of reference.

Exactly. And the first law takes on even larger significance when modified by GR to say that in the absence of forces, objects follow the paths determined by gravity, generalizing the concept of what it means to "keep moving like it was." As D H said, to know how a force changes the motion (2nd law), you first have to know what the motion would have been without the force (1st law). So the first law ended up being quite a bit more profound than the second law! The irony is, the "inertial frames" do not depend on the "inertia" of the objects, and indeed even light is ruled by the limiting inertial frames set by gravity.

 

[Ken G]

What I requested was a link to a site that defines it as you did :"Inertia is the concept of how much objects accelerate when forces are exerted on them". Instead you have linked to two sites which are saying, in effect, "Inertia is the concept of how much objects DON'T accelerate when forces are exerted on them, how much they RESIST acceleration."

There's no important distinction in those phrasings, my comments were not intended to carry the way inertia depends on the acceleration achieved, what was relevant to the discussion about the first law was simply that inertia is the concept that relates to how much acceleration you get. I assume everyone here knows F=ma, so the sense of the dependence was not the issue.

The concept of inertia as a resistance is the one your definition does not have.

I am fine with the concept being about resistance to change, that's what I've said all along. My point, and the point of the whole thread, is that the first law does not reference the inertia of the body, because the first law has nothing to do with "resistance." So if you feel resistance is crucial, you are making my point for me, thank you.