Talk:Newton's laws of motion

Incorrect formula for variable mass

I had to fix the formula for variable mass displayed in the article. A common misconception among physicists is that

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

is the most general form of Newton's equations, valid both for constant and variable mass. That opinion is absurd, as can be readily seen by applying the derivative:

$F=m{\dot {v}}+v{\dot {m}}$

and noticing that it is not Galilean invariant! Any classical physical law must, by necessity, be invariant under Galilean transformations; otherwise, it would yield different physical results for observers moving at different speeds.

As an example, imagine that a bucket filled with sand is put on a support, and that a hole is made in the bottom, such that the sand can now fall to the ground, reducing the mass of the bucket. Since both $v_{x}$, ${\dot {v_{x}}}$ and $F_{x}$ are 0 in the bucket's frame of reference, the equation checks out. However, if an observer is moving, and looking at the same system, he would find out that

$F_{x}=mv_{x}$

since the velocity is constant, but non-null. In other words, the moving observer would find out that there is a horizontal force in a system just because the sand is flowing downwards, which is absurd. The forces computed in every frame of reference must be the same.

People who give this wrong opinion (that $F={\frac {dp}{dt}}$) frequently give examples where the mass ejection happens at the same coordinate axis as the velocity. They, then, neglect the fact that the ejected mass produces a force. Those cases are conveniently select where the force produced by the ejected mass is $-v{\dot {m}}$, yielding the former equation when you completely disregard the fact that this term should be in the "force" side of the equation, not on the other one.

It turns out that $F=ma$ is the correct equation, both for constant and variable mass, which can be easily verified if you adopt the frame of reference where the object is currently at rest, since then $v=0$ and $F=ma$ in that frame, but, from the principle of covariance, that means the same equation must be true in all frames of reference, since both sides are galilean invariants. — Preceding unsigned comment added by Jocryptowiki (talk • contribs) 16:08, 6 March 2025 (UTC)

If you have a source which backs your claim then we can add it to the article. Johnjbarton (talk) 17:13, 6 March 2025 (UTC)

There is no source for the claim that F=dp/dt for variable mass, which is a evidently wrong equation that violates Galilean invariance. If you require a source at all, then no statement should be left on the article regarding variable mass, especially a statement as shocking as "the relativity principle of Galileo does not hold for variable mass". I advise that, if a source for either F=ma or F=dp/dt is required, then any mention to variable mass should be removed from the article until sources are provided. Otherwise, you'd be acting like someone who insists that a statement like "145*26=3800" should be left in an article, unless it is provided a specific source that 145*26=3770 instead. My opinion is that, if we require sources to anything, then the obviously wrong statement "145*26=3800", while lacking a source, should be removed. Yet, any source claiming such an absurdity should also be immediately regarded as non reliable.

If, on the other hand, your worry is about whether F=ma is the correct equation (instead of any other possibility), then I should remark that it becomes immediately obvious if you realize that F=ma is valid for each classical particle (atoms of each element not changing mass), and that F = sum_i F_i = sum_i m_i a = ma, by the aditivity of these quantities, at any given time. Jocryptowiki (talk) 19:53, 6 March 2025 (UTC)

Contrary to your assertion that There is no source for the claim that F=dp/dt for variable mass, you may read Chapter 4 of

• Kleppner, Daniel; Kolenkow, Robert J. (2014). An introduction to mechanics (2nd ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-19811-0. OCLC 854617117.

The later parts of the chapter include multiple examples of variable mass systems. Johnjbarton (talk) 23:34, 6 March 2025 (UTC)

This, here, is a direct reference regarding the matter.

https://articles.adsabs.harvard.edu/full/seri/CeMDA/0053//0000227.000.html

I should point out that, if Wikipedia ought to be regarded as at least internally consistent, we should either delete the entirety of the article https://en.wikipedia.org/wiki/Variable-mass_system and replace all the formulas expressed there with F=dp/dt, or address the issue more intelligently. Newton's second law, as an expression of the conversation of momentum, should in general state that the applied forces, MINUS the momentum leaving the system, equals the change in momentum in the system. Jocryptowiki (talk) 17:18, 7 March 2025 (UTC)

I see some edits were made simultaneously (so I'm assuming no bad faith on your part, we both want to address the issue). I've put more references (such as Sommerfeld's textbook), and tried to address your claims, but I think the text can be made to be more succinct, while referencing the other article.

I still think that, either nothing should be mentioned regarding variable mass (only the main article pointed to) or the correct, principled, formulas should be presented. F=dp/dt is wrong in principle. It is the exact same situation as if you stated that the heat applied to a system is the variation of internal total energy in the system, WHEN there is matter leaving the system. That cannot be true. The heat, MINUS the kinectic energy of the mass leaving the system, would be the amount of energy leaving, etc.

Many different sources point out F=dp/dt as a mistake (not a "non-careful application"), which seems to come from Kleppner's book. Indeed, you need to make careful applications for a wrong equation to yield the correct results! The total variation in the momentum of a system is the force applied PLUS the momentum entering directly via movement of mass. That momentum that is entering (or leaving) the imaginary boundaries of the "system" cannot be regarded as a force, since it is a mere product of inertia. Jocryptowiki (talk) 18:26, 7 March 2025 (UTC)

I included a description of why F=dp/dt can lead you astray. Sommerfeld makes essentially the same arguments as Kleppner. Johnjbarton (talk) 19:27, 7 March 2025 (UTC)

Split proposal

Greetings! When I came across this page, I'm rather surprised that there are no individual articles for all three laws. This notion is simply due to the fact that they are so important, and should deserve individual articles for more detailed description. However, I'm not very sure, so I'm asking for opinions here. Pygos (talk) 11:03, 28 January 2025 (UTC)

This page, of course, shall remain, as it describes the underlying assumptions of the laws and their historical background. Pygos (talk) 11:07, 28 January 2025 (UTC)

The article is really an introduction to Newtonian mechanics, which happens to be described in three parts. Each individual law is not, by itself, useful or interesting. I believe three articles would end up being mostly repetition in order to explain how each law contributes to what is a single thing. Johnjbarton (talk) 16:38, 28 January 2025 (UTC)

The three laws together form a conceptual unit. Each one really needs to be understood in the context of the others. Splitting them into separate articles would make for needless repetition. XOR'easter (talk) 20:07, 28 January 2025 (UTC)

@Pygos It seems that your proposal did not get traction. Would you consider removing the tag in the article? Johnjbarton (talk) 02:03, 7 March 2025 (UTC)

Done Pygos (talk) 04:32, 7 March 2025 (UTC)

how do i close this discussion Pygos (talk) 02:04, 18 March 2025 (UTC)

 Done Dolphin (t) 03:16, 18 March 2025 (UTC)

Any linguist is the room?

Neither English nor Latin are my first language. However I can understand the meaning of «unless» and «except insofar as» sounds quite cryptic to me, but it seems as a pretentious way to say unless.

What Newton wrote was

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

• nisi means unless, except
• quatenus means in the extent that

Example:

Eadem est asini et cuiusvis imperatoris post modicum tempus gloria, nisi quatenus memoria alterutrius scriptorum beneficio prorogatur.

— John of Salisbury, Policraticus, Prologus,

The reputation of the fool and the emperor is the same after a moderate period of time except in the extent that the memory of either is prolonged by the beneficence of writers.

— Translation from Latin

I do not get why there was the change made to that more obscure translation, I've not been able to find a single Latin dictionary translating quatenus as «insofar as» and I do not think that is the traditional translation into English of the first law. So, why???

--77.75.179.1 (talk) 00:28, 20 February 2025 (UTC)

The current phrasing "except insofar as it is acted upon by a force." is just utter nonsense. No body speaks or thinks that way. It appears as a brute force attempt of word-by-word translation. kbrose (talk) 19:48, 21 February 2025 (UTC)

A Possible Corrected and or Refined Restatement on the First Law of Motion

The original:

1. A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force.

The corrected and or refined restatement:

1. A body remains at rest and or in motion at a constant speed in a straight line, unless it is blocked by another body and or acted upon by a force.

Consider this philosophical anecdote from the African fable The Lion, the Hyena and the Rabbit: https://web.archive.org/web/20250622233431/https://www.worldoftales.com/African_folktales/African_Folktale_41.html#gsc.tab=0

... "I am thinking," said he, with a grave, philosophical air, "about those two stones, one big and one little; the little one does not go up, nor does the big one go down."....

The apple which fell during Newton's discovery got blocked by the earth (supposedly by his head in humourous version). So force and or blockage is necessary for the phenomenon to occur. — Preceding unsigned comment added by 106.222.223.16 (talk) 12:43, 25 July 2025 (UTC)

"Blockage" occurs when the blocker exerts a force during the collision. DMacks (talk) 12:51, 25 July 2025 (UTC)