Talk:Newton's laws of motion

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Semi-protected edit request on 21 July 2024

In the paragraph:

"Acceleration can likewise be defined as a limit:$$a={\frac {dv}{dt}}=\lim _{\Delta t\to 0}{\frac {v(t+\Delta t)-v(t)}{\Delta t}}.$$Consequently, the acceleration is the second derivative of position, often written ${\frac {d^{2}s}{dt^{2}}}$."

Change the equation:

${\frac {d^{2}s}{dt^{2}}}$

to:

${\frac {d^{2}p}{dt^{2}}}$

So that p matches the position variable name Traviskaufman (talk) 22:44, 21 July 2024 (UTC)

References

No, the variable for position is s. Johnjbarton (talk) 14:39, 22 July 2024 (UTC)

Inaccurate paraphrasing of newton's second law

Newton's second law is paraphrased as "At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time.". Change in momentum is only equal to mass times change in acceleration if the mass of the body is constant. It might be best to simply remove the part about acceleration times mass and rephrase it as "At any instant of time, the net force on a body is equal to the rate at which the body's momentum is changing with time." Michaelmay123 (talk) 18:28, 19 September 2024 (UTC)

It is my understanding that both statements of Newton's 2nd law are only true if the mass of the body remains constant. It is common to see Newton's 2nd law refer specifically to a particle or rigid body, rather than simply a body. The implication is that the mass of a particle or rigid body does not change with time. See Euler's laws of motion; I have added this to "See also".

When dealing with a body whose mass is changing with time, such as a rocket accelerating as the result of thrust associated with ejection of a high-speed mass of gas from a nozzle, a slightly different equation is required. Dolphin (t) 03:05, 20 September 2024 (UTC)

The "changing mass" Newton's formula is often misused, some/many would argue. Yes, it works, but the notion of a body as an entity that loses its mass by becoming more than one body is, philosophically, quite, ahm,... silly? Take for example a rubberband gun: the gun of mass M-m and a bullet of mass m are taken as two bodies (total mass M). And so should be a rocket of mass M-dm and the expelled gas of mass dm, at any instant of time. Ponor (talk) 14:39, 20 September 2024 (UTC)

" zeroeth law"

zero is not an ordinal. Fail Fail Fail Athanasius V (talk) 13:13, 22 September 2024 (UTC)

Sometimes used in physics. For example, see Zeroth law of thermodynamics. Dolphin (t) 13:19, 22 September 2024 (UTC)

Is the so-called "modern form" of Newton's second law compatible with Newton's authentic law?

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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The article introduces the second law in the modern form F = ma. Newton's authentic law, however, reads that the force F is not "equal" but proportional to its effect on the motion of the body on which it is impressed. Provided that this effect should be correctly measured ma, the authentic law of Newton would read F ~ ma, or, algebraically, F = ma times constant of proportionality. As this constant is missing in the "modern form", it must be inferred that this form is not compatible with Newton's authentic law, in other words: it is not Newton's law, and "classical" mechanics, which is undoubtedly based on F = ma, is not Newtonian mechanics. This should be mentioned, to say the least. 2003:D2:9724:5375:5978:EDD7:4D63:85CD (talk) 16:32, 17 October 2024 (UTC)

If you have a source to support this claim, post it. Otherwise I will go on assuming that mass is defined as the proportionality constant implied by Newton. Johnjbarton (talk) 16:44, 17 October 2024 (UTC)

We agree that there is "a proportionality constant implied by Newton", as you put it. Now, there are two terms, F and (ma), which are said to be "proportional" to each other. "Mass" m is a part of the term (ma) that is said to be proportional to F. Therefore, by basic mathematical reasoning, m is not available as "proportionality constant" between F and (ma). Note, please, that the proportion reads F ~ (ma), not F ~ a, and, algebraically written, not F/a = m, but F/ma = c = constant. This can also clearly be seen if one writes (dp/dt) instead of (ma). If F ~ (dp/dt), and F/(dp/dt) = c = constant, it is evident that the constant cannot be m. Right? 2003:D2:9724:5357:95E5:D83:52F7:AC49 (talk) 07:52, 26 October 2024 (UTC)

The term "Newtonian mechanics" is ubiquitously used as a catch-all that includes many ideas not introduced by Newton himself, e.g., the principle of inertia, and the concepts of work and energy. There's nothing that Wikipedia can or should do to change this terminology. Moreover, the article as it stands already explains this. XOR'easter (talk) 20:20, 17 October 2024 (UTC)

Of course Wikipedia can and should do something. It is not required to "change the terminology", if only here and there Wikipedia would point to the fact (here admitted) that "Newtonian mechanics" is NOT Newton's mechanics, and that the famous "second law of motion", F = ma, is NOT Newton's law but Leonhard Euler's: See L. Euler, Découverte d'un nouveau principe de Mécanique, Mem. Acad. Roy. Sci. Berlin, vol. 6, 1750 (1752), pp. 185-217. I take this reference from Giulio Maltese, La Storia di 'F = ma', Firenze (Olschki), 1992, p. 218. 2003:D2:9724:5357:95E5:D83:52F7:AC49 (talk) 08:02, 26 October 2024 (UTC)

The Maltese reference seems to be in Italian. Here is another more recent book chapter by Maltese on the same subject:

• Maltese, G. (2003). The Ancients’ Inferno: The Slow and Tortuous Development of ‘Newtonian’ Principles of Motion in the Eighteenth Century. In: Becchi, A., Corradi, M., Foce, F., Pedemonte, O. (eds) Essays on the History of Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8091-6_9

Contrary to your claim, the essential message of the Maltese work is that the modern form of the physical model attributed to Newton was developed over many years by many people. (This is a very common story line in the history of science). This is inline with the History section of the article. As always, these sections can be improved but no radical change is needed. For that purpose this reference is probably better:

• Coelho, R.L. On the Concept of Force: How Understanding its History can Improve Physics Teaching. Sci & Educ 19, 91–113 (2010). https://doi.org/10.1007/s11191-008-9183-1

Johnjbarton (talk) 14:41, 26 October 2024 (UTC)

My claim concerns the true meaning of Newton's second law. I do not doubt "that the modern form of the physical model attributed to Newton was developed over many years by many people". - My question is what Newton's authentic second law says if expressed in mathematical symbols. Newton's central message is the "proportionality" between impressed force and change in motion. Proportionality is a mathematical term. It stems from Euclid, Elements, Book V, Definitions. Euclid defines "ratios" (logos) between quantities of a same kind, and "proportions" (ana-logos) between quantities of a different kind. Newton rightly understands "force" and "change in motion" as quantities of a different kind (cf. Principia 1713, Book I, Scholium after Lemma X). Thereforce he puts them proportional, not equal, as it is mistakenly done in nearly all the papers on this subject through 300 years, beginning perhaps with the Principia edition of Thomas Leseur and Francois Jacquier, Rome 1739. Newton's law evidently requires a "proportionality constant". This is shown in my paper "Die Newtonische Konstante" (Philos. Nat. 22 nr. 3/1985, p. 400), followed in a way by I. B. Cohen's and Anne Whitman's Principia edition Berkeley 1999. The "Newtonian constant" (as I termed it) has been suppressed and dismissed from the beginning by writers who, ignorant of the meaning of "proportions", in the footsteps of Newton's antipode G. W. Leibniz (!!) have put "force" and "change in motion" equal, F = (ma), or F = (dp/dt). What I want to say, regarding the historical truth, is that this law F = (ma), in whatever a form it is expressed, is NOT "Newton's second law", contrary to the article and to all textbooks over the world. It is evident, by the way, that everything in theoretical physics, and that the whole modern world view, would change if the physicists would erect their science on the true foundation laid by Galileo Galilei and Isaac Newton more than 300 years ago. 2003:D2:9724:5371:95E5:D83:52F7:AC49 (talk) 09:17, 27 October 2024 (UTC)

"...contrary to the article and to all textbooks over the world." When the textbooks change we can change the article, even it that means stumbling along in ignorance for another 300 years. Johnjbarton (talk) 15:18, 27 October 2024 (UTC)

This means that he who wants to understand Newton's laws of motion should not read Newton but a modern physics textbook instead, which tells him, for example, that Newton's second law of motion reads F = ma; right? In other words: If Newton's teaching does not correspond to modern textbooks, so much worse for Newton. What is truth? Oh my God ... 2003:D2:9724:5371:95E5:D83:52F7:AC49 (talk) 22:35, 27 October 2024 (UTC)

Wikipedia does not claim to present "truth", nor is there any practical way for it to do so. Rather it claims to summarize knowledge as represented in reliable sources, a practical though still challenging goal. That is why I requested reliable sources in my first reply. Johnjbarton (talk) 22:48, 27 October 2024 (UTC)

The "reliable source" to answer the question "what are Newton's laws of motion" - isn't it Newton's Principia? What if this source contradicts all textbooks, as it is evidently the case? Should the reader then rely on the textbooks? Really? 2003:D2:9724:5381:95E5:D83:52F7:AC49 (talk) 10:02, 28 October 2024 (UTC)

Wikipedia policy is to rely on secondary sources, so no Newton's Principia, as a primary source, is not considered the best choice. In this case it would be a bad choice because language and science changes over the centuries. There are many excellent historical analyses for Newton. Textbooks are excellent sources for concepts because they are typically very well reviewed and designed to explain concepts.

This article isn't about Newton's historical words but rather about the physics taught today which is traced back to Newton's work. So yes, "so much the worse for Newton" if the modern differs in some detail from his words. We have an entire long article on Philosophiæ Naturalis Principia Mathematica and a sad little article on History of classical mechanics about historical issues. Johnjbarton (talk) 15:39, 28 October 2024 (UTC)

With all due respect: No, Sir. This article of course claims to truly represent Newton's historical words! Under the headline "Newton's laws of motion" it claims that Newton's second law would read F = dp/dt = ma! Which, however, is not true if one reads Newton's Principia! Therefore I accuse Wikipedia of telling the reader not the truth but a myth. Nowhere does the article inform the reader that the modern reading F = dp/dt = ma differs from Newton's words "because language and science changes over the centuries", or, because "the modern form of the physical model attributed to Newton was developed over many years by many people", as you put it in your first reply. Once again: So long as Wikipedia does not change the article it is evident that this encyclopedia contrary to truth represents not Newton's laws of motion but something different; fiction instead of science. 79.198.227.190 (talk) 18:21, 28 October 2024 (UTC)

I don't see where this discussion is going. How would adding a (linear?) proportionality constant (now 1) to each and every force equation change physics? This F is only a middleman; a program, as Feynman (I believe) called it. Take one F formula for causes, take another F formula for the effects, forget about F. The ideas are Newtons', so is the mechanics. Just like the equations are Heaviside's, but the grand idea is Maxwell's. Ponor (talk) 19:54, 28 October 2024 (UTC)

The article already gives the quotation from Newton. It already says that $\mathbf {F} ={\dot {\mathbf {p} }}=m\mathbf {a}$ is the "modern form" of Newton's second law. It already says that expressing the law as $\mathbf {F} =m\mathbf {a}$ was Euler's idea. There is literally nothing we need to do here. XOR'easter (talk) 20:53, 28 October 2024 (UTC)

The article does NOT give "the quotation from Newton" which reads (main part): "Mutationem motus proportionalem esse vi motrici impressae". Sorry that this is Latin. It is Newton's language. It says that a force impressed on a body ("vis motrix impressa") is proportional - NOT EQUAL! - to the generated change in the body's motion ("mutatio motus"). No "acceleration"! By no means can Newton's formulation be identified with F = ma, which should be Newton's law according to the article! Never did Euler express Newton's law as F = ma! Quite to the contrary, in 1750 in Berlin, when he introduced F = ma to the public, he explicitly and rightly claimed that this was "a new (!) principle of mechanics" which he (HE!) had discovered ("decouverte")! No mentioning of Newton! Note that nobody has ever accused Euler of plagiarism! - Why is it so difficult to simply admit the evident fact that F = ma (F = dp/dt) is not Newton's second law?? 2003:D2:9724:5381:95E5:D83:52F7:AC49 (talk) 22:13, 28 October 2024 (UTC)

Wikipedia re-publishes information that is already published in reliable sources, but does so without plagiarism. At Wikipedia:Verifiability it says If reliable sources disagree with each other, then maintain a neutral point of view and present what the various sources say, giving each side its due weight.

Wikipedia does not arbitrate on which source is correct, and which is incorrect. Dolphin (t) 23:17, 28 October 2024 (UTC)

Obviously Wikipedia arbitrates on which source is "reliable" and which is not. According to Wiki reliable is what modern textbooks say about Newton's laws; what Newton himself says is not reliable. Really? 2003:D2:9724:5317:9C9E:E62D:57C8:D9A7 (talk) 08:03, 29 October 2024 (UTC)

Wikipedia is not the place to argue that every physics book is wrong.

Wikipedia is not the place to argue that all physicists should change what they mean by "Newton's laws".

Wikipedia is not the place to invent controversies that do not exist. XOR'easter (talk) 01:01, 29 October 2024 (UTC)

1) Wikipedia tells the reader about Newton's (!) laws something that is not true. I'm trying to correct that. Isn't this a most normal case? Or is Wikipedia always true, never to be corrected?

2) Wikipedia is certainly the place to inform physicists and others of "what are Newton's laws"; Newton's! not Euler's, and not what modern textbooks say. This exaxtly, namely to show what Newton's laws are saying, is what Wiki does in the article; but wrongly, alas.

3) That Wikipedia is wrong here is easily demonstrated by the fact that those who aim at defending the article rightly argue that the "second law" as shown in the article is a product of centuries-long evolution. I agree; so this evolutionary product is certainly not "Newton's law" as one finds it in the Principia of 1687. To which source Wikipedia, however, mistakenly and misleadingly refers, even by illustrating the article with a copy of that outdated (?) source's title page! 2003:D2:9724:5317:9C9E:E62D:57C8:D9A7 (talk) 08:36, 29 October 2024 (UTC)

Ponor on 28 Oct asked "how would adding a proportionality constant to each and every force equation change physics?" This question doesn't belong to the subject of this discussion. Nonetheless it is an important one. The answer is given with the identification of the "Newtonian constant", that is, the proportionality constant c between "Force" F and "change in motion", delta p. F/delta p = c = constant. This constant c bears dimensions, not just "1" but "element of space, s, over element of time, t": c [s/t], as it follows from a careful study of Newton's principles. So the "Newtonian constant" coincides with the "c" of modern science. If added according to F/delta p = c it guarantees that the force F will generate a change im motion delta p NOT instantaneously (which absurdity F/delta p = 1, of F = delta p insinuates), but in space and time, in full accordance with natural experience for the first time. 2003:D2:9724:5317:9C9E:E62D:57C8:D9A7 (talk) 17:57, 29 October 2024 (UTC)

I see what you mean. He definitely says "Force" ~ Δ(mv). However:

In his Scholium after Corollary VI he says: When a body is falling, the uniform force of its gravity acting equally, impresses, in equal particles of time, equal impulses upon that body, and therefore generates equal velocities. (there are other similar examples; his way of thinking is discrete, geometrical)

To us, that sounds about right, no? The only thing is that Newton didn't use the word impulses but forces. But if the force of its gravity is uniform and acting equally, why would he have to say "in equal particles of time"? With our definition of the word "force", his statement would have to be "force of its gravity impresses in equal and different particles of time equal forces upon that body". Total force does not depend on time, impulse does. So Newton's force is most likely our impulse, though probably not consistently throughout the book: "Newton's Force" = F Δt ~ Δ(mv) → F ~ ma.

Anyway, this is not something we should discuss here. You're free to propose changes, with good sources. I haven't read the article and can't say what should be said differently. We should, perhaps, rely on our modern understanding of the words, not Newton's, and not quote him literally mixed with our modern formulas. Ponor (talk) 01:05, 30 October 2024 (UTC)

Thank you, Ponor. Indeed, as you say, Newton's way of thinking is discrete, geometrical. Accordingly, in the Scholium after Corollary VI he DISTINGUISHES between "the uniform force of gravity" and the discrete "impressed forces" (not "impulses"), as he also does it in Def. 4. Here the uniform force of gravity, called "centripetal force" (synonymously), is described as a "source of" discretely impressed forces. Therefore, "the total impressed (!) force DOES depend on time, it is "the sum over time" of discretely and successively impressed forces. The "total force" is NOT "the uniform of gravity" and it is NOT our "impulse", but it is "proportional to" the impulse: F ~ delta(mv), which is in algebraic form: F/delta(mv) = c = constant. c is the "Newtonian constant". May I refer you to my paper "Inertia, the innate force of matter", in P. B. Scheurer and G. Debrock (eds.), Newton's Scientific and Philosophical Legacy, Kluver (1988), pp. 227-237 (a "reliable source"??), with further readings. Thank you in advance for reading me.

Ed Dellian, Berlin, Germany. 2003:D2:9724:5305:51E3:FFE1:2229:7E99 (talk) 08:12, 30 October 2024 (UTC)

We are entering Wp:NOTFORUM territory now. Multiple editors have listened and concluded that no change to the article needs to be made. Thanks for the suggestions. Johnjbarton (talk) 01:38, 30 October 2024 (UTC)

It is o. k. to show the user of Wikipedia the modern form F = ma as the foundation of "classical mechanics". It is NOT o. k. to call this form "Newton's law". If at all, then it is Euler's law. This to find in a revised version of the article was my only aim from the beginning. 2003:D2:9724:5305:51E3:FFE1:2229:7E99 (talk) 08:43, 30 October 2024 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.