Talk:Newton's laws of motion

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[edit] Disputed section: Paragraphs deleted from Third Law section

I deleted these paragraphs: The forces acting between particles A and B lie along parallel lines, but need not lie along the line connecting the particles. One example of this is a force on an electric dipole due to a point charge, when the dipole points in a direction perpendicular to the line connecting the point charge and the dipole. The force on the dipole due to the point charge is perpendicular to the line connecting them, so there is a reaction force on the point charge in the opposite direction, but these two force vectors are parallel and, even when extended to a line, they never cross each other in space. (Delete this whole Paragrph. This is not true)

For long-range forces such as electricity and gravitation, the third law may cease to apply.(Delete this Sentence, even for long distance forces this law applies equally well)

because discussions should be on the discussion page, not in the article. I'm not expressing a view on which contributor is right. --Heron 12:37, 30 January 2006 (UTC)

[edit] Newton's third law limitations

The third law is not always true. It fails to hold for electromagnetic forces, for example, when the interacting bodies are far apart or rapidly accelerated and, in fact, it fails for any force which propagate from one body to another with finite velocities.
Source: Mechanics, by Keith R. Symon, University of Wisconsin, Addison-Wesley Publishing Company, Inc., chap. 1-4

But in situations in which bodies influence each other at a distance, as for example through the long-range forces of electricity or gravitation, Newton's third law may cease to apply.
 Source: Physics - A new introductory course, Particles and Newtonian Mechanics, by A. P. French and A. M. Hudson, by the Science Teaching Center at the Massachusetts Institute of Technology, p. 13-8.

with cases of extreme acceleration, problems do not fall under newtonian physics; they are analyzied with reletivistic physics. The claim about gravity is outright false. Indeed, earth is gravitationally drawn towards stars hundreds of light-years away, but since gravity drops off as the inverse square of distance, the force is incredibly minute. I have seen at least 4 physics books and none of them ever mention newton's third law not applying. I'm not sure about the electromagnetic forces, but I know gravity is still equal and opposite even at great distances.

College Physics seventh edition, by Raymond A. Serway, Jerry S. Faughn, Chris Vuille, and Charles A. Bennett (published by Thomson Brooks/Cole) says "an isolated force can never occur in nature" (page 90). --Crucible Guardian 08:47, 17 February 2006 (UTC)

If no valuable counter-references is brought in, the Wikipedia:Neutral point of view official policy will have to be applied.
--Aïki 00:29, 31 January 2006 (UTC)

Newton's third law as formulated by Newton is valid only when for electrostatic force and gravitational force instantaneous action at a distance is assumed.
However, it would be very silly to state that newton's third law is wrong because it fails to be a relativistic law of physics.
The demand on a theory of physics is that it forms a self-consistent system, and that it agrees with observation to within the accuracy of available observational data.
On a more abstract level we can see that Newton's third law asserts conservation of momentum. The principle of conservation of momentum is just as important in relativistic dynamics as in newtonian dynamics, so in a more abstract sense Newton's third law is still just as valid. --Cleonis | Talk 14:34, 21 February 2006 (UTC)

Newton's third law does not hold exactly for magnetic forces, even with instantaneous action at a distance. The force between two steady current elements, from the Biot-savart force law, does not obey newton's third law. JohnFlux (talk) 12:49, 23 January 2008 (UTC)

[edit] a question ?

say theres two cars 1 in motion and 1 stationary , the car in motion strikes the stationary car , which car will have the most damage ? would the stationary car absorb the momentum from the car in motion therefore causing more damage to the stationary car? please help me on this one ?

Assuming that the cars have the same mass they will sustain similar damage. This regardless of whether they remain welded together or bounce apart. This is most easily seen from the 3rd law 'action and reaction are equal and opposite'. The driver of the moving car sees the other 'approaching' at speed. This is the same in his frame of reference as the driver of the stationary car sees in his. Alacrid 19:32, 15 November 2006 (UTC)

As movement can only every be expressed in relative terms, there is no difference between the stationary car and the moving car. The stationary car is only considered stationary due to the frame of reference. Rolo Tamasi (talk) 18:12, 27 January 2008 (UTC)

Just so there's no misunderstanding, if they remain 'welded' together, then there will be more damage done than if they bounced apart. JohnFlux (talk) 12:42, 23 January 2008 (UTC)


Do you have a proof of this theory? Rolo Tamasi (talk) 18:12, 27 January 2008 (UTC)


More Answer: So long as the bodies have the same form and hold the same material properties (say, coefficient of restitution), they will deform identically because, as this is a matter simply of motion in frames of reference, the two bodies are indistinguishable in space. —Preceding unsigned comment added by 130.126.215.2 (talk) 08:45, 27 February 2008 (UTC)

[edit] Newton's 3rd law for bodies in motion

Does Newton's third law apply to bodies in motion ? (not in a state of equilibrium).

SPECIFICALLY:

A 1 ton box falling in a column of almost empty air, containing only a few air molecules ?

The box will fall under gravity and exert a force (equal to it's weight) on the air molecule.

The air molecule will exert the SAME force back on the box.

By newton's third law.

Therefore the box should not move at all.

UNLESS the air molecule moves.

But then the system is not in equilibrium and newtons' third law cannot really be held to apply to this system as a whole, correct ?


A body in motion is in equilibrium, it is impossible to distinguish between a body in motion and a body that is stationary as speed can only be determined relative to another body.
The force between the box and the air molecules will only be equal to the weight of the box when the box reaches its terminal velocity, at this speed the forces between the box and the air will equal the weight of the box. The box will then stop accelerating and continue falling at a constant speed. The air molecules will move, the total force on them causing them to accelerate will equal the total force on the box. Rolo Tamasi (talk) 08:36, 22 February 2008 (UTC)
Newton's 3rd Law still holds. Newton's 3rd Law refers to pairs of forces: if object is exerting a force on object 2, object 2 is exerting a force on object 1 that is equal in magnitude and opposite in direction. The presence of acceleration does not alter this. In your example, when the falling box hits an air molecule it exerts a force on the air molecule (that is not equal to the weight of the box) and the air molecule exerts the same force back on the box. This does not result in zero acceleration though since the two forces are not acting on the same object. As for the box, there is the force of gravity acting down and the force due to the air molecule acting up. The mistake in your example was assuming that the force of the box on the air molecule equals its weight. PhySusie (talk) 11:57, 22 February 2008 (UTC)
Except, at terminal velocity the force does equal the weight of the box and 3rd law still applies. 128.91.26.30 was therefore not wrong to say the force equals the weight as long as it is appreciated that this is a specific not a general occasion. I think the error (in addition to the error that a body in motion is not in equilibrium) was to say that when this happens the box should not move at all. That is wrong, when the force equals the weight the box stops accelerating it does not stop moving. Rolo Tamasi (talk) 20:21, 22 February 2008 (UTC)
PhySusie said: "The mistake in your example was assuming that the force of the box on the air molecule equals its weight". My question: Why is the force on the air molecule not equal to the weight of the box ?
To Rolo: I am SPECIFICALLY talking about 1 SINGLE air molecule in my example, so why are you bringing up "air" and terminal velocity ?
The reason I am talking about terminal velocity is that is the only time when the force on the box from impact with the air is equal to the weight of the box, which was the condition stated.
But now I understand your scenario. We are not really talking a bout a box in air at all. We are talking about a single collision between two objects of hugely different mass.
As this is a momentary incident the fact that the box is being accelerated by gravity is also irrelevant. The only relevant issues are that the box and the molecule have a speed differential and a big mass differential and that they collide.
The question is what is the force of that impact? There is little reason why it would be equal to the weight of the box (or, equally, the weight of the molecule).
The calculation of the force of the impact is not easily determined because it depends upon the nature of the collision, specifically the time it takes. If it is zero time the force is infinite but for a zero time – pretty unhelpful stuff!
What we do know is the force will be applied equally to the two objects and thus the effect of the impact on their speeds will be inversely proportional to their relative masses. If we knew the speed differential and the mass relativities and assumed no energy was absorbed by the impact we could calculate the speed changes.
Thus we can see that the molecule will “ping” off the surface of the box experiencing a substantial acceleration while the change of speed of the box will be almost undetectable.
Hope that helps. Rolo Tamasi (talk) 10:49, 23 February 2008 (UTC)
Rolo: Thanks for that very illuminating post. I think I get it now ! —Preceding unsigned comment added by 71.242.39.174 (talk) 23:41, 23 February 2008 (UTC)


Your example appears to confuse force with acceleration. Consider the second law F=ma. If the forces on the air molecule and the box are equal and opposite, then the net change in the acceleration of the box will be negligible. You can just check this with some plausible numbers if you don't believe it. Silly rabbit (talk) 03:47, 23 February 2008 (UTC)

[edit] Better Representation?

Hi I am only a year 7 student, and I could be very wrong, but the picture on the page with the two ice skaters pushing against each other may not be the best representation of the third law. They aren't necessarily of the same strength or weight, therefore, one may be pushed back more. I think that the recoil of a firearm would be a much better representation.Nelsondog (talk) 05:18, 16 March 2008 (UTC)Nelsondog

Thanks for checking- but Newton's 3rd Law applies even if one is more massive or is stronger. The force between them will always be the same. PhySusie (talk) 12:45, 16 March 2008 (UTC)

[edit] Abit confused

I'm confused with what d is. From what I remember from school shouldn't say a=dv/dt be a=Δv/Δt ?? and if d==Δ then y use d instead of Δ? —Preceding unsigned comment added by Yellow Onion (talk • contribs) 05:45, 19 March 2008 (UTC)

The statement a = dv/dt refers to the first derivative of the velocity function with respect to time. It gives the slope of the line on a velocity vs time graph at that instant in time. The expression you gave using the delta symbol refers to an average over time (so it is not instantaneous) - which is used as an approximation - particularly in algebra based physics courses. PhySusie (talk) 15:25, 19 March 2008 (UTC)

[edit] Question about the Motte translation

I'm a bit confused after reading the Motte translation of Newton's second law: "If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively"

If Newtons 'motion' is equal to modern day 'momentum' (as stated elsewhere on the page), isn't his concept of 'force' a bit different from the modern concept? Since Newtons laws state that forces generate *change* in momentum, a double force would create double the *change* in momentum. Also, the last part about applying the force altogether or gradually seems weird - if the force was not applied for the same amount of time, you would not end up with the same momentum. His concept of force here seems to be closer to what we call the 'impulse' (force x time), doesn't it? Mhc (talk) 21:44, 20 March 2008 (UTC)

[edit] Descriptive name for second law

I have changed this name from "law of acceleration" to "law of resultant force". My reasons are: (i) Newton never referred to acceleration, (ii) a more historically accurate version would refer to "rate of change of momentum" (see Feynman Lectures, vol. 1) (iii) The law refers explicitly to "resultant force" and Newton focussed on the resultant force for many pages, describing how the resultant could be found by vector addition. Moreover, this law does have the purpose of introducing the term force, which pervades all uses of mechanics. See also Williams to support the notion that force is the defining objective of the second law. It seems silly to mis-translate the law to name it in a form that is is less accurate, both historically, and from the viewpoint of relativity and, in fact, from the viewpoint of this article itself. Brews ohare (talk) 15:52, 15 April 2008 (UTC)

On Google, "Law of resultant force" gives two results (including this Wikipedia article), while "Law of acceleration" gives 58.000 results. Since Wikipedia is an online encyclopedia, and verifiability is essential (see WP:V), I propose to revert to the original "Law of acceleration". Further, regarding your edits, note this is an article made for a broad audience. Specially the lead section and first section are read by many people without an academic background. Concepts like rate of change of momentum are, in my opinion, to difficult to start with in the article lead.
Further please have a look at the discussions on this talk page and it archives. For instance, there have been several discussions on the 3rd law, resulting in the abbreviation "To every action, there is an equal and opposite reaction", which you have changed into "For every action ..." (more strongly implying a causal relationship between the two forces). Crowsnest (talk) 21:34, 16 April 2008 (UTC)
Not guilty - To my knowledge I have not tinkered with the third law.
As for momentum - a link is provided to the article on that subject. Personally, I find momentum an easier topic than acceleration, because it shows up not only in common everyday English, but in many other areas of mechanics, e.g. the law of conservation of momentum.
And, as the citations show, formulation in terms of momentum has taken place beginning with Newton in 1687, and continuing to today. It is by no means a "high brow" or "new" approach, although this formulation has shown to be compatible with relativity (1905, wasn't it?), as pointed out later in the article.
I get 7,370 hits for "law of acceleration" using "Newton" as a qualifier to eliminate bogus references. Of course, my objective in naming the "law of resultant force" was to emphasize the "force" aspect of the law. Using "resultant force" + "Newton" gives 48,100 hits, "resultant force" + "second law" provides 24,200 hits. So resultant force is a biggy. Brews ohare (talk) 15:46, 17 April 2008 (UTC)
You are right about the 3rd law change, my apologies for linking you to that change.
Regarding the 2nd law, as you stated yourself, it is your personal preference to use the momentum approach, but it is uncommon to be learned about Newton's 2nd law that way. Using a constant mass, and acceleration is simpler to start with. Regarding your "Law of resultant force", while Google hits don't say anything about the correctness of a statement, it does say something about what is common. This is not about truth, i.e. whether ultimately the 2nd law is about change of momentum or acceleration, but on how to present something in an encyclopedia, without losing most of your audience already in the lead section. So starting simple, in terms of acceleration, and expand to more general case later on. The phrasing you use is original thought, hardly found elsewhere in this formulation. Crowsnest (talk) 16:04, 17 April 2008 (UTC)
You might look at the template in the article. which shows the equation explicitly in terms of momentum
Classical mechanics
History of ...
Formulations
Newtonian mechanics
Lagrangian mechanics
Hamiltonian mechanics
This box: view • talk • edit
The "change of momentum" approach is very common, as the citations show. More than common, it's time-honored – it's been used since 1687!  :-)
Whether acceleration or momentum is the "easier" way is open to discussion. For some problems, momentum is easier (and/or more accurate) and for other problems it is acceleration. As for what is more natural or more easily absorbed by the reader (unrelated to advantages for any particular problem), I believe the momentum approach has the edge. Being more fundamental, the reader who goes on to the relativity section, or who wants to look into other topics, like the collisions of billiard balls etc. doesn't have to change gears. The historically interested person doesn't have to ask why Newton's correct initial statement has been changed for a less fundamental version.
As a guess, you have in mind problems where acceleration works best. However, solving such problems is not the universe of all problems, and also may neither have bearing on the ease of access to an encyclopedia article, nor to its value as introduction to other articles, nor to its value as general background of a qualitative sort (e.g. philosophical or historical value).
Have you thought a bit about the possible goals of different readers, possible backgrounds, and what would serve their purposes? Brews ohare (talk) 17:33, 17 April 2008 (UTC)
What I have in mind, when starting with acceleration, is that it directly relates to ones own experience. To get acquaintance with Newton's 2nd law most easily, is by direct experience. Which almost everybody has: in an accelerating or decelerating car, a playground swing, roller coaster, etc. You feel the force, while you see the acceleration. That is what makes it easy to relate to Newton's second law. Just because in most instances our own mass is near constant. Momentum, and momentum change rate other than by acceleration, are not in general a direct physical experience of most people. It needs explanation and verification at a higher level of abstraction. Crowsnest (talk) 18:55, 17 April 2008 (UTC)
One can just start with F=ma, and state under which conditions it applies, and later on extend to the rate of change of momentum. This is not about the fundamentally most correct formulation, but about how to present things. Crowsnest (talk) 18:59, 17 April 2008 (UTC)
You have outlined one approach and argued that it the most transparent. I have argued a different approach and argued that it is (i) at least equally transparent, (ii) more fundamental, (iii) historically predominant, (iv) used in many other articles in Wikipedia including this article, (v) adopted by reputable authors ranging from Newton to Feynman, and (vi) useful to a wider variety of readers, who undoubtedly have a wide range of agendas when consulting this article, ranging from philosophy to physics. Brews ohare (talk) 13:44, 18 April 2008 (UTC)
Since nobody else supports my view in this, I will stop with this discussion. Crowsnest (talk) 14:06, 18 April 2008 (UTC)

[edit] Recent reversions

User:Jok2000 reverted my edits without response to my explanations on talk page, and without explanations of his own. With the possible exception of the change in name for the second law, which was discussed above, the reverted changes are totally noncontroversial. I expect comment before, for example, addition of a reference is reverted. I believe these reverts were simply a "knee-jerk" reaction without justification, stated or imagined. I have added citations for the statement of Newton's second law, which is an almost literal translation of the Latin and has been used for centuries. Citations I've added go back to 1911 only. This statement of the law is used in this article itself later on. I've also added reference to Moller for relativity - a definitive reference in this area, for those who may not know these simple relations. Brews ohare (talk) 03:11, 16 April 2008 (UTC)

Tell me more about my "imagined" reasons. The 2nd law is F=ma [1]. So now take out your changes to it. Jok2000 (talk) 21:03, 16 April 2008 (UTC)

The article quotes Newton as "Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.", which I'd guess trumps Wolfram as an authority on the matter of Newton's laws. Moreover, I've provided multiple references to show that this wording persists to this day. The formulation in terms of acceleration is a more limited, less accurate formulation. You might also look at the template in the article. which shows the equation explicitly in terms of momentum Brews ohare (talk) 14:24, 17 April 2008 (UTC)
Strange, I thought it was you who removed that bit. Must have been some vandal. I retract the request. Its a bit funny actually, I repaired this once before in October 2007, if you check the history, to be what's there now. The vandals hit this thing twice a day. I can't be here all of the time, I guess. Jok2000 (talk) 15:18, 17 April 2008 (UTC)


[edit] Change the 'Classical mechanics' diagram's sub-legend ?

The ‘Classical mechanics’ diagram here and this article historically misrepresent at least Newton’s second law of motion. Here I copy below a discussion of this issue from the diagram’s Template Talk page [2] for further consideration here as perhaps the most relevant article.

Change the diagram's sub-legend

I propose the diagram's sub-legend 'Newton's second law of motion' be changed to 'The second law of motion of classical mechanics'.

The diagram is mistaken because its sub-legend 'Newton's second law of motion' is historically mistaken and if anything should be rather 'The second law of motion of classical mechanics'.

This is certainly not Newton's second law stated in the Principia, which was that THE change of motion [referred to in the first law] is proportional to the motive force impressed, i.e. Dmv @ F, or F --> Dmv (where 'D' = 'the absolute change', Delta, '@' = 'is proportional to', and '->' is the logical symbol for if... then...).

The misrepresentation of Newton's second law as F = ma or similar has the logical consequence that a = F/m and thus a = 0 when F = 0, whereby Newton's first law would be logically redundant just as Mach claimed it was.

But Newton's second law only deals with changes of motion produced by impressed force such as mentioned in the first law, and does not itself assert there is no change of motion without the action of impressed force as the law F = ma does, where F denotes impressed force rather than inertial force. And in fact both Galileo's 1590 Pisan impetus dynamics and Kepler's 'inertial' dynamics, both of which claimed motion would terminate without the continuing action of what Newton called 'impressed force', denied this principle.

But the logical function and historical purpose of Newton's first law is precisely to assert this principle, that there is no change of motion unless (i.e. If not) compelled by impressed force, and thus whereby Dmv <=> F, rather than just F --> Dmv. (Here <=> is the logical equivalence symbol for 'if and only if', and '-->' the symbol for 'If...then...') Thus Mach’s logical criticism was wrong by virtue of his ahistorical misinterpretation of Newton’s second law as F = ma.

Classical mechanics, whatever that might be, needs to be differentiated from Newton's mechanics.

--Logicus (talk) 18:20, 16 April 2008 (UTC)

Hi Logicus. Well, I don't know. The article on Newton's laws of motion says that the Newton second law is "The Rate of change of momentum is proportional to the resultant force producing it and takes place in the direction of that force". Isnt it the same thing that the formula on the template? (or maybe according to you, both article and template are wrong?) I do not oppose you change the sub-lengend, but honestly i'm not sure i see a true difference. Even if the formula is not as Newton stated it, it's greatly inspired by no :)?? And history remembers it as the Newton second law (improved?). Am I wrong? But your comment is interresting. Is this information on Newton laws of motion article???
Frédérick Lacasse (talk · contribs) 13:03, 17 April 2008 (UTC)

First of all, the relevant text is at wikisource, and I'll begin by saying that I disagree with Logicus on her/his proposal. Newton's second law is not stated, as such, mathematically. (Perhaps it is later in the Pricipia, I do not know.) For clarity, its statement under Axioms, or Laws of Motion reads:

The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the straight line in which that force is impressed.

(Emphasis mine, in order to make clear that this is certainly an if and only if statement. Note that Logicus has failed to quote that word in presenting his/her argument.) Since Newton used Calculus in conjunction with this law to calculate planetary orbits and such, it is not too crude to use modern calculus notation in the box, even if we choose Leibniz' d / dt notation over Newton's dot. For that matter, we use vectorial notation when Newton had none. Therefore, clearly, in modern notation, Newton's second law reads

\vec F = \frac{\mathrm{d}}{\mathrm{d}t}m\vec v, and I have no problem with identifying this equation (or an equivalent one) as Newton's Second Law or Newton's Second Law of Motion. Or, see Goldstein, Poole, and Safko, Classical Mechanics (3rd ed.) page 1, where \mathbf{F} = \frac{d\mathbf{p}}{dt}\equiv\dot\mathbf{p} is identified as Newton's second law of motion.

Regarding the other stuff you've said about Mach, historical interpretations, and other irrelevant (for the purposes here) things, perhaps this can help. Newton's second law, which can be expressed as F = ma cannot imply that "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" (Law 1), without presupposing the existence of inertial frames, which is what the first law, in effect, does. The fundamental disconnect between Newton and Mach, as I understand it, concerns the existence of a preferred inertial frame.

If, unlike I've read in many sources over the years, you have sources that claim Newton never equated force with a time-rate-of-change of momentum, you might be able to begin to find people willing to change their ways. However, the classical mechanics template talk is not the place for that discussion. — gogobera (talk) 20:10, 17 April 2008 (UTC)

Logicus's response to Frederick Lacasse, written before Gogobera's contribution: Thanks Frederick. Yes, BOTH the article on Newton’s laws of motion and the template are wrong, because the article mistranslates the Principia’s second law’s phrase 'mutationem motus' as ‘rate of change of momentum’, whereas it should be ‘The change of motion’, with no reference to any rate of change. It referred to an absolute change of motion as produced by an impulse, as in Cartesian vortical mechanics. May I refer you to Bernard Cohen’s ‘Guide to Newton’s Principia’ in the 1999 Cohen & Whitman Principia new translation for a good discussion of this issue, which was also touched on in the recent BBC Radio 4 ‘In Our Time’ programme on Newton’s Laws of Motion and drew the following comment from a listener published on the BBC website @ http://www.bbc.co.uk/radio4/history/inourtime/inourtime_haveyoursay.shtml
“Andrew, Newton's 3 laws
Simon Schaffer might have done well to see in this archive (dating from the programme on Popper), "if you study the original version of Newton's Second Law - not the modern F=ma - you realise that Newton regarded force as a function of time, equivalent to the modern notion of an impulse. It was change of momentum: mass *or* velocity; thus even if mass increases with increased velocity so does the force required, and Newton holds." The insertion of 'rate' in 'rate of change of motion (momentum)', giving F=ma, isn't a flaw of Newton's - it's a mistranslation of 'mutationem motus'. “
The true difference, as I have already pointed out, is that rather than Newton being illogically foolish in his axiomatisation is respect of stating a logically redundant axiom, namely Law 1, as Mach implied, because it was logically entailed by his Law 2, rather his first law states a logically independent axiom which, for example, ruled out Kepler’s theory of inertia according to which the inherent force of inertia resists and terminates all motion. For in Newton’s theory which revised the keplerian theory of inertia the force of inertia only resists accelerated motion and causes uniform straight motion like impetus did in late scholastic Aristotelian and Galilean impetus dynamics.
This is all important for understanding the logic and history of scientific discovery and such as how and why ‘classical mechanics’ emerged, the project started by Duhem that was the major research project of 20th century history and philosophy of science.. But there seems to be some considerable logical confusion and contradiction in Wikipedia articles about Newton’s dynamics and about classical mechanics and what it is and how it relates to Newtonian mechanics. For example the article on ‘Classical mechanics’ says on the one hand the two are equivalent, but on the other hand they are not equivalent because classical mechanics was created later and goes well beyond Newton’s mechanics, as in the following statements:
“There are two important alternative formulations of classical mechanics: Lagrangian mechanics and Hamiltonian mechanics. They are equivalent to Newtonian mechanics, but are often more useful for solving problems.”
Versus
“While the terms classical mechanics and Newtonian mechanics are usually considered equivalent (if relativity is excluded), much of the content of classical mechanics was created in the 18th and 19th centuries and extends considerably beyond (particularly in its use of analytical mathematics) the work of Newton.”
This confusion needs sorting out, but a bigger job than I have time for. I was just trying to reduce this confusion a little, as it cropped up on the Galileo article, but I now see this diagram is pretty ubiquitous in relevant articles. Sorry just to pick on your otherwise no doubt helpful diagram.
I fear the article on Newton’s laws of motion is currently virtually wall to wall ahistorical nonsense, apparently being devoted to teaching some version of 19th century mechanics or A-level Physics rather than the history of physics.
Re your following comment
“Even if the formula is not as Newton stated it, it's greatly inspired by no :)?? And history remembers it as the Newton second law (improved?). Am I wrong?”
One problem with the first claim that Newton greatly inspired the law F = ma is that the Wikipedia classical mechanics article is currently claiming
“The proportionality between force and acceleration, am important principle in classical mechanics, was first stated by Hibat Allah Abu'l-Barakat al-Baghdaadi,[7] Ibn al-Haytham,[8] and al-Khazini.[9] “
- although I have no idea whether this is true or not.
All in all I think I should implement the proposed edit if you have no further comments or objections. But it is still unsatisfactory given it is unclear from Wikipedia what exactly classical mechanics is, whereby such as Lagrangian and Hamiltonian mechanics and even Newtonian mechanics are said to be alternative formulations of it.
The outstanding pedagogical question for your view is surely that if you claim that Newton’s second law was essentially
F = ma, then why did he think he needed to state the first law as his first axiom ? The simple answer is because it gives the equivalence between change of motion and the action of impressed force that the second law does not, because the second law is only at most Dmv α F and not Dmv = F. Logicus (talk) 20:34, 17 April 2008 (UTC)

-- Further to my observation above that this article seems to be in serious conflict between the aim of teaching some form of ‘classical mechanics’ (or A-level Physics) under its various categories on the one hand of ‘Classical mechanics’, ‘Introductory physics’ and ‘Experimental physics’ etc for example, and on the other hand that of explaining what Newton’s laws of motion were under the categories of ‘History of physics’, ‘Isaac Newton’, ‘Latin texts’ etc., I further suggest that what this article and that on ‘classical mechanics’ misleadingly call ‘Newtonian mechanics’ may in fact rather be Laplacean mechanics as distinct from ‘Newtonian mechanics’ insofar as the latter term refers to the mechanics of one Isaac Newton as expounded in his Principia, and Laplacean mechanics may possibly be what is common to both Lagrangean and Hamiltonian mechanics whereby they are inexplicably both said to be forms of some ‘classical mechanics’, but which is itself never properly identified in any corresponding axiomatic form. For example the article says

“The term classical mechanics was coined in the early 20th century to describe the system of mathematical physics begun by Isaac Newton and many contemporary 17th century workers”.

But one major difficulty of many here is that Newton himself said in his Principia Axioms Scholium that its three laws of motion were already accepted by mathematicians and such contemporary figures as Huygens, Wallace and Wren, but also by his non-contemporary Galileo and also even (essentially correctly) pointed out its first law was even current in Greek antiquity, including in Aristotle’s principle of interminable locomotion in a void (Physics 4.8.215a19-22). --Logicus (talk) 16:01, 20 April 2008 (UTC)

Excuse me if I am being a mite blunt but this appears to be a little self centred. It is not up to Wiki editors to decide what Newton intended. Rather it is to publish the balanced view i.e. on the one hand some think Newton meant F=ma on the other had they don’t. I hope ego is not getting in the way here, it is not nearly as complex as the rhetoric implies. Rolo Tamasi (talk) 20:20, 20 April 2008 (UTC)
Unfortunately, I still do not agree with your position, Logicus. Perhaps you were planning on addressing my comments before you changed the template? I believe we ought to use the term Newton's second law for the template for the reasons stated above in my previous comment. I have given a source claiming the equation to be identified as Newton's second law. Here is a list of sources that identify F = \dot p, F = ma, F = m(dv / dt), or some other equivalent formulation as "Newton's Second Law":
  • Danby, John M.A. Fundamentals of Celestial Mechanics. Richmond, VA: Willmann-Bell, 1992. page 44.
  • Feynman, Richard P., Robert B. Leighton, and Matthew Sands. The Feynman Lectures on Physics: Mainly Mechanics, Radiation, and Heat. Reading, MA: Addison-Wesley, 1977. pages 9-1,2.
  • Goldstein, Herbert, Charles Poole, and John Safko Classical Mechanics. 3rd ed. New York, NY: Addison Wesley, 2002. page 1.
  • Hirose, Akira and Karl E. Lonngren. Introduction to Wave Phenomena. Malabar, FL: Krieger Pub. Co, 2003. page 4.
  • Marsden, Jerrold E. and Anthony J. Tromba. Vector Calculus. 5th ed. New York, NY: W.H. Freeman and Co., 2003. page 264.
  • Penrose, Roger. The Road to Reality. New York, NY: Alfred A. Knopf, 2005. page 389.
  • Thornton, Stephen T. and Jerry B. Marrion. Classical Dynamics of Particles and Systems. 5th ed. Belmont, CA: Brooks/Cole, 2004. page 50.
Wikipedia is not about original research. The previous sources are from advanced and introductory textbooks, as well as books for the mathematical layperson. This list is only limited by my desire to stop pulling books off my shelf. Suffice it to say that the equation presented on this template is commonly known as Newton's Second Law. I don't think there is any disagreement over that fact. The idea that "some think Newton meant F=ma" and some don't is an issue for the history of science. The fact is that today, F = ma is identified as "Newton's second law" universally.
Logicus, your arguments have a tendency to sway away from the issue at hand. For instance, your comment about the inconsistency in Wikipedia's treatment of the equivalence of Newtonian mechanics and classical mechanics. However, to clarify, it should be stated that there is an equivalence between the Newtonian, Lagrangian, and Hamiltonian formulations of classical mechanics. So that statement that says "[Lagrangian and Hamiltonian mechanics] are equivalent to Newtonian mechanics" is true (if sloppily worded). Also, saying that classical mechanics has "extend[ed] considerably beyond … the work of Newton." [emphasis mine] is also true, since Newton's work was limited in scope. However, in principle, mechanical results can be derived using any of the formulations. The amount of work to do so can vary tremendously.
If Logicus wants to add cited material discussing Newton's intentions and their historical interpretation, I have no qualms with that. This discussion began, and should be focused on the use of the term "Newton's second law" to describe the equation on the template. Though my understanding is that Newton did mean his second law to be understood as F = \dot p, the point can be made with less ambiguity by discarding historical interpretation: the equation, as written, is commonly identified as Newton's second law. Therefore, I will change the template back. — gogobera (talk) 19:26, 25 April 2008 (UTC)
Logicus to gogobera: You said "Perhaps you were planning on addressing my comments before you changed the template?", but I presumed you would appreciate your criticisms were dealt with by my reply to Lacasse. Apparently not. I shall explain later. —Preceding unsigned comment added by Logicus (talk • contribs) 18:18, 29 April 2008 (UTC)

[edit] Second Law and Impulse

I believe that it is historically incorrect to state Newton's Second Law as F=dp/dt. Motte's 1729 translation (as stated in the article) reads The alteration of motion is ever proportional to the motive force impressed.. At first sight this appears to be saying that force is proportional to motion (velocity??) which is the very concept that Newton is supposed to be discarding. However, a reading of Newton's definitions in the Principia makes it clear that by motion he means momentum and by force he means impulse in modern terminology. So what Newton actually said, using modern symbols, is;

I \propto \Delta p

Obviously, using SI units and differentiating yields the usual form;

\frac {dI}{dt} = F = \frac{dp}{dt}

However, it is unhelpful that the article states the law in this form right after quoting Newton's original words. The impulse version of the law should be stated first together with Newton's definition of his terms.

It has been noted in comments on this talk page already by others that what is written in the article about force does not make sense but with no satisfactory explanation ever been given. Anyone want to tell me I'm wrong? SpinningSpark 08:31, 2 May 2008 (UTC)

The set-up does suggest that the mathematical equation is a direct implementation of Newton's words. That should be fixed if your history is accurate. Can you substantiate your beliefs about the historical background?
Whether historical statements of the law should come first is debatable, as history is an interest of only a subset of readers. Also the introduction of impulse is pretty opaque to the modern reader, and a bit of a digression in applications. Its use at the beginning of the article would make it all rather indigestible. An historical section may become necessary to give room to explain about the historical role of impulse and its connection to rate of change of momentum. Brews ohare (talk) 20:37, 3 May 2008 (UTC)
I did not introduce the historical diversion into this article, it was there already. I have no view on whether it should be in this article or another. However, given that it is here, it is necessary qualify Motte's translation with the modern terms and show that the modern form of the law can be derived from Newtons form (it is only one simple step). Several comments furhter up the talk page verify that this is indeed causing confusion. As for my source, it is Newton's Principia, the definition of motion (=momentum) is given at definition 2 here [3], I am hoping you can get through the paywall (just hit cancel at login) or else try this one [4]. As for force, the text given in the article makes the point, If a force generates a motion, a double force will generate double the motion . . . whether that force be impressed altogether and at once, or gradually and successively. That only makes any sense if impulse is meant rather than force. If it really meant force a step function would produce the same motion as a ramp function - clearly nonsense. SpinningSpark 01:02, 4 May 2008 (UTC)
You will find an earnest attempt to implement what I understand from your remarks at Impulse. Brews ohare (talk) 02:13, 4 May 2008 (UTC)
You obviously put some effort into that, but I have changed it because Newton from his wording cleary does not restrict the concept to an infinitesimal time (neither does our own article, or NASA). I have changed the reference too, presumably that's what your ref says. My ref is a pretty low level one - the ones on the impulse article might be better but I have not looked them up. SpinningSpark 02:43, 4 May 2008 (UTC)
Logicus: Your discussion might well benefit from studying Cohen's analysis of this issue in his 1999 Guide to Newton's Principia in the 1999 Cohen & Whitman Principia --Logicus (talk) 14:46, 4 May 2008 (UTC)
A reference to I Cohen is added to the Impulse subsection. Brews ohare (talk) 15:55, 4 May 2008 (UTC)

[edit] Equivalence. What equivalence ?

Gogobera claimed above 25 April:"...it should be stated that there is an equivalence between the Newtonian, Lagrangian, and Hamiltonian formulations of classical mechanics. So that statement that says "[Lagrangian and Hamiltonian mechanics] are equivalent to Newtonian mechanics" is true (if sloppily worded). Also, saying that classical mechanics has "extend[ed] considerably beyond … the work of Newton." [emphasis mine] is also true, since Newton's work was limited in scope. However, in principle, mechanical results can be derived using any of the formulations. The amount of work to do so can vary tremendously."

From a logical point of view for any two theoretical systems to be equivalent every axiom and theorem of one system must be an axiom or theorem of the other. But where, when and by whom was any such logical equivalence between Lagrangian, Hamiltonian and Newtonian mechanics ever demonstrated ? If Wikipedia makes such logico-historical claims, they need source documentation. Are any of the various mechanical systems of Lagrange, Hamilton, Laplace, Newton (Principia Ed. 3) and the elusive 'classical mechanics' logically equivalent ? And what were the axioms of each of these systems, especially of the latter three (e.g. is Corollary 1 of the Principia a theorem or really an axiom, as in earlier versions i.e is Newton's proof of theoremhood valid, or invalid as Bernoulli presumed in tryit to reprove it?).--Logicus (talk) 14:46, 4 May 2008 (UTC)

To support my claim, I will quote from Section 7.7 of Stephen Thornton and Jerry Marion's Classical Mechanics (p. 257) titled Essence of Lagrangian Dynamics:

We elected to deduce Lagrange's equations by postulating Hamilton's Principle because this is the most straightforward approach and is also the formal method for unifying classical dynamics.

First, we must reiterate that Lagrangian dynamics does not constitute a new theory in any sense of the word. The results of a Lagrangian analysis or a Newtonian analysis must be the same for any given mechanical system. The only difference is the method used to obtain these results.

…

The differential statement of mechanics contained in Newton's equations or the integral statement embodied in Hamilton's Principle (and the resulting Lagrangian equations) have been shown to be entirely equivalent. Hence, no distinction exists between these viewpoints, which are based on the description of physical effects. [emphasis original]

I am not sure if I can be any clearer, except by presenting, in its entirety, section 7.6 of the same book, titled Equivalence of Lagrange's and Newton's Equations which begins: "As we have emphasized from the outset, the Lagrangian and Newtonian formulations of mechanics are equivalent: The viewpoint is different, but the content is the same. We now explicitly demonstrate this equivalence by showing that the two sets of equations of motion are in fact the same." (p. 254) The text continues with a mathematical development of the claim.
Thornton and Marion do go on to clarify that a philosophical difference exists:

In the Newtonian formulation, a certain force on a body produces a definite motion—that is, we always associate a definite effect with a certain cause. According to Hamilton's Principle, however, the motion of a body results from the attempt of nature to achieve a certain purpose, namely, to minimize the time integral of the difference between kinetic and potential energies. [N.B.] The operational solving of problems in mechanics does not depend on adopting one or the other of these views. [emphasis original](p. 258)

Does this make my position clear? I would welcome anyone else's opinions as well. — gogobera (talk) 23:39, 22 May 2008 (UTC)

[edit] Inertial frames

Any particle, regardless of what forces act on it, is at rest relative to the reference frame whose origin is defined to coincide with the particle. The non-trivial point about inertial reference frames in Newtonian mechanics is that they are the same for all physical objects. I corrected the formulation.

Taneli HUUSKONEN (talk) 14:12, 5 June 2008 (UTC)

I'm not sure what change you've made, but I hasten to add that while a particle is at rest, by definition, relative to the frame whose origin coincides with the particle, that frame is frequently not an inertial frame. — gogobera (talk) 22:54, 5 June 2008 (UTC)