Editing Moment (physics) (section)

==History==

[[File:Lever Principle 3D.png|thumb|right|A lever in balance]]
In works believed to stem from [[Ancient Greece]], the concept of a moment is alluded to by the word [[wikt:ῥοπή|ῥοπή]] (''rhopḗ'', {{lit.}} "inclination") and composites like [[wikt:ἰσόρροπα|ἰσόρροπα]] (''isorropa'', {{lit.}} "of equal inclinations").<ref name=mersenne>{{cite book
 |last1=Mersenne
 |first1=Marin
 |author-link=Marin Mersenne
 |title=Les Méchaniques de Galilée
 |date=1634
 |location=Paris
 |url=https://books.google.com/books?id=X-UPAAAAQAAJ&pg=PA7
 |pages=[https://books.google.com/books?id=X-UPAAAAQAAJ&pg=PA7 7–8]
}}</ref>{{r|clagett2}}<ref name=lsj1>{{LSJ|r(oph/|ῥοπή|ref}}</ref> The context of these works is [[mechanics]] and [[geometry]] involving the [[lever]].<ref name=clagett1>{{cite book
 |last1=Clagett
 |first1=Marshall
 |author-link=Marshall Clagett
 |title=The Science of Mechanics in the Middle Ages
 |date=1959
 |location=Madison, WI
 |publisher=University of Wisconsin Press
}}</ref> In particular, in extant works attributed to [[Archimedes]], the moment is pointed out in phrasings like:

:"[[Commensurability (mathematics)|Commensurable]] magnitudes ({{wikt-lang|grc|σύμμετρα}} {{wikt-lang|grc|μεγέθεα}}) [A and B] are equally balanced ({{wikt-lang|grc|ἰσορροπέοντι}}){{efn|An alternative translation is "have equal moments" as used by [[Francesco Maurolico]] in the 1500s.{{r|clagett2}} A literal translation is "have equal inclinations".}} if their distances [to the center Γ, i.e., ΑΓ and ΓΒ] are [[Proportionality (mathematics)#Inverse proportionality|inversely proportional]] ({{wikt-lang|grc|ἀντιπεπονθότως}}) to their weights ({{wikt-lang|grc|βάρεσιν}})."<ref name=clagett2>{{cite book
 |last1=Clagett
 |first1=Marshall
 |author-link=Marshall Clagett
 |title=Archimedes in the Middle Ages
 |type=5 vols in 10 tomes
 |date=1964–84
 |publisher=Madison, WI: University of Wisconsin Press, 1964; Philadelphia: American Philosophical Society, 1967–1984.
}}</ref><ref>{{cite book
 |last1=Dijksterhuis
 |first1=E. J.
 |author-link=Eduard Jan Dijksterhuis
 |title=Archimedes
 |date=1956
 |publisher=E. Munksgaard
 |location=Copenhagen
 |page=[https://archive.org/details/archimedes0000dijk/page/288 288]
 |url=https://archive.org/details/archimedes0000dijk/page/288
}}</ref>

Moreover, in extant texts such as ''[[The Method of Mechanical Theorems]]'', moments are used to infer the [[center of gravity]], area, and volume of geometric figures.

In 1269, [[William of Moerbeke]] translates various works of [[Archimedes]] and [[Eutocius of Ascalon|Eutocious]] into [[Latin]]. The term ῥοπή is [[transliteration|transliterated]] into ''ropen''.{{r|clagett2}}

Around 1450, [[Iacopo da San Cassiano|Jacobus Cremonensis]] translates ῥοπή in similar texts into the [[Latin]] term ''momentum'' ({{lit.}} "movement"<ref>{{cite encyclopedia
 |title=moment
 |encyclopedia=Oxford English Dictionary
 |year=1933
 |url=https://archive.org/details/in.ernet.dli.2015.271836/page/n1125
}}</ref>).<ref>{{cite book |title=Venezia, Biblioteca Nazionale Marciana, lat. Z. 327 (=1842) |date=c. 1450 |location=Biblioteca Marciana |url=https://ptolemaeus.badw.de/jordanus/ms/10379}}</ref>{{r|clagett2|page=331}} The same term is kept in a 1501 translation by [[Giorgio Valla]], and subsequently by [[Francesco Maurolico]], [[Federico Commandino]], [[Guidobaldo del Monte]], [[Adriaan van Roomen]], [[Florence Rivault]], [[Francesco Buonamici (philosopher)|Francesco Buonamici]], [[Marin Mersenne]]{{r|mersenne}}, and [[Galileo Galilei]]. That said, why was the word ''momentum'' chosen for the translation? One clue, according to [[Treccani]], is that ''momento'' in medieval Italy, the place the early translators lived, in a transferred sense meant both a "moment of time" and a "moment of weight" (a small amount of weight that turns the [[Steelyard balance|scale]]).{{efn|[[Treccani]] writes in its entry on [https://www.treccani.it/vocabolario/momento moménto]: "[...] alla tradizione medievale, nella quale momentum significava, per lo più, minima porzione di tempo, la più piccola parte dell’ora (precisamente, 1/40 di ora, un minuto e mezzo), ma anche minima quantità di peso, e quindi l’ago della bilancia (basta l’applicazione di un momento di peso perché si rompa l’equilibrio e la bilancia tracolli in un momento);"}}

In 1554, [[Francesco Maurolico]] clarifies the Latin term ''momentum'' in the work ''Prologi sive sermones''. Here is a Latin to English translation as given by [[Marshall Clagett]]:{{r|clagett2}}

<blockquote>
"[...] equal weights at unequal distances do not weigh equally, but unequal weights [at these unequal distances may] weigh equally. For a weight suspended at a greater distance is heavier, as is obvious in a [[Steelyard balance|balance]]. Therefore, there exists a certain third kind of power or third difference of magnitude—one that differs from both body and weight—and this they call '''moment'''.{{efn|In Latin: ''momentum''.}} Therefore, a body acquires weight from both quantity [i.e., size] and quality [i.e., material], but a weight receives its moment from the distance at which it is suspended. Therefore, when distances are reciprocally proportional to weights, the moments [of the weights] are equal, as [[Archimedes]] demonstrated in ''[[On the Equilibrium of Planes|The Book on Equal Moments]]''.{{efn|The modern translation of this book is "on the equilibrium of planes". The translation "on equal moments (of planes)" as used by Maurolico is also echoed in his four-volume book called ''De momentis aequalibus'' ("about equal moments") where he applies Archimedes' ideas to solid bodies.}} Therefore, weights or [rather] moments like other continuous quantities, are joined at some common terminus, that is, at something common to both of them like the center of weight, or at a point of equilibrium. Now the [[center of gravity]] in any weight is that point which, no matter how often or whenever the body is suspended, always inclines perpendicularly toward the universal center.

In addition to body, weight, and moment, there is a certain fourth power, which can be called impetus or force.{{efn|In Latin: ''impetus'' or ''vis''. This fourth power was the intellectual precursor to the English [[Latinism]] ''[[momentum]]'', also called ''quantity of motion''.}} [[Aristotle]] investigates it in ''On Mechanical Questions'', and it is completely different from [the] three aforesaid [powers or magnitudes]. [...]"
</blockquote>

in 1586, [[Simon Stevin]] uses the [[Dutch language|Dutch]] term ''staltwicht'' ("parked weight") for momentum in ''[[De Beghinselen Der Weeghconst]]''.

In 1632, [[Galileo Galilei]] publishes ''[[Dialogue Concerning the Two Chief World Systems]]'' and uses the [[Italian language|Italian]] ''momento'' with many meanings, including the one of his predecessors.<ref>{{cite book
 |last1=Galluzzi
 |first1=Paolo
 |title=Momento. Studi Galileiani
 |date=1979
 |location=Rome
 |publisher=Edizioni dell' Ateneo & Bizarri
}}</ref>

In 1643, Thomas Salusbury translates some of Galilei's works into [[English language|English]]. Salusbury translates Latin ''momentum'' and Italian ''momento'' into the English term ''moment''.{{efn|This is very much in line with other Latin ''-entum'' words such as ''documentum'', ''monumentum'', or ''argumentum'' which turned into ''document'', ''monument'', and ''argument'' in [[French language|French]] and English.}}

In 1765, the [[Latin]] term ''momentum inertiae'' ([[English language|English]]: ''[[moment of inertia]]'') is used by [[Leonhard Euler]] to refer to one of [[Christiaan Huygens]]'s quantities in ''[[Horologium Oscillatorium]]''.<ref name=euler>{{cite book
 |last=Euler
 |first=Leonhard
 |author-link=Leonhard Euler
 |title=Theoria motus corporum solidorum seu rigidorum: Ex primis nostrae cognitionis principiis stabilita et ad omnes motus, qui in huiusmodi corpora cadere possunt, accommodata [The theory of motion of solid or rigid bodies: established from first principles of our knowledge and appropriate for all motions which can occur in such bodies.]
 |publisher= A. F. Röse
 |location= Rostock and Greifswald (Germany)
 |date=1765
 |page=[https://archive.org/details/theoriamotuscor00eulegoog/page/n202 166]|url= https://archive.org/details/theoriamotuscor00eulegoog
 |language=latin
 |isbn=978-1-4297-4281-8
}} From page 166:  ''"Definitio 7.  422.  Momentum inertiae corporis respectu eujuspiam axis est summa omnium productorum, quae oriuntur, si singula corporis elementa per quadrata distantiarum suarum ab axe multiplicentur."'' (Definition 7.  422.  A body's moment of inertia with respect to any axis is the sum of all of the products, which arise, if the individual elements of the body are multiplied by the square of their distances from the axis.)</ref> Huygens 1673 work involving finding the [[center of oscillation]] had been stimulated by [[Marin Mersenne]], who suggested it to him in 1646.<ref>{{cite book
 |last1=Huygens
 |first1=Christiaan
 |title=Horologium oscillatorium, sive de Motu pendulorum ad horologia aptato demonstrationes geometricae
 |date=1673
 |page=[https://gallica.bnf.fr/ark:/12148/bpt6k1523597w/f111.item 91]
 |url=https://gallica.bnf.fr/ark:/12148/bpt6k1523597w/f111.item
 |language=latin
}}</ref><ref>{{cite web
 |last1=Huygens
 |first1=Christiaan
 |author-link=Christiaan Huygens
 |title=Center of Oscillation (translation)
 |date=1977–1995
 |translator-last1=Mahoney
 |translator-first1=Michael S.
 |url=https://www.princeton.edu/~hos/mike/texts/huygens/centosc/huyosc.htm
 |access-date=22 May 2022
}}</ref>

In 1811, the French term ''moment d'une force'' ([[English language|English]]: ''moment of a force'') with respect to a point and plane is used by [[Siméon Denis Poisson]] in ''Traité de mécanique''.<ref>{{cite book
 |last1=Poisson
 |first1=Siméon-Denis
 |author-link=Siméon Denis Poisson
 |title=Traité de mécanique, tome premier
 |date=1811
 |url=https://gallica.bnf.fr/ark:/12148/bpt6k903370/f99.item
 |page=[https://gallica.bnf.fr/ark:/12148/bpt6k903370/f99.item 67]
}}</ref> [https://babel.hathitrust.org/cgi/pt?id=mdp.39015067064249 An English translation] appears in 1842.

In 1884, the term ''[[torque]]'' is suggested by [[James Thomson (engineer)|James Thomson]] in the context of measuring rotational forces of [[machine]]s (with [[propeller]]s and [[rotor (electric)|rotor]]s).<ref>{{cite book
 |last1=Thompson
 |first1=Silvanus Phillips
 |title=Dynamo-electric machinery: A Manual For Students Of Electrotechnics
 |url=https://archive.org/details/dynamoelectricm17thomgoog/page/n125
 |publisher=New York, Harvard publishing co 
 |date=1893
 |edition=4th
 |page=[https://archive.org/details/dynamoelectricm17thomgoog/page/n125 108]
}}</ref><ref>{{cite book
 |url= https://archive.org/details/collectedpapers00larmgoog/page/n110
 |title= Collected Papers in Physics and Engineering
 |page=civ
 |first1= James
 |last1= Thomson
 |first2= Joseph
 |last2= Larmor
 |publisher= University Press
 |date= 1912
}}</ref> Today, a [[dynamometer]] is used to measure the torque of machines.

In 1893, [[Karl Pearson]] uses the term ''n-th moment'' and <math>\mu_n</math> in the context of [[curve fitting|curve-fitting]] scientific measurements.<ref>{{cite journal
 |last1=Pearson
 |first1=Karl
 |title=Asymmetrical Frequency Curves
 |journal=Nature
 |date=October 1893
 |volume=48
 |issue=1252
 |pages=615–616
 |doi=10.1038/048615a0
|bibcode=1893Natur..48..615P
 |s2cid=4057772
 }}</ref> Pearson wrote in response to [[John Venn]], who, some years earlier, observed a peculiar pattern involving [[Meteorology|meteorological]] data and asked for an explanation of its cause.<ref>{{cite journal
 |last1=Venn
 |first1=J.
 |title=The Law of Error
 |journal=Nature
 |date=September 1887
 |volume=36
 |issue=931
 |pages=411–412
 |doi=10.1038/036411c0
|bibcode=1887Natur..36..411V
 |s2cid=4098315
 |url=https://zenodo.org/record/1696687
 }}</ref> In Pearson's response, this analogy is used: the mechanical "center of gravity" is the [[mean]] and the "distance" is the [[Deviation (statistics)|deviation]] from the mean. This later evolved into [[Moment (mathematics)|moments in mathematics]]. The analogy between the mechanical concept of a moment and the [[statistics|statistical]] function involving the sum of the {{math|n}}th powers of deviations was noticed by several earlier, including [[Pierre-Simon Laplace|Laplace]], [[Christian Kramp|Kramp]], [[Carl Friedrich Gauss|Gauss]], [[Johann Franz Encke|Encke]], [[Emanuel Czuber|Czuber]], [[Adolphe Quetelet|Quetelet]], and [[Erastus L. De Forest|De Forest]].<ref>{{cite book
 |last1=Walker
 |first1=Helen M.
 |author-link=Helen M. Walker
 |title=Studies in the history of statistical method, with special reference to certain educational problems
 |page=[https://archive.org/details/studiesinhistory00walk/page/71 71]
 |date=1929
 |publisher=Baltimore, Williams & Wilkins Co.
 |url=https://archive.org/details/studiesinhistory00walk/page/71
}}</ref>