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Did Newton know that force is mass times acceleration?
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Did Newton know that force equals mass times acceleration? Is that implied by his description of force?
If yes, why he didn't use the relation $F = m \times a$?
physics<br>newton<br>classical-mechanics
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edited 4 hours ago
José Carlos Santos
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asked yesterday
Elizabeth
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$\begingroup$<br>As a general heuristic, I think it is quite rare for a famous scientist to have been unaware of a law that has been named after him. Therefore, in the absence of strong evidence of the contrary, it seems reasonable to answer this question with a summary "yes."<br>$\endgroup$
R.P.
R.P.
2026-05-26 20:28:32 +00:00
Commented<br>yesterday
$\begingroup$<br>@R.P. it is very fun to note that Newton had no idea of Newton's fractal, but yes, this is one of the exceptions that proves the rule.<br>$\endgroup$
naturallyInconsistent
naturallyInconsistent
2026-05-26 22:41:22 +00:00
Commented<br>yesterday
$\begingroup$<br>This question is similar to: F = ma -- How was did we come to understand that this compact form expressed what Newton said in words?. If you believe it’s different, please edit the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem.<br>$\endgroup$
Mauro ALLEGRANZA
Mauro ALLEGRANZA
2026-05-27 06:59:27 +00:00
Commented<br>16 hours ago
$\begingroup$<br>There are modern translations of Principia, but also overviews: "The modern F=ma form of Newton's second law nowhere occurs in any edition of the Principia even though he had seen his second law formulated in this way in print during the interval between the second and third editions in J.Hermann's Phoronomia of 1716. Instead, it has the following formulation: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed."<br>$\endgroup$
Mauro ALLEGRANZA
Mauro ALLEGRANZA
2026-05-27 07:04:38 +00:00
Commented<br>16 hours ago
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You could have read his 1687 Principia and checked that he
defined momentum $\vec p=m\vec v$
defined Newton's 2$^\text{nd}$ Law (N2L) as $\sum\vec F=\frac{\mathrm d\vec p}{\mathrm dt}$
$\frac{\mathrm d\vec p}{\mathrm dt}=m\vec a$ only when $\frac{\mathrm dm}{\mathrm dt}=0$
which makes a tonne of sense because the law of conservation of mass was definitively stated in 1773, by the work of Antoine Lavoisier, almost a century after the Principia and just before the French Revolution.
That is, there is no good reason for Newton, who had plenty of opponents, to restrict himself to the special case of constant mass bodies. There would have been variable-mass systems that he would want to at least have staked his claim on, before the restriction to constant mass for many useful practical calculations.
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answered yesterday
naturallyInconsistent
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$\begingroup$<br>so Newton was aware if mass is constant then F=mxa, but he want to make universal law?<br>$\endgroup$
Elizabeth
Elizabeth
2026-05-27 07:15:32 +00:00
Commented<br>16 hours ago
$\begingroup$<br>Newton is definitely aware. He made a lot of use of that, and he already had the product rule of differentiation derived. There is no chance he would ever be mistaken on this.<br>$\endgroup$
naturallyInconsistent
naturallyInconsistent
2026-05-27 07:18:03 +00:00
Commented<br>16 hours ago
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Here is a searchable PDF of the original book:
https://www.gutenberg.org/files/28233/28233-pdf.pdf
Here is an English transcription:
https://web.math.princeton.edu/~eprywes/F22FRS/newtonprincipia.pdf
To me, this paragraph answers @Elizabeth's question positively (page 94):
This is from the cited transcription by Andrew Motte, 1846. If you add the facts that Newton was the first to describe his observations, and that there hadn't been an established physical language in 1686, and that language in general was a very different one 340 years ago, then it is clear that it was about acceleration. If you argue that this is due to the translation 160 years later, then study the original text in Latin, which is why I added the link.
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edited 10 hours ago
answered 10 hours ago
Marius S.L.
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