Talk:Newton's laws of motion/Archive 6

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Fourth law was given by Newton

The article currently claims Newton did not state the principle of the superposition of forces or the "fourth law" but only assumed it. The claim is backed up by three references, two of which are physics textbooks not focused on classical mechanics and can be considered of low importance. The third one is the classical mechanics textbook by Greiner and it does not support the claim. On the contrary, it tells (on page 135) that that "Newton essentially formulated his axioms as follows:" and then goes on to describe the four laws. In Principia, the superposition of forces, or the paralleogram of forces, is given as the Corollary I immeadiately after the laws. (Principia at Wikisource) It is not named as the fourth law, but it is definitely "stated", not "assumed". -Jähmefyysikko (talk) 21:09, 4 February 2022 (UTC)

As you note in your revision to the article, this so-called "fourth law" is presented as a corollary, and the text of the corollary claims to be a logical deduction from the first and second laws, so it would be redundant to state this as an axiom. In the succeeding three centuries commentators have generally accepted this as a valid deduction, so it is rather brave of Grenier to imply that Newton got this wrong! It's worth noting that when Newton talks about "force impressed" in this corollary he means in modern terms an impulse. It certainly follows from the 1st and 2nd laws that if two impulses are applied in quick succession the motion will be close to the diagonal of the parallelogram, in fact arbitrarily close as the time of application gets arbitrarily small. Newton does not spell this out in so many words but it is implicit. Mathematicians today might niggle about the difference between "simultaneous" and "with an infinitesimal delay" but physicists will not. Also, I suspect that the superposition of forces was already widely understood in the context of statics long before Newton, but I don't have time to check that. PaddyLeahy (talk) 11:24, 10 February 2022 (UTC)

Symbols definition

Please define the symbols used in equations. dv/dt, what do they mean? Do not assume the reader knows what you know. Even in textbooks symbols are explained. Much more in Wiki, which is for the general public. — Preceding unsigned comment added by George Hearth (talk • contribs) 04:37, 1 March 2022 (UTC)

Third law

"For example, consider a book at rest upon a table. The Earth's gravity pulls down upon the book. The "reaction" to that "action" is not the support force from the table holding up the book, but the gravitational pull of the book acting on the Earth"

What if we remove the table? — Preceding unsigned comment added by Tireatute (talk • contribs) 09:52, 23 May 2022 (UTC)

My "opinion":

1. "at rest": the book is not "at rest" on the table regarding gravity. It is "at rest" in horizontally directions and "stationary" in vertical direction, being equally subject to gravity in one direction and to the resistance of the table in the opposite direction.

2. Actually; the "gravitational pull" allegedly opposing to the fall of the book is the negation of gravity, as it is considered to be equal to it and acting in the opposite direction: G- Gp = 0

3. If we remove the table, the book will fall to the floor, on which it will stop and stay stationary. During its fall (in the void), its resistance to it is only proportinal to its inertia / own mass. — Preceding unsigned comment added by Tireatute (talk • contribs) 10:21, 23 May 2022 (UTC)

@Tireatute: “What if we remove the table?” No problem, the situation remains unchanged. The book accelerates towards the centre of the Earth in response to the force of gravity (weight) that the Earth exerts on the book, and the book exerts a similar force (identical in magnitude but opposite in direction) on the Earth. Newton’s third law of motion applies to all forces in all situations regardless of whether the two bodies are separated by a distance that is constant or changing at a fixed rate or accelerating. Dolphin (t) 13:02, 10 July 2022 (UTC)

Woops i think someone forgot basic structure design here ;)

I'd say whatever is under the book keeps it from falling down any further because the materials it is made of are offering a resistance equal to -or greater than Earth's gravity without breaking apart. I am not saying that the mass of the book doesn't generates a gravitational pull of totally neglectable magnitude, it does, but when you think of it, the book's own gravity pull does not prevent the book from falling down further, quite the contrary: it adds to the gravity pull of the Earth on the book (the book tries to pull the Earth upwards wich makes the total force of the attraction slightly greater than without the book). I think the book example in the article is meant to be an analogy to the Moon or something in orbit but sorry, badly chosen for that in my opinion: something in orbit has other means of resisting to Earth's gravity pull than a table !

We could take the book + table example further (out of topic you could say) and explain that the floor under the table also plays a role, then again this floor is held by the ground and eventually it comes down to that one thing: does the ground breaks under the total weight of the "structure" or is it capable of resisting it. You need to do some stress tests to determinate how much pressure (pascal or other unit) it can withstand and design the foundations accordingly. This design process should suffice without having to take into account the gravity pull the whole structure is exerting on earth. Plus you should take G=10m per sec just as a precaution, since 9.81 or 9.80xxx is actually only a matter of norms and doesn't represent the exact mesure at the structure's location (in English: depending on where you mesure gravity at ground level on Earth, you might get different values, so you take the worst possible value as a security factor). But again: totally out of topic. 80.215.157.141 (talk) 20:14, 12 July 2022 (UTC)

I'm sorry to say I'm not able to follow this discussion or how it relates to the contents of the page. What specific change is being proposed to this article, and why? - Astrophobe (talk) 22:11, 12 July 2022 (UTC)

This discussion thread begins with a quote from our article: “For example, consider a book at rest on a table.” The quoted sentences are correct and accurate. No change to the article is required or warranted. All good. Dolphin (t) 05:29, 13 July 2022 (UTC)

The Incomplete Newton's Third Law of Motion

The weak form of the Newton's third law of motion ignores one of the independent aspect of the law. It's collinearity. The forces between the two objects must not only be equal in magnitude, opposite in direction, but also must be along the line connecting the representative points of the two particles. The Newton's third law says that the objects do not exert forces on each other in such a way that the forces are not collinear. Natha.rahul (talk) 16:44, 12 August 2022 (UTC)

The article introduces the laws in terms of pointlike or particle masses, so collinearity is guaranteed. Then it explains thinking about extended bodies as collections of particles, and what the center of mass is. I don't think we need to elaborate more. XOR'easter (talk) 17:17, 12 August 2022 (UTC)

Wikipedia acknowledges Euler's laws of motion which are applicable to rigid bodies. Euler’s laws play a role because Newton’s laws of motion are stated to apply only to particles. Collinearity is therefore an important constraint in Euler’s laws of motion. Dolphin (t) 02:35, 13 August 2022 (UTC)

That article does not mention collinearity anywhere, but it does discuss torque, which is definitely not collinear. SpinningSpark 11:35, 13 August 2022 (UTC)

And as it says, Euler's laws can be derived by integrating Newton's laws over particle distributions. XOR'easter (talk) 16:14, 13 August 2022 (UTC)

Article needs simplification

The laws here are explained as if the reader is an undergraduate, while most people that read this article are either teachers or primary/secondary/high school students. No wonder why people hate physics. The information here should be presented in the article in a more reader-friendly manner. CactiStaccingCrane (talk) 18:56, 14 August 2022 (UTC)

Just to be clear, the technical info should NOT be removed, but that the explanation should be more gradual and accessible. See also: WP:TECHNICAL. CactiStaccingCrane (talk) 18:57, 14 August 2022 (UTC)

Why shouldn't teachers be expected to understand material taught in the first year of college? For that matter, why are we out of compliance with WP:GENERAL-ADVICE-TAKEN-AS-GOSPEL-BECAUSE-IT-HAS-A-CAPITALIZED-SHORTCUT if the intro is written at a high-school level and the article gets somewhat more advanced from there? Nothing in the discussion of derivatives, vectors, etc., would be out of place in AP Physics. It might be more terse than an AP Physics textbook, but it's an encyclopedia article, not a handholding introduction from scratch. (Indeed, policy forbids a lot of the kind of writing which that would entail.) XOR'easter (talk) 19:38, 14 August 2022 (UTC)

I agree. However, I think our explanation on the article right now isn't the best as it can be. CactiStaccingCrane (talk) 09:49, 15 August 2022 (UTC)

Simplification kills meaning - it's a wrong concept that everything should be explained in the level of 5 years old child. It's an encyclopedia article, it should be rigor in its explanation. And yes, every teacher should understand derivatives, if that's the only problem with the article. Artem.G (talk) 20:24, 14 August 2022 (UTC)

I acknowledge the principles at WP:Make technical articles understandable but we are also reminded that Wikipedia is not a textbook or guide book – see WP:NOTGUIDE. User:CactiStaccingCrane should also become familiar with the Simple English Wikipedia; it may be better suited to the primary and secondary students they have in mind. The Simple English Wikipedia has an excellent article titled "Newton's Laws of Motion". Dolphin (t) 04:41, 15 August 2022 (UTC)

Newton's second law

Contrary to what is said in the article, Newton's second law does not state an equality of force and change in motion but rather a geometric proportionality. Note that geometric proportionality connects natural entities such as force and change in motion only insofar as they are of a different kind (see Newton, Principia (ed. 1713), Book 1 Sect. 1, Scholium after Lemma X). Consequently, the Newtonian interrelation between force and change in motion can never result in just '1' or any other mere number. Ed Dellian2003:D2:9705:8928:892A:6C7B:3FA0:A602 (talk) 15:28, 21 April 2022 (UTC)

Please phrase your edit request using particular suggested changes to the article with reference to reliable sources which support that change. This message does not make it clear what change you are suggesting or why. - Astrophobe (talk) 19:03, 21 April 2022 (UTC)

"Newton's second law does not state an equality of force and change in motion but rather a geometric proportionality." Really? The authors of hundreds of reliable published sources will disagree. Considering the nature of Ed Dellian's claim it is clearly unsatisfactory to say to readers "See Newton's Principia, Book 1, Sect 1" etc. If Ed wants to be taken seriously he needs to provide the essential text for readers to peruse, not imagine that all readers have a copy of an English translation of the Principia on their bookshelves. Dolphin (t) 12:36, 22 April 2022 (UTC)

The Principia is accessible online, eg gbooks relevant passage. The Scholium referred to seems to me to be merely Newton defining what is meant by proportionality. I'm not sure how anything deeper is to be read into that. SpinningSpark 12:53, 22 April 2022 (UTC)

The changes between Newton's original statements and what we now consider "Newtonian" mechanics are a rabbit hole of considerable depth. It's true that Newton himself didn't write the second law as $F=ma$, for example, that being due to Hermann and Euler some time later [1]. It's also true that getting deep into that in Section 1 of an article like this would be a pointless distraction. XOR'easter (talk) 17:13, 22 April 2022 (UTC)

Once again: It is not true that Newton stated an equality of force and change of motion in the second law. The law reads in Newton's original Latin: "Mutationem motus proportionalem esse vi motrici impressae". In English: The change in motion is proportional to the impressed force. "Proportional" is not "equal". Proportionality belongs to geometry, equality belongs to arithmetic. If A and B are proportional, you get A/B = C = constant. If A and B are equal, you get A = B; no constant! This is so clear that it would be up to the dissenters to prove me wrong. In any case it would be correct here to write that the formula F = ma is not Newton's but Euler's. He introduced it to the scientific world in Berlin on Sept. 3, 1750, as his "Découverte d'un nouveau principe de Mécanique" (see Mem. Acad. Roy. Sci. Berlin vol. 6 1750 (1752) pp. 185-217). 2003:D2:971D:DF15:110B:B215:C49C:BD45 (talk) 13:53, 1 January 2023 (UTC)

The standard for inclusion in Wikipedia is verifiability; not truth. Wikipedia’s mission is to present information that is provided in reliable, published sources. It is not part of Wikipedia’s mission to arbitrate on what is correct, and what is not. The information published here about Newton’s second law is taken from reliable published sources. The best place for you to raise your concerns is in a peer-reviewed journal; if your ideas are accepted by the Physics community they will quickly find their way into reliable published sources, and ultimately into encyclopaedias. Dolphin (t) 00:01, 2 January 2023 (UTC)

Thank you, Dolphin. Well, I would say the best source to inform about Newton's formulation of the second law is Newton's Principia. The correct Wikipedia information of the public would be to point to the fact that the secondary sources attribute to Newton a "second law" which however is not his but Euler's (according to the quoted primary sources). To assert that Newton (Newton! Not Euler?) put change in motion and impressed force "equal" is simply false, even though one finds this evident misinterpretation in every physics textbook around the world. 2003:D2:971D:DF15:110B:B215:C49C:BD45 (talk) 07:23, 2 January 2023 (UTC)

Read WP:PRIMARY, particularly policy #4. SpinningSpark 14:33, 2 January 2023 (UTC)

The relevant source for what an author has written is the author's work, of course, at least if there is no space for "interpretation". And there is none, since Newton's wording "proportional" does certainly not mean "equivalent" or "equal" according to the generally accepted mathematical language. Nevertheless, I can even refer to a prominent "secondary source": Max Jammer, Concepts of Mass in Contemporary Physics and Philosophy, Princeton University Press, Princeton (NJ), 2000, pp. 5, 12, 17. ("Newton's second law, in Euler's formulation..."). 2003:D2:971D:DF51:1DFA:78C4:D591:5836 (talk) 17:58, 2 January 2023 (UTC)

The issue here is not what Newton said, but what is meant by the modern conception of the law. You cannot cite Newton for that. Nor can you use Newton to interpret the law – because Newton is primary. Having said that, I tend to agree with you. When I was at school, we would always say "proprtional" because with the system of units in use at the time there really was a constant of proportionality in the 2nd law. Actually, there still is with SI units. It's just hidden because it happens to be unity. SpinningSpark 14:57, 3 January 2023 (UTC)

We agree that there is a modern conception of the law for which one cannot cite Newton (one could cite Euler). It is my point of criticism, however, that the article does just that, citing Newton, that is, by writing "When a body is acted upon by a force, the time rate of change of its momentum equals the force". This to attribute to Newton is simply wrong. I wonder why Wikipedia doesn't clear the point by informing the user that Newton's authentic second law differs (in several respects) from its modern conception?- By the way, Wikipedia is certainly not the place to discuss the question what Newton really meant with his authentic second law. I just want to point out that I have been publishing a lot on this question since 1985, in German and in English (cf. my paper "Inertia the innate force of matter a legacy from Newton to modern physics", in P. B. Scheurer and G. Debrock, Newton's Scientific and Philosophical Legacy, Kluwer Academic Publishers, 1988, pp. 227-237). So I do know that you are absolute right: One cannot cite Newton for what is erroneously called "Newton's second law" in modern textbooks! 2003:D2:971D:DF51:1DFA:78C4:D591:5836 (talk) 09:09, 4 January 2023 (UTC)

Again, you can't cite Euler as the orginator of the F=ma form. You need an independent source to verify that. However, note that the article already discusses Euler's role at Newton's laws of motion#After the Principia. SpinningSpark 10:33, 4 January 2023 (UTC)

The matter is - as you already have admitted! - that "one cannot cite Newton" for the modern conception of the "second law". This, and only this, is my point of criticism. - As to Euler, by the way, I have already cited the independent source you ask me for: It is Max Jammer, Concepts of Mass in Contemporary Physics and Philosophy. Here is another one: Giulio Maltese, La Storia di 'F = ma' ", Firenze 1992. On p. 197 he writes: "La seconda legge del moto in forma moderna fu enunciato per la prima volta nel 1750 da Eulero". In English: The second law of motion in modern form was for the first time published by Euler in 1750. 2003:D2:971D:DF51:1DFA:78C4:D591:5836 (talk) 11:21, 4 January 2023 (UTC)

I'm not disputing this can be cited, I was replying to your statement "one can cite Euler" for something alleged to be due to Euler. But I now see that does not really seem to be your point. Perhaps you didn't mean "cite" in the sense of a verifying reference. If I understand you correctly, you are objecting to F=ma being called Newton's 2nd law at all. Well, get over it, rightly or wrongly that is what it is called. Our guideline WP:COMMONNAME and the essay section WP:Righting Great Wrongs are relevant here. SpinningSpark 12:16, 4 January 2023 (UTC)

There is a difference between a formula "being called Newton's second law", or "being Newton's second law". My point of criticism is that the WP article insinuates the latter (contrary to better knowledge). - I confess it my "fault" to believe that a primary source like Newton's "Principia" would serve best to show what Newton actually has written. So I must look for secondary sources, which, however, is not really a problem. There are many many many sources that state, for instance, what can be read in the most prominent American historian of science, the late I. B. Cohen's, "Guide to Newton's Principia" (published together with his and Anne Whitman's most prominent modern English Principia-Edition, Berkeley 1999). On p. 111-117 Cohen demonstrates in all detail what he initially says, namely that "Newton's second law ... sets forth a proportionality between 'force' and the resulting 'change in motion'" (my emphasis). Therefore, to insinuate that the equality F = d(mv)/dt would be, or "is" Newton's law, is equally false as to say that, for instance, Planck's formula E = hf would read "energy equals frequency". 2003:D2:971D:DF51:1DFA:78C4:D591:5836 (talk) 14:23, 4 January 2023 (UTC)

Incorrect statement of the Third Law

The statement "If two bodies exert forces on each other, these forces have the same magnitude but opposite directions" does not rule out the possibility that only one body exerts a force on another. The traditional statement is that "for every action," etc., (with no exception). The statement should begin with something like "if one body exerts a force on another...." Marty39 (talk) 17:57, 26 December 2022 (UTC)

I agree. The cited source is Thornton and Marion (2004). Can someone clarify exactly what is said in this source? Dolphin (t) 21:28, 26 December 2022 (UTC)

The direct quote from Thornton and Marion is If two bodies exert forces on each other, these forces are equal in magnitude and opposite in direction. They follow it up with a discussion of the subtleties that arise when you have fields carrying momentum. Their choice of phrasing seems rather deliberate. For a long time, the statement of the laws in the intro here was lifted from them verbatim (attributed, but with no indication that the sentences were taken word-for-word). They've been lightly edited since. XOR'easter (talk) 23:59, 9 January 2023 (UTC)

inappropriate intro

"Limitations to Newton's laws have also been discovered; new theories are necessary when objects move at very high speeds (special relativity), are very massive (general relativity), or are very small (quantum mechanics)."

I fail to see any Limitations to Newton's laws of motion. All three special relativity, general relativity and quantum mechanics completely respect these laws, AFAIK. They found limitation sin Newton's law of gravitation, the way energy was understood, and take into account forces Newton was unaware of, etc. but this is not what this article is about. 2A01:E0A:1DC:4570:A189:BEB6:DAAB:405F (talk) 13:27, 14 May 2023 (UTC)

I agree. The sentence in question is not adequately supported by Sections 8.3, 8.4, and 8.5. The lead is expected to be a summary of material presented in detail, and with citations, later in the article. This sentence goes beyond what is presented in 8.3 - 8.5. Dolphin (t) 23:22, 14 May 2023 (UTC)

Wiki Education assignment: 4A Wikipedia Assignment

This article was the subject of a Wiki Education Foundation-supported course assignment, between 21 August 2023 and 16 December 2023. Further details are available on the course page. Student editor(s): Meme2611 (article contribs). Peer reviewers: Tortuga424, Elkinhernandes.

— Assignment last updated by Kmijares (talk) 22:40, 15 November 2023 (UTC)

It's probably a bad idea to attempt a significant rewrite of one of the most highly-visible physics articles on Wikipedia without first becoming thoroughly conversant with rules like Wikipedia not being a textbook. Language like Simply put, Understanding Inertia through Everyday Examples, To delver [sic] deeper, let's explore, etc., is suitable for other places, but not here. XOR'easter (talk) 20:19, 15 November 2023 (UTC)

Special relativity

Why my edit has been removed ? All I wrote was clearly cited in sources, correct and used in accelertors physics. It is very usefull to calculate the power radiated by a relativist charge which depend on acceleration magnitude and well kwown since ages. That's too bad that this relativist expression of the second law does not appear in this article. Here is an extract of a french Lecture where all the calculus are detailed and correct. https://physique.cmaisonneuve.qc.ca/svezina/nyc/note_nyc/NYC_XXI_Chap%204.9b.pdf — Preceding unsigned comment added by Jlpons (talk • contribs) 05:23, 5 December 2023 (UTC)

This edit [2] was cited to a non-peer-reviewed arXiv preprint, which is not a suitable source for our purposes. The other added content [3] was not in the source provided. More specifically, the first formula appears on a different page, and the second line doesn't appear anywhere. Page 299 discusses motion in a single spatial dimension, so the statement about the angle between the speed direction and the acceleration direction doesn't make sense. I don't have a fundamental objection in principle to having more formulae in that section, but we'd have to write the treatment very clearly, and at the moment it seems to me that details of that sort are better suited for an article like Relativistic mechanics. XOR'easter (talk) 19:46, 5 December 2023 (UTC)

You're right in [2] for the perpendicular acceleration, the centripetal acceleration is used instead just after. The formulas I wrote are correct and the acceleration magnitude well depend on the angle between acceleration (or force if you prefer) and velocity. This is why, for a same force, a charged particle emits $\gamma ^{2}$ times less when the acceleration and speed are paralell. This is a well know result that you can find in any accelerator physics book.

Unfortunately, this formula is "too obvious" to be fullly developped except in few lectures as i mentionned.

I didn't mentionned that the source from arXiv was not published, to be honest when i read it, I was a bit surprised that such a job could be published as it is already well known.

Do what you want, if want to reaad this formula or not. From my point of view this could be a nice illustration and could show that the second law is still usefull even in special relativity... Jlpons (talk) 20:15, 5 December 2023 (UTC)

Because this is a big-picture kind of article, it might make more sense to say something like, "The relativistic version of Newton's second law is used in accelerator physics, for example" and link to another page for the details. XOR'easter (talk) 20:23, 5 December 2023 (UTC)

If you want to have a look at what we have in accelerator physics books, you can have a look at this one:

https://cds.cern.ch/record/398429/files/p437.pdf

where the underlying calculus are not explicit and you just have the results

In page 3, "Thus, for the same applied force (dp/dt) the power radiated is a factor of γ2 larger than for linear motion" which is a direct consequence of what i cited in my french citation above where all calculus are detailed for student. Jlpons (talk) 20:55, 5 December 2023 (UTC)

A link in english where paralell and perpendicular force are well explained in special relativity. The notations i used are also used in eq (7) and eq (10) and the full Newton second law eq (3) is writen using ${\vec {\beta }}={\vec {v}}/c$ but very easy to replace. This is very very basic stuff.

https://makingphysicsclear.com/force-and-acceleration-in-special-relativity/

The aim of Wikipeida is also education, no ? Jlpons (talk) 10:57, 6 December 2023 (UTC)

Just because Wikipedia aims to educate doesn't mean that we should include every way of writing Newton's laws (or every application of Newton's laws, or every notation for Newton's laws) in this specific article. Unless we take care to organize what we write, we end up with articles jammed with distractions that treat minor details as more important than central ideas, and no one learns anything. Some things belong in Newton's laws of motion, while others fit better into Relativistic mechanics or Larmor formula or Synchrotron radiation. Your first source, the chapter on synchrotron radiation, would by itself suggest that this fits into one of the latter two: it presents the results for a specific application without details of how they were derived. The mindset is "here is the power radiated by a moving electron" rather than "this is the way to think about Newton's second law in special relativity". The second is somebody's personal hobby website, which we have to use with care. (I mean, I'm a physicist and I could make a blog about something I think is interesting, but that by itself wouldn't be reason to justify a section on it in the most visible physics article on Wikipedia.)

Like I said earlier, I don't yet have a firm opinion about whether or how to expand that section. I'm just thinking about what would be most pedagogically useful. XOR'easter (talk) 16:29, 6 December 2023 (UTC)

That's too bad. You have a section "relation to other theories" and this would perfectly fit even without without speaking about synchrotron radiations or Larmor formula or other more complex stuff. Just to say how the special relativity impacts the second law. There are already few nices sentences in the article that could be completed with 2 or 3 formulas and why not a nice plot.

I gave you 2 sources that well explain this and only this with all the derivation fully explained. I agree that my 2 first sources was not very appropirate but it is difficult to find online sources of such basic stuff. Jlpons (talk) 18:15, 6 December 2023 (UTC)

The equation I gave are well detailed in this wiki articleAcceleration_(special_relativity)#Acceleration_and_force

They did a full decomposition for the transverse plane and the longitidinal axis.

I would suggest to rewrite the equation (4b) in the format of this article for better undertsanding and link to the above article section.

What do you think ? Jlpons (talk) 04:15, 7 December 2023 (UTC)

I kind of like (4d) more than (4b), but either way, they'd need supporting text. We don't want to drop a formula on the reader without explaining why it's important and what all the symbols in it mean. And it's worth noting that the "Special relativity" section here already links to Relativistic mechanics, which is where Acceleration (special relativity) says to look for more information. The big question, I think, is what conceptual point needs to be explained that the section currently doesn't, and which equations (if any) are obligatory to get that point across? (I'm looking at the discussion in Chapter 7 of French's Special Relativity, which suggests some possible points to emphasize, as does Chapter 5 of Rindler's Essential Relativity, but sampling a few more textbooks might be helpful here.) XOR'easter (talk) 06:14, 7 December 2023 (UTC)

From my point of view the important point to notice here is how the special relativity impacts the second law and that the acceleration magnitude is also impacted by the angle between force and velocity.

A common mistake is to think that ${\vec {p}}=\gamma m{\vec {v}}$ can be simply derived to ${\vec {F}}=\gamma m{\vec {a}}$. I know that the article mention that $\gamma$ is also a function of the velocity but a formula and an appropriate link can help to clarify.

Thanks ;) Jlpons (talk) 08:13, 7 December 2023 (UTC)

Third Law explanation is wrong

Text: .../..."For example, consider a book at rest on a table. The Earth's gravity pulls down upon the book. The "reaction" to that "action" is not the support force from the table holding up the book, but the gravitational pull of the book acting on the Earth."

This is complete nonsense to me. If you push against a wall, it becomes clear that all at the contrary, it is the "support force" that comes into play. The example of gravity is totally irrelevant and wrong as a general statement. 141.135.7.88 (talk) 20:45, 13 December 2023 (UTC)

Can you please clarify what the objection is exactly? Based on what you've written here, I can't quite wrap my mind around what the disagreement is. How would you re-word the text to make it correct? - Astrophobe (talk) 21:02, 13 December 2023 (UTC)

It's well explained in the following link, and it is the opposite of what is shown in Wikipedia: https://www.britannica.com/science/Newtons-laws-of-motion 141.135.7.88 (talk) 16:40, 18 December 2023 (UTC)

That's actually not a good explanation, because there are three bodies of importance in this example: the table, the book, and the Earth. That means there are three pairs to consider: book-Earth, book-table, and table-Earth. Our page is talking, correctly, about the book-Earth pair. The Britannica article is talking about the book-table pair. Remember, the action and the reaction have to be on two different bodies. The weight of the book and the support force from the table upon the book are two forces on the same body. (The Britannica article also suffers because it tries to explain both the third law and mechanical equilibrium at the same time.) XOR'easter (talk) 17:12, 18 December 2023 (UTC)

I think you're mixing the third law and mechanical equilibrium. Both give equal and opposing forces, but for very different reasons. To see the difference, consider a situation where the table is not rigid, but is made of some viscous material: when gravity acts on the book and the book pushes on the table, the table slowly deforms and the book slowly accelerates downwards. In this case the normal force acting on the book does not equal the gravity, and it is clear that those two forces cannot be identified as the action-reaction pair. Jähmefyysikko (talk) 21:05, 13 December 2023 (UTC)

See example 5.9 in the OpenStax University Physics volume 1. And try working out the free body diagram for the book, the table, and the Earth. Compare that to the free body diagrams for your example of a person pushing against a wall. XOR'easter (talk) 22:07, 13 December 2023 (UTC)

I disagree with the original assertion although I concede that this situation confuses many people, particularly students who are new to Newton’s laws of motion. Newton’s third law seems to be easily comprehended in the case of a pair of contact forces. However, gravitational forces (weights) are body forces so there is often no point of contact between the two bodies.

For example, the sun exerts a large force of gravitational attraction on the planet Neptune; and Neptune exerts an identical force of gravitational attraction on the sun, even though these two bodies are a very, very long distance apart. (The two forces are identical in magnitude but opposite in direction.) These observations are entirely compatible with Newton’s third law of motion. This situation is identical in principle to the example of a book resting on a table except that in the case of the sun and Neptune, there is no table, or any other object, between the sun and the planet, touching both.

In the case of the sun and Neptune, these two objects are constantly accelerating towards each other (centripetal acceleration), but in the case of the book and the Earth, the two are not accelerating towards each other because of the presence of the table. Newton’s third law applies equally in both cases. This law applies to all pairs of forces, regardless of whether the bodies involved are accelerating or not. Dolphin (t) 07:30, 14 December 2023 (UTC)

Also see Action at a distance. Dolphin (t) 20:41, 14 December 2023 (UTC)

The second law is incorrectly defined

The second law should be words to the effect that the force is equal to the rate of change of momentum. As it is stated, it is only true for constant mass. I appreciate that variable mass is discussed later, but the statement of the law should be in its most general form. JohnoOz (talk) 02:51, 16 December 2023 (UTC)

The statement in the introduction did refer to the rate of change of momentum until this edit. I would (and did) write it in terms of momentum instead of acceleration, but I don't think there's a great difference either way. Both momentum and acceleration are everyday words loaded with a technical meaning of basically the same conceptual difficulty. Neither form is more general for any Newtonian purposes; "changing mass" is just bits of matter moving about. XOR'easter (talk) 03:19, 16 December 2023 (UTC)

Hi XOR’easter. I challenge your suggestion that the word momentum, with its scientific meaning, is an everyday word. Momentum equal to mass times velocity is not in our popular language. The more common description of Newton’s second law involves mass times acceleration, and there are many reliable published sources to support this description. WP:Make technical articles understandable, MOS:INTRO and similar sources of guidance advocate that, wherever possible, the introduction to an article should be written in a way that can be understood by the widest possible audience. This suggests the lead should use “mass times acceleration”. Later in the article it is reasonable to use more esoteric concepts such as “time rate of change of momentum” and systems of varying mass. Dolphin (t) 04:22, 16 December 2023 (UTC)

I didn't say that "momentum, with its scientific meaning, is an everyday word". I said that the everyday meaning of momentum is about as close to the technical meaning as the everyday meaning of acceleration is to its technical meaning. Acceleration being the second derivative of position is not exactly "in our popular language" either. (For that matter, the physics meaning of mass is not the everyday meaning.) I don't think "the widest possible audience" would get much more or much less from either version. MOS:LEAD might even suggest that we do both together. ${\vec {F}}=m{\vec {a}}$ is the more common opening gambit, ${\vec {F}}=d{\vec {p}}/dt$ has the older pedigree, and the main text of the article covers both. Right now, there's a discrepancy that MOS:LEADREL would suggest we resolve, e.g., by adding "Equivalently. ..." to the lead's summary of the second law. XOR'easter (talk) 14:31, 16 December 2023 (UTC)

XOR'easter: You have written "${\vec {F}}=m{\vec {a}}$ is the more common opening gambit". I agree with that, and I think it is highly relevant to the current discussion because it points to what should be stated in the lead of this article.

The first derivative of velocity; and the second derivative of position, are relevant to Newton's second law but fortunately we have the word acceleration as a widely-understood alternative, so the Second law can be made accessible to readers who understand "acceleration" but have no understanding of calculus. On the other hand, the time derivative of momentum has no widely-understood alternative except perhaps "time rate of change of momentum". If the lead describes the Second law in terms of momentum it is only accessible to readers who understand both momentum and calculus. Guidance material related to the lead urges us to make the lead understandable by the widest possible audience. Information that is more technically rigorous and historically accurate can be presented later in the article. Dolphin (t) 11:58, 18 December 2023 (UTC)

"The rate at which momentum changes" or even just "the change in momentum" could be workable at the level of a verbal paraphrase, which is what the intro promises. And the everyday meaning of acceleration is different enough from the technical (only really including getting faster and not slowing down or changing direction), so relying upon it is questionable. XOR'easter (talk) 15:05, 18 December 2023 (UTC)

I don't usually comment on these things (hence no username), but this edit seems particularly egregious to me. When I saw the wording, and that the citation was Marion and Thornton, I went straight for my copy (4th ed.). The wording in my edition is roughly that the time rate of change of momentum equals the force acting upon a body. The force is described as "acting upon" a body. That's an external force. (In addition to what I say below, if we cite Marion and Thornton, I think it's most honest to actually cite what they have given rather than our own interpretation of it. Marion and Thornton had their reasons for stating the second law as they have.)

Consider the two possible statements of the law:

(1) the time rate of change of momentum equals the force applied to a body.

(2) mass times acceleration equals the force applied to a body.

Technically speaking, if we interpret the force purely as an external force (1) is more general than (2) as (2) is only correct for constant mass. I agree that (1) and (2) are equivalent if for (2) we also consider internal forces acting between parts of a body. (I understand that what is or is not one body is somewhat arbitrary).

To reproduce conservation of momentum as a theorem derivable from the second law you either need to have (1), or (2) along with a consideration of the internal forces.

Consider the rocket equation as an example of this (sec. 2.7 in Marion and Thornton, 4th ed.). If you have (1) there are no external forces. So the time rate of change of the momentum is zero, and you only need to consider the total momentum of the system as the rocket expels mass as propellant. If you only have (2) then you'll also need to consider the force of the rocket on the propellant, and conversely the force of the propellant on the rocket (the internal forces) making the problem much more difficult.

While you might understand that the two versions of the law are equivalent, from a mathematical point of view which wants to clearly see the internal logic of Newtonian mechanics (rather than a purely "shut up and calculate" point of view) these distinctions do matter. 2600:1700:97E0:BC60:31E5:BA35:C9BA:3685 (talk) 21:22, 17 December 2023 (UTC)

At one point, the wording was taken verbatim from Marion and Thornton, with a citation but without any indication that the wording was actually verbatim. XOR'easter (talk) 03:04, 18 December 2023 (UTC)

I have inserted an in-line citation (Resnick & Halliday) to support description of Newton’s second law as F=ma.

As I read through this discussion thread I see a number of contributions from people who seem to be advocating that this article, and its lead in particular, should be written in a style that is pleasing to college graduates and professional scientists. I remind everyone that Wikipedis is not a textbook or scientific journal. At MOS:INTRO it emphasises that the lead to an article should be written so it is understandable by the widest possible audience. When a lead is written in this way it will inevitably conflict with some of the principles currently applying to the writing of textbooks and scientific journals.

I think this discussion thread has taken the exchange of ideas about as far as it can. If anyone wishes to further explore the subject of the article lead, I think the best way will be to make use of the Request for Comment. This process will run for about a month and will attract !votes of either Support or Not Support from a significant number of Users. Dolphin (t) 04:35, 19 December 2023 (UTC)

I don't think that saying "momentum" instead of "acceleration" will make the difference between an article comprehensible to, say, high-school students and an article "pleasing to college graduates". The idea that MOS:INTRO by itself makes a case one way or the other in this instance just doesn't make sense to me. If anything, the ethos of being as clear as possible while providing a capsule summary of the whole article that follows would mean doing it both ways. (The fact that Wikipedia is not a scientific journal seems beside the point. An article in a scientific journal wouldn't waste time explaining introductory physics. Likewise, the fact that Wikipedia is not meant to be a textbook actually means that we don't need to phrase things exactly like a textbook would or go through things step-by-step the way that textbooks do.) Coming at the question from the perspective of someone who has taught the subject: sometimes there's no way to make the explanation simple enough, while sometimes, the "advanced" explanation is what makes the lightbulb finally go off. XOR'easter (talk) 07:20, 19 December 2023 (UTC)

An additional point not related to pedagogy: momentum is one of the central concepts which Newton introduced when formulating his laws, and features prominently in this article. Not having it in the introduction would be an omission. I agree with the solution proposed by XOR'easter. Jähmefyysikko (talk) 09:57, 19 December 2023 (UTC)

The statement should be defined in terms of momentum. A statement equivalent to F = ma is wrong if the mass is not constant (e.g. a rocket taking off). Newton's original statement was that force is proportional to the rate of change of momentum. Ok, our units allow us to put equals instead of proportional, but the next step is f = d(mv)/dt. If (and only if) 'm' is a constant, then it can be taken outside the differential to give F = m dv/dt or F = ma (which is the form in which you first meet it at school). Otherwise, the statement F = ma is incorrect. I learnt this a bit later on at school and well before I did my physics degrees. Claip (talk) 19:46, 22 December 2023 (UTC)

Newton's laws of motion vs Newtonian mechanics?

Newtonian mechanics redirects to this page. I would say this page starts out strongly on the Laws, but it does not introduce the concept of a full "mechanics" and the topics there-in. Then it takes a turn and covers some of the mechanics topics and two sections on relations that seem like relations to Newtonian mechanics. Thus to me the page does not fulfill the mission of "Newtonian mechanics" and yet consumes many of its topics.

On the other hand classical mechanics introduces what is essentially Newtonian mechanics without claiming so or being clear that is what it is doing. I would like to compress that content down to a summary so that classical mechanics deals with the overview/relationship.

As simple fix would change "Prerequisites" in this article in to "Newtonian mechanics", explaining that the Laws are the core bits of this larger thing. Johnjbarton (talk) 00:40, 5 January 2024 (UTC)

I don't think "Prerequisites" should be replaced by anything else, as that would just delay explaining what Newton's laws themselves are. XOR'easter (talk) 01:11, 5 January 2024 (UTC)

Yes, well that's fine but the problem remains: where is the explanation of "Newtonian mechanics"?

I'm not proposing to replace the content of "Prerequisites", beyond a sentence or two introducing the Laws their core and renaming the section.

Do you have a proposal for the mechanics problem (no intro and then a bunch of not-really-Newton's-laws content?) Johnjbarton (talk) 01:27, 5 January 2024 (UTC)

I don't think there is a "bunch of not-really-Newton's-laws content". The "Work and energy" section is about how to express force as the gradient of a potential; "Rigid-body motion and rotation" is about how to apply Newton's laws to extended bodies; "Chaos and unpredictability" is about how to rewrite Newton's laws for fluids and some features those laws display; "Relation to other formulations of classical physics" is about how the laws themselves appear in other approaches (rather than all the other things one could say about those other approaches).

I added a line to the beginning of "Examples" that introduces the term "Newtonian mechanics". Calling a section that's all prerequisites except for two sentences "Newtonian mechanics" seems confusing to me; that sounds like a mismatch between heading and content. XOR'easter (talk) 01:39, 5 January 2024 (UTC)

Of course you can say these are all related to Newton's laws, because all of Newtonian mechanics is related to Newton's laws.

There already is a confusion of heading and content, if this page represents Newtonian mechanics. Johnjbarton (talk) 01:46, 5 January 2024 (UTC)

To expand on this issue: almost none of the links that redirect through Newtonian mechanics don't make sense we land on this page. For example:

• In Dynamical systems: "The concept of a dynamical system has its origins in Newtonian mechanics". But the landing gives Laws, not mechanics. I think it confusing this way.

Johnjbarton (talk) 01:44, 5 January 2024 (UTC)

How is clicking on "Newtonian mechanics" and getting "Newton's laws of motion" confusing? I'm willing to suppose that it could be, but I don't believe it's likely to be a problem in practice. But even if there is a potential for confusion there, the problem isn't necessarily with anything in this article itself. Perhaps articles linking to the redirect need revision, or perhaps the redirect itself should point somewhere else. For example, I could see a case for retargeting it to Classical mechanics, which is a term sometimes used synonymously. It might make sense to make the first section of Classical mechanics an overview called "Newtonian mechanics", and follow it up with overviews of other formulations. XOR'easter (talk) 01:49, 5 January 2024 (UTC)

Ok thanks. I think I applied a reasonable fix in the intro.

The article previous connected Newton's laws to classical mechanics, now it says Newtonian mechanics and introduces classical mechanics as the larger topic later in the intro. Johnjbarton (talk) 03:02, 5 January 2024 (UTC)

That seems reasonable. XOR'easter (talk) 03:07, 5 January 2024 (UTC)

Semi-protected edit request on 24 October 2023

Change "A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force." to "A body remains at rest, or in motion at a constant speed in a straight line, except insofar acted upon by a force. Averroes8 (talk) 23:18, 24 October 2023 (UTC)

 Question: Why? The current phrasing seems far clearer to me – I don't think "except insofar acted upon by a force" is even grammatically correct. Tollens (talk) 00:57, 25 October 2023 (UTC)

@Tollens: look a few sections up. This is a tendentious fork of an open discussion. Astrophobe (talk) 01:43, 25 October 2023 (UTC)

Whoops – should've looked. In that case, not done as there appears to be no consensus for the change. Tollens (talk) 02:00, 25 October 2023 (UTC)

I wrote more on the other section, but I'll directly answer your "why" question. Newton wrote the law in Latin: “Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum illum mutare.” Newton never published an English translation. It appears "unless" is not an accurate translation; and "except insofar as" is an accurate translation. (In the other section, I included a link to a new article that argues for why the better translation is more correct.) Darlingm (talk) 22:26, 19 January 2024 (UTC)

Statement of the First Law of Motion should be adapted/modified

As was recently reported in Scientific American, the Motte translation of the First Law used in this article is incorrect. Also the "unless" in the paraphrase should be changed to "except insofar as". The original article pointing this out is Hoek 2023. 2001:468:C80:C105:81EA:C534:C0F0:2602 (talk) 15:59, 1 October 2023 (UTC)

Does changing "unless" to "except insofar as" actually change the meaning, or is that a distinction without a difference? Maybe, but as a native English speaker, "except insofar as" just sounds to me like a longer way of saying the same thing. And reading the Hoek article, he presents what he calls his "strong reading" of the first law as something that has "never been clearly articulated or explicitly defended in print." Since we're here to provide the mainstream/consensus view before anything else, I'm wary of changing a prominent part of this article based on a single paper and a pop-science news item about it. Hoek's discussion of why the "weak statement" and "strong statement" aren't logically equivalent involves calling several previous exegeses of Newton wrong (pp. 63–64) and then getting deep into the weeds about the second law and what Newton meant by terminology that is obsolete now anyway. (The Scientific American story, although better than a lot of pop science, doesn't try to summarize all this, so it's not that great of a secondary reference for Hoek's argument.) This could all be interesting in the "History" section of the article, but when we are first introducing the laws, we should explain what they have come to be, rather than what was on Newton's mind in 1687, which didn't even include $F=ma$.

When I first tried accessing Hoek's paper via the SciAm story, I hit a paywall and had to resort to my university library, but there's an arXiv version that appears to be substantially identical. XOR'easter (talk) 16:57, 1 October 2023 (UTC)

For what it's worth, Cohen and Whitman's excellent 1999 translation of the Principia renders the first law as "Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed." Generally I think Cohen & Whitman is a better translation than Motte, but in this case I tend to agree with @XOR'easter that there's not a big difference in the meaning of the two English translations. I am neutral as to whether the translation in our article should be changed. CodeTalker (talk) 17:55, 1 October 2023 (UTC)

I support changing "unless" to "except insofar as". These are Newton's laws. Newton was the one who decided how to word them. He wrote it in Latin, and it was translated incorrectly. The most accurate translation should be used. As far as if there's a big difference, I don't think that is relevant. Newton said what he said, and it should be worded with the correct translation. But, Science Alert just wrote an article that explains why there is a big difference, why it isn't symantics, and why it's scientifically important and relevant. Rather than paraphrase it and not do it justice, I'd suggest reading the article. Darlingm (talk) 22:16, 19 January 2024 (UTC)

That's not a new story. It's a repost of the same churnalism piece they posted last September. It just repeats Hoek and copies from the Scientific American item already discussed above. A pop-science fluff website like "Science Alert" is not a reliable source for a serious question about the history and philosophy of physics. XOR'easter (talk) 22:36, 19 January 2024 (UTC)

The text erroneously implies that Newton's second law in the form F = dp/dt is valid for variable mass systems.

In the main text, it states, 'If the mass does not change with time, then the derivative acts only upon the velocity, and so the force equals the product of the mass and the time derivative of the velocity, which is the acceleration.' This implies that the equation F = dp/dt is applicable to variable mass systems. However, it is not. To see why, realize that if it did apply to variable mass systems, then the equation could be rewritten as F = vdm/dt + ma, which is not Galilei-invariant. This also contradicts the correct equation F = ma - udm/dt, where u is the velocity of the exhaust relative to the rocket. NameIchose (talk) 23:03, 28 January 2024 (UTC)

I agree with Namelchose. Objects of variable mass, such as a rocket or a jet-engine aircraft, must be analysed in a slightly different way. My reference is Resnick and Halliday (1966) Physics, Section 9-7 “Systems of Variable Mass”. Dolphin (t) 23:40, 28 January 2024 (UTC)

Press the link labeled "edit" ;-) Johnjbarton (talk) 00:04, 29 January 2024 (UTC)

Also see Variable-mass system. Dolphin (t) 23:54, 28 January 2024 (UTC)

suggestion to add this sentence

In fluid mechanics Newton second law is called the linear momentum equation. Can anyone add this point to this wiki article. I found this point in Fluid mechanics Frank M White 7th edition pg:140 — Preceding unsigned comment added by B.NIROSHAN (talk • contribs) 09:36, 26 February 2024 (UTC)

Proportionality

Newton's second law states a "proportionality" between impressed force and change in motion. Why does the article replace the term "proportionality" by "equality"? Note that a proportionality of quantities A and B reads A/B = C = constant, which is clearly different from the equality A = B = A. 2003:D2:972D:D312:5467:1AF8:F3D8:6E2E (talk) 19:37, 1 March 2024 (UTC)

The article quotes the 2nd law using "proportionality". Newton's Definition #2 defines momentum. The modern forms in the article are paraphrases as is clearly stated. I added a ref to Feather, Norman. An Introduction to the Physics of Mass, Length, and Time. United Kingdom, University Press, 1959. Johnjbarton (talk) 22:09, 1 March 2024 (UTC)

Any proportionality can be converted to an equality by the use of the constant of proportionality. If A is directly proportional to B, the equation can be written:

$A=B\times k$ where k is the constant of proportionality.

For example, in the English engineering system of units, the force and the mass are both measured in pounds, the acceleration is measured in feet per second squared, and the constant of proportionality is the reciprocal of g_c which is 32.17 ft/s².

$F={\frac {m}{g_{c}}}\times a$ where F is a force in pounds (lbf), m is a mass in pounds (lbm), and a is an acceleration in ft/s². A force of 1 lbf is required to give a mass of 1 lbm an acceleration of 32.17 ft/s²

An alternative is to define a new unit of force so the constant of proportionality is unity and so can be ignored. This has been done in SI units by defining the newton as the unit of force so that a force of 1 newton is required to accelerate a mass of 1 kilogram by 1 m/s²:

$F=m\times a$ where F is a force in newtons, m is a mass in kilograms, and a is an acceleration in metres per second squared. Dolphin (t) 05:12, 2 March 2024 (UTC)

Sorry, no. It is not true that "any proportionality can be converted to an equality". For example, take A/B = C = constant, with A = 12, B = 3, C = 4 = constant. A and B are proportional. 2A/2B = 24/6 = 4; 3A/3B = 36/9 = 4, etc.(Euclid's law of equal integer multiples). So how do you obtain A = B ?? Note, by the way, that Newton explains in the Scholium after Lemma X (Principia 1713!) that proportionality deals with "indeterminate quantities of a different kind". So A and B (or "force" and "change in motion") are a priori of a different kind in Newton's teaching, and therefore they can never be equal. 2003:D2:972D:D374:5467:1AF8:F3D8:6E2E (talk) 09:09, 2 March 2024 (UTC)

You wrote the equality in your second sentence: A/B = C. It's not that the two proportional variables can be said to be equal, but that you can write an equation (equality) using the proportionality constant (C in your example). CodeTalker (talk) 00:54, 3 March 2024 (UTC)

If A is directly proportional to B we write:

$A\propto B$

If we wish, we can then write:

$A=k\times B$ where k is the constant of proportionality.

In your example, k is 4 so your equation is:

$A=4\times B$

As you can see, this equation never becomes $A=B$ Dolphin (t) 00:57, 3 March 2024 (UTC)

That's what I'm saying. You cannot simply skip the constant of proportionality in order to obtain A = B! But that's what they're doing who erroneously assert that "any proportionality can be converted to an equality". Should this be true we would never have discovered the constant c that governs Maxwell's laws and special relativity, nor would Max Planck have discovered the constant h that governs quantum mechanics. Natural constants are always proportionality constants which cannot be dismissed ad hoc. The same with Newton's second law. If you write it according to A/B = C, you have to realize the proportionality constant c. As a matter of fact, Newton's law stems from Galileo (Newton himself ascribes it to his predecessor, in Principia (1713), Book I, Scholium after Corollary VI to the laws of motion). In Galileo's Discorsi of 1638, you can find this law, and there you will find that the required proportionality constant bears dimensions "element of space over element of time", [L/T]. It is the "parameter" of the spacetime reference system of Galileo's (and Newton's) natural reference system of motion "in space and time". I discovered it already in 1985 (Philos. Nat. 22 nr.3 p. 400). It was only banned from mechanics when in the 18th century Euler and others invented "analytical mechanics", which they made the new theory of motion, replacing Galileo's and Newton's geometric mechanics, and basing it on F = ma. Should we return to Galileo and Newton, respecting their geometric method and the said constant altogether, so that the second law would read F = delta (mv)*c, mechanics would again be rooted in the reality of space and time, and everything in mechanics would change. 2003:D2:972D:D312:89AB:3E1B:33AA:525A (talk) 07:53, 3 March 2024 (UTC)

Perhaps my statement would be less likely to confuse if I change it to “any proportionality can be converted to an equation.” Look above in my previous edit to see an example. Dolphin (t) 11:52, 3 March 2024 (UTC)

No, sorry again. We speak of a proportionality between quantities A and B different in kind. This relationship can be symbolized by A~B, where the proportionality constant is implicit. You can make this constant explicit writing an equation according to A/B = C = constant, or A = B*C. But this equation is not an equality A=B!

So F~(ma) as an equation reads F/ma = C = constant, or F = (ma)*C, but never can you arrive at F = ma! Now, since F = ma is certainly the most basic principle of "classical" mechanics, one must see that classical mechanics (Euler, d'Alembert, Lagrange etc.), working with equations and equalities, is not Newtonian mechanics which works with geometric proportions A~B, or A/B = C, the "second law" reading F~delta(mv), or F/delta(mv) = c [L/T]. 2003:D2:972D:D312:89AB:3E1B:33AA:525A (talk) 14:17, 3 March 2024 (UTC)

This is another version of the much discussed variable-mass issue. We should sort it out. Johnjbarton (talk) 16:16, 3 March 2024 (UTC)

I made some small edits to the article to help avoid this confusion.

However to answer the original question

• Why does the article replace the term "proportionality" by "equality"?

The article, written for modern readers, uses modern definitions of "change of motion of an object" and "force" in which case, by these definitions, the proportionality factor is 1.0.

If you have information to contradict my claim (supported by references in the article), please post or add the reference. Johnjbarton (talk) 16:28, 3 March 2024 (UTC)

Just a comment. You're right stating that for modern readers the equality (equivalence) of "force" and "change of motion" is valid. Actually it is the basis of "classical" continuum mechanics. But, as has been shown, it is not Newtonian! Newton's laws is different. It requires a constant of proportionality that is not a dimensionless 1 (Principia 1713, Scholium after Lemma X). The message then is that Newton's (Galileo's!) theory of motion basically differs from that of "classical" mechanics. 2003:D2:972D:D368:F9CE:C42A:76B8:49DB (talk) 07:54, 5 March 2024 (UTC)

Wiki Education assignment: 4A Wikipedia Assignment

This article was the subject of a Wiki Education Foundation-supported course assignment, between 12 February 2024 and 14 June 2024. Further details are available on the course page. Student editor(s): Wkuehl9947 (article contribs). Peer reviewers: Lupe.b007.

— Assignment last updated by Ahlluhn (talk) 00:57, 31 May 2024 (UTC)

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)