Conservation of Momentum - true?

[D H]

The principle of conservation of momentum applies to total momentum of a closed system.
Pete

I disagree. The principle of conservation of momentum, Newton's First Law, applies to a body, not to a closed system of bodies:

Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

or in English,

A body remains at rest or in uniform motion unless acted upon by a force.

A closed system has no external forces acting upon it. The all-important qualifier unless acted upon by a force is tautologically zero for a closed system.

The First Law doesn't say much -- to paraphrase it, "A body remains in uniform motion except when it doesn't". The First Law is a generalization of Galileo's Principle to all directions of travel. It introduces the concept of a force but does not define what that is. The Second Law defines forces, and the First Law can be derived from the Second. So why did Newton even write his First Law? The reason is that First Law threw out Aristotle's physics, thereby creating the need for a new physics.

I have not yet said that conservation of momentum does not apply on the Earth, period. I said that it does not apply in the case of a book falling because it has an external force acting upon it.

Zapper previously asked

If what you're saying is correct, then we, on earth, cannot apply the conservation of momentum, just because our "reference frame" is inappropriate for it! Would you like to stand by this claim?

To infinite precision, conservation of momentum does not apply to an Earth-fixed (or even Earth-centered) reference frame. Newton's Laws (including the first) are valid only to an observer in an inertial reference frame. The Earth rotates about its axis, creating the need for fictitious forces such as the Coriolus force. The Earth accelerates toward the Sun and Moon (and the center of the galaxy and ...), creating the need for fictitious forces such as third-body accelerations.

 

[Physics Monkey]

DH,

Is Newton's First Law really as empty as you make it sound? In particular, isn't the first law essentially a statement about the existence of inertial frames. Certainly it isn't true that a body free from forces will execute uniform motion in every reference frame. In this sense, the first law defines the frames of reference where the second law is valid.

 

[D H]

DH,

Is Newton's First Law really as empty as you make it sound? In particular, isn't the first law essentially a statement about the existence of inertial frames. Certainly it isn't true that a body free from forces will execute uniform motion in every reference frame. In this sense, the first law defines the frames of reference where the second law is valid.

Newton's First Law is a bit vacuous. The interpretation of it as "Every particle continues in its state of rest or uniform motion in a straight line except insofar as it doesn't" was made by Sir Arthur Eddington, not me. Why have a First Law? It is a trivial consequence (in the mathematical sense of the word trival) of the Second Law.

That the First Law defines the concept of "inertial reference frames" is a modern view. My view is that Newton had something more mundane in mind, such as throwing out all of Aristotle's physics with one simple statement. Geniuses have a knack for making apparently simple statements that are anything but simple -- e.g., the speed of light is the same to all observers.

 

[ZapperZ]

I wasn't arguing, I was just saying it is irrelevant to the question. The additional acceleration for occupants in the line of motion will appear to be gravity. They cannot, in the Earth's rest-frame, measure an increase in the Earth's momentum, since it was then and it is now at rest.
But you are kind of illustrating my point. The effects when the object is the size of the Earth rather than Halliday and Resnick (the book, not the people) are much greater. And we can easily say: yes, the Earth is being accelerated towards the object even though in our reference frame it is not. Likewise the Earth is being accelerated towards the book in the Earth+book system even though in our reference frame it is not. The fact that we can feel one and not the other is not pertinent to the question. The fact that momentum is apparently not conserved in either case due to being in its rest frame is. Sure, you can measure the increased gravity and infer the force acting on the Earth, but nonetheless in the rest frame from of an Earth-bound observer the momentum of the Earth is fixed by definition.

I still disagree, and I'm not just trying to be difficult here. I will illustrate.

Take 2 Earth masses. Separate them apart at a distance. You are on Earth 1, I am on Earth 2. We are both on the side facing each other. At t<0, they are fixed in the center of mass frame. At t=0, some Divine creature let go of both masses. Would you now notice a difference than when t<0? I would! I would feel an extra gravity emerging all of the sudden.

But take this a step further. What if you have a brother on the OTHER side of Earth 1. Not only will he suddenly lose weight all of the sudden, but even if the forgot about t=0 (maybe it was 50 years ago when both Earth's were let go), both of you can still figure how you are accelerating by surveying all over the planet the weight change of a fixed mass. You will clearly see that your planet is accelerating towards something. You will not be fooled, like droping a book, that you are at rest and not moving.

Zz.

 

[Physics Monkey]

But is it really a trivial consequence of the Second Law? The Second Law is valid only for inertial frames, and so you still have to define these frames. I don't think Newton could have overlooked this, especially given his amazing prescience on a number of other issues. I believe that Newton did intend for the First Law to describe how to find inertial frames in which to use the Second Law. I think this idea is supported by the fact that Newton was certainly aware of non-inertial frames and the complications that such frames entailed. I suppose I find it hard to believe that Newton would bother stating as a law something which could be trivially derived. I mean, in your view, he could have just as easily stated the Second Law and then made the comment that it immediately precludes Aristotle's system. Eddington's comment is of course half in joking, but I agree that geniuses of the caliber of Newton do have a habit of making simple yet profound statements. I just think that in the case of the First Law, Newton was well aware of what he was doing, even if the subtlety was perhaps lost on others for a long time.

Anyway, I suppose this could really only be resolved with the careful study of Newton's own writings. Thoughts?

 

[El Hombre Invisible]

I still disagree, and I'm not just trying to be difficult here. I will illustrate.
Take 2 Earth masses. Separate them apart at a distance. You are on Earth 1, I am on Earth 2. We are both on the side facing each other. At t<0, they are fixed in the center of mass frame. At t=0, some Divine creature let go of both masses. Would you now notice a difference than when t<0? I would! I would feel an extra gravity emerging all of the sudden.
But take this a step further. What if you have a brother on the OTHER side of Earth 1. Not only will he suddenly lose weight all of the sudden, but even if the forgot about t=0 (maybe it was 50 years ago when both Earth's were let go), both of you can still figure how you are accelerating by surveying all over the planet the weight change of a fixed mass. You will clearly see that your planet is accelerating towards something. You will not be fooled, like droping a book, that you are at rest and not moving.
Zz.

Yes, you can complicate the system by adding more bodies to it and asking different questions about those different bodies and we will see things that will advise us as to what's really going on but nothing changes the fact that something appears to be at rest in its rest frame. However many different examples you choose, however many additional complications you include, this one truth will always prevail and will always be the general answer to all the variants of the author's question.

Again, LOOK at the question. It is a question about reference frames.

In fact, it's a very simple question with a very simple answer. (My answer was over-complicated due to the slight intoxicated state I was in when I wrote it.) The question is really: must Newton's laws (from which you can derive the law of momentum conservation) hold in non-intertial frames? The answer is simply: no, an inertial frame is defined as one in which Newton's laws hold true. There is no obligation for momentum to be conserved in non-intertial frames. There you have the author's question and the approprtiate answer. Your specific answers to special cases such as the OP's example and my counter-example are perfectly true, but they are not relevant to the actual question being asked which is about Newton's laws in non-intertial frames.

End of story. Refer to previous paragraph for any argument you have because it sums up all that is relevant in this dispute. Enjoyed the argument nonetheless.

 

[TiBaal89]

El Hombre you are absolutely correct that the simple answer to my first post is to point out the fact that it is a non-inertial frame of reference. However I do appreciate everyone's input!

There are, as we see, many arguments that off-shoot from this simple example. Interesting stuff, thanks.

 

[pmb_phy]

I disagree. The principle of conservation of momentum, Newton's First Law, applies to a body, not to a closed system of bodies:

Therein lies the mistake.

re "A body remains at rest or in uniform motion unless acted upon by a force." - That's true with no doubt. But you've changed beats here. An individual body's momentum will change as F = dp/dt. But the total momentum of a system is what is being conserved, not that of a single body. Please read

http://scienceworld.wolfram.com/physics/ConservationofMomentum.html

Pete