Talk:Newton's laws of motion

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)

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wrong (pp. 63–64) and then getting deep into the weeds about the second law and what Newton meant by terminology that is obsolete now anyway.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&#39;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&#39;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)

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 gc 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)

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