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<!-->{{More citations needed|date=August 2014}}<--> | <!-->{{More citations needed|date=August 2014}}<--> | ||
{{Classical mechanics|Topic=Fundamental concepts}} | {{Classical mechanics|Topic=Fundamental concepts}} | ||
'''Inertia''' is the natural tendency of objects in [[motion]] to stay in motion and objects at rest to stay at rest, unless a [[force]] causes | '''Inertia''' is the natural tendency of objects in [[motion]] to stay in motion and objects at rest to stay at rest, unless a [[force]] causes its [[velocity]] to change. It is one of the fundamental principles in [[classical physics]], and is described by [[Isaac Newton]] in his [[Newton%27s_laws_of_motion#First law|first law of motion]] (also known as The Principle of Inertia).<ref>{{cite web|last=Britannica|first=Dictionary|url=https://www.britannica.com/dictionary/Inertia|title=definition of INERTIA|access-date=2022-07-08}}</ref> It is one of the primary manifestations of [[mass]], one of the core quantitative properties of [[physical system]]s.<ref>{{cite encyclopedia |last=Britannica |first=Science |title=inertia physics |encyclopedia=Encyclopedia Britannica |url=https://www.britannica.com/science/inertia |access-date=2022-07-08}}</ref> Newton writes:<ref>Andrew Motte's English translation: {{Citation| last = Newton| first = Isaac| title = Newton's Principia: the mathematical principles of natural philosophy (3rd edition)| publisher = Daniel Adee| year = 1846| location = New York| url = https://archive.org/details/newtonspmathema00newtrich/page/n87/mode/2up| pages= 83}}</ref><ref>Andrew Motte's 1729 (1846) translation translated Newton's "nisi quatenus" erroneously as ''unless'' instead of ''except insofar''. {{Cite journal |journal=Philosophy of Science |date=2023 |title=Forced Changes Only: A New Take on Inertia |pages=60–73 |volume=90 |issue=1 |first=D. |last=Hoek|doi=10.1017/psa.2021.38 |hdl=10919/113143 |arxiv=2112.02339 }}</ref><ref> | ||
{{Cite web |date=2023-08-17 |title=What Newton really meant {{!}} Daniel Hoek |url=https://iai.tv/articles/what-newton-really-meant-daniel-hoek-auid-2579 |access-date=2023-09-29 |website=IAI TV - Changing how the world thinks |language=en-GB}}</ref><ref>{{Cite journal |journal=Scientific American |date=5 September 2023 |title=Mistranslation of Newton's First Law Discovered after Nearly Nearly 300 Years |pages= |volume= |issue= |first=Stephanie |last=Pappas |url=https://www.scientificamerican.com/article/mistranslation-of-newtons-first-law-discovered-after-nearly-300-years1/}}</ref> | {{Cite web |date=2023-08-17 |title=What Newton really meant {{!}} Daniel Hoek |url=https://iai.tv/articles/what-newton-really-meant-daniel-hoek-auid-2579 |access-date=2023-09-29 |website=IAI TV - Changing how the world thinks |language=en-GB}}</ref><ref>{{Cite journal |journal=Scientific American |date=5 September 2023 |title=Mistranslation of Newton's First Law Discovered after Nearly Nearly 300 Years |pages= |volume= |issue= |first=Stephanie |last=Pappas |url=https://www.scientificamerican.com/article/mistranslation-of-newtons-first-law-discovered-after-nearly-300-years1/}}</ref> | ||
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=== Early understanding of inertial motion === | === Early understanding of inertial motion === | ||
<!-->[[Joseph Needham]]<-->Professor [[John H. Lienhard]] points out the [[Mozi (book)|Mozi]] – based on a Chinese text from the [[Warring States period]] (475–221 BCE) – as having given the first description of inertia.<ref>{{cite web|url= | <!-->[[Joseph Needham]]<-->Professor [[John H. Lienhard]] points out the [[Mozi (book)|Mozi]] – based on a Chinese text from the [[Warring States period]] (475–221 BCE) – as having given the first description of inertia.<ref>{{cite web|url=https://www.uh.edu/engines/epi2080.htm|title=No. 2080 The Survival of Invention|website=www.uh.edu}}</ref> Before the European [[Renaissance]], the prevailing theory of motion in [[western philosophy]] was that of [[Aristotle]] (384–322 BCE). On the surface of the Earth, the inertia property of physical objects is often masked by [[gravity]] and the effects of [[friction]] and [[Drag (physics)|air resistance]], both of which tend to decrease the speed of moving objects (commonly to the point of rest). This misled the philosopher [[Aristotle]] to believe that objects would move only as long as force was applied to them.<ref>{{Citation| last = Aristotle: Minor works| title = ''Mechanical Problems'' (''Mechanica'')| publisher = Loeb Classical Library Cambridge (Mass.) and London| year = 1936| location = [[University of Chicago Library]]| url = https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Aristotle/Mechanica*.html<!-->#:~:text=stops%20when%20the%20force<--> | page= 407|quote=...it [a body] stops when the force which is pushing the travelling object has no longer power to push it along...}}</ref><ref>Pages 2 to 4, Section 1.1, [https://books.google.com/books?id=_ZNxDwAAQBAJ&q=skating "Skating"], Chapter 1, "Things that Move", Louis Bloomfield, Professor of Physics at the [[University of Virginia]], ''How Everything Works: Making Physics Out of the Ordinary'', John Wiley & Sons (2007), hardcover, {{ISBN|978-0-471-74817-5}}</ref> Aristotle said that all moving objects (on Earth) eventually come to rest unless an external power (force) continued to move them.<ref>{{cite book |title=Aristotle's Science of Matter and Motion |first1=Christopher |last1=Byrne |publisher=University of Toronto Press |year=2018 |isbn=978-1-4875-0396-3 |page=21 |url=https://books.google.com/books?id=kYllDwAAQBAJ}} [https://books.google.com/books?id=kYllDwAAQBAJ&pg=PA21 Extract of page 21]</ref> Aristotle explained the continued motion of projectiles, after being separated from their projector, as an (itself unexplained) action of the surrounding medium continuing to move the projectile.<ref>Aristotle, ''Physics'', 8.10, 267a1–21; <!-->[http://etext.library.adelaide.edu.au/a/aristotle/a8ph/]<--> [https://www.documentacatholicaomnia.eu/03d/-384_-322,_Aristoteles,_02_Physics,_EN.pdf Aristotle, ''Physics'', trans. by R. P. Hardie and R. K. Gaye, <small>'projectile'</small>] {{webarchive|url=https://web.archive.org/web/20070129111002/http://etext.library.adelaide.edu.au/a/aristotle/a8ph/ |date=2007-01-29 }}.</ref> | ||
Despite its general acceptance, Aristotle's concept of motion<ref name=Darling_2006>{{Cite book | last = Darling | first = David | title = Gravity's arc: the story of gravity, from Aristotle to Einstein and beyond | publisher = John Wiley and Sons | date = 2006 | pages = [https://archive.org/details/gravitysarcstory00darl/page/17 17], 50 | url = https://archive.org/details/gravitysarcstory00darl | url-access = registration | isbn = 978-0-471-71989-2}}</ref> was disputed on several occasions by notable philosophers over nearly two [[millennia]]. For example, [[Lucretius]] (following, presumably, [[Epicurus]]) stated that the "default state" of the matter was motion, not stasis (stagnation).<ref>Lucretius, ''On the Nature of Things'' (London: Penguin, 1988), [https://upload.wikimedia.org/wikipedia/commons/2/27/Lucretius_On_the_nature_of_things_%28IA_lucretiusonnatu00lucr%29.pdf pp. 80–85, <small>'all must move'</small>]</ref> In the 6th century, [[John Philoponus]] criticized the inconsistency between Aristotle's discussion of projectiles, where the medium keeps projectiles going, and his discussion of the void, where the medium would hinder a body's motion. Philoponus proposed that motion was not maintained by the action of a surrounding medium, but by some property imparted to the object when it was set in motion. Although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction.<ref>{{cite book|last=Sorabji|first=Richard|title=Matter, space and motion : theories in antiquity and their sequel|url=https://books.google.com/books?id=TN_aAAAAMAAJ&q=inertia|date=1988|publisher=Cornell University Press|location=Ithaca, N.Y.|isbn=978-0801421945|edition=1st |pages=227–228}}</ref><ref>{{cite encyclopedia |url= | Despite its general acceptance, Aristotle's concept of motion<ref name=Darling_2006>{{Cite book | last = Darling | first = David | title = Gravity's arc: the story of gravity, from Aristotle to Einstein and beyond | publisher = John Wiley and Sons | date = 2006 | pages = [https://archive.org/details/gravitysarcstory00darl/page/17 17], 50 | url = https://archive.org/details/gravitysarcstory00darl | url-access = registration | isbn = 978-0-471-71989-2}}</ref> was disputed on several occasions by notable philosophers over nearly two [[millennia]]. For example, [[Lucretius]] (following, presumably, [[Epicurus]]) stated that the "default state" of the matter was motion, not stasis (stagnation).<ref>Lucretius, ''On the Nature of Things'' (London: Penguin, 1988), [https://upload.wikimedia.org/wikipedia/commons/2/27/Lucretius_On_the_nature_of_things_%28IA_lucretiusonnatu00lucr%29.pdf pp. 80–85, <small>'all must move'</small>]</ref> In the 6th century, [[John Philoponus]] criticized the inconsistency between Aristotle's discussion of projectiles, where the medium keeps projectiles going, and his discussion of the void, where the medium would hinder a body's motion. Philoponus proposed that motion was not maintained by the action of a surrounding medium, but by some property imparted to the object when it was set in motion. Although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction.<ref>{{cite book|last=Sorabji|first=Richard|title=Matter, space and motion : theories in antiquity and their sequel|url=https://books.google.com/books?id=TN_aAAAAMAAJ&q=inertia|date=1988|publisher=Cornell University Press|location=Ithaca, N.Y.|isbn=978-0801421945|edition=1st |pages=227–228}}</ref><ref>{{cite encyclopedia |url=https://plato.stanford.edu/entries/philoponus/#2.1 |encyclopedia=Stanford Encyclopedia of Philosophy |title=John Philoponus |date=8 June 2007 |access-date=26 July 2012}}</ref> This view was strongly opposed by [[Averroes]] and by many [[Scholasticism|scholastic]] philosophers who supported Aristotle. However, this view did not go unchallenged in the [[Islamic Golden Age|Islamic world]], where Philoponus had several supporters who further developed his ideas. | ||
In the 11th century, Persian [[polymath]] [[Ibn Sina]] (Avicenna) claimed that a projectile in a vacuum would not stop unless acted upon.<ref>Espinoza, Fernando. "An Analysis of the Historical Development of Ideas About Motion and its Implications for Teaching". Physics Education. Vol. 40(2). [https://profilpelajar.com/article/History_of_classical_mechanics#:~:text=ibn Medieval thought.]</ref> | In the 11th century, Persian [[polymath]] [[Ibn Sina]] (Avicenna) claimed that a projectile in a vacuum would not stop unless acted upon.<ref>Espinoza, Fernando. "An Analysis of the Historical Development of Ideas About Motion and its Implications for Teaching". Physics Education. Vol. 40(2). [https://profilpelajar.com/article/History_of_classical_mechanics#:~:text=ibn Medieval thought.]</ref> | ||
===Theory of | ===Theory of Impetus=== | ||
{{Main|Theory of impetus}} | {{Main|Theory of impetus}} | ||
{{See also|Conatus}} | {{See also|Conatus}} | ||
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The term "inertia" was first introduced by [[Johannes Kepler]] in his ''[[Epitome Astronomiae Copernicanae]]''<ref>Lawrence Nolan (ed.), ''The Cambridge Descartes Lexicon'', Cambridge University Press, 2016, "Inertia.", p. 405</ref> (published in three parts from 1617 to 1621). However, the meaning of Kepler's term, which he derived from the Latin word for "idleness" or "laziness", was not quite the same as its modern interpretation. Kepler defined inertia only in terms of resistance to movement, once again based on the [[axiom|axiomatic assumption]] that rest was a natural state which did not need explanation. It was not until the later work of Galileo and Newton unified ''rest'' and ''motion'' in one principle that the term "inertia" could be applied to those concepts as it is today.<ref>{{Cite book|url=https://books.google.com/books?id=S39FDQAAQBAJ&pg=PT130|title=Restoring the Bioelectrical Machine|last=Biad|first=Abder-Rahim|date=2018-01-26|publisher=Lulu Press, Inc|isbn=9781365447709|language=en}}{{Dead link|date=September 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> | The term "inertia" was first introduced by [[Johannes Kepler]] in his ''[[Epitome Astronomiae Copernicanae]]''<ref>Lawrence Nolan (ed.), ''The Cambridge Descartes Lexicon'', Cambridge University Press, 2016, "Inertia.", p. 405</ref> (published in three parts from 1617 to 1621). However, the meaning of Kepler's term, which he derived from the Latin word for "idleness" or "laziness", was not quite the same as its modern interpretation. Kepler defined inertia only in terms of resistance to movement, once again based on the [[axiom|axiomatic assumption]] that rest was a natural state which did not need explanation. It was not until the later work of Galileo and Newton unified ''rest'' and ''motion'' in one principle that the term "inertia" could be applied to those concepts as it is today.<ref>{{Cite book|url=https://books.google.com/books?id=S39FDQAAQBAJ&pg=PT130|title=Restoring the Bioelectrical Machine|last=Biad|first=Abder-Rahim|date=2018-01-26|publisher=Lulu Press, Inc|isbn=9781365447709|language=en}}{{Dead link|date=September 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> | ||
The principle of inertia, as formulated by Aristotle for "motions in a void",<ref>7th paragraph of section 8, book 4 of Physica</ref> includes that a mundane object tends to resist a change in motion. <!--According to Newton, an object will stay at rest or stay in motion (i.e. maintain its velocity) unless acted on by a net external force, whether it results from [[gravity]], [[friction]], contact, or some other force.--> The Aristotelian division of motion into mundane and celestial became increasingly problematic in the face of the conclusions of [[Nicolaus Copernicus]] in the 16th century, who argued that the Earth is never at rest, but is actually in constant motion around the Sun.<ref>Nicholas Copernicus, [ | The principle of inertia, as formulated by Aristotle for "motions in a void",<ref>7th paragraph of section 8, book 4 of Physica</ref> includes that a mundane object tends to resist a change in motion. <!--According to Newton, an object will stay at rest or stay in motion (i.e. maintain its velocity) unless acted on by a net external force, whether it results from [[gravity]], [[friction]], contact, or some other force.--> The Aristotelian division of motion into mundane and celestial became increasingly problematic in the face of the conclusions of [[Nicolaus Copernicus]] in the 16th century, who argued that the Earth is never at rest, but is actually in constant motion around the Sun.<ref>Nicholas Copernicus, [https://www.webexhibits.org/calendars/year-text-Copernicus.html#:~:text=revolution%20around%20the%20sun ''The Revolutions of the Heavenly Spheres''], 1543</ref>[[File:Portrait of Sir Isaac Newton, 1689.jpg|thumb|Isaac Newton, 1689]][[File:Galileo.arp.300pix.jpg|thumb|Galileo Galilei]] | ||
[[Galileo]], in his further development of the [[Copernican model]], recognized these problems with the then-accepted nature of motion and, at least partially, as a result, included a restatement of Aristotle's description of motion in a void as a basic physical principle: | [[Galileo]], in his further development of the [[Copernican model]], recognized these problems with the then-accepted nature of motion and, at least partially, as a result, included a restatement of Aristotle's description of motion in a void as a basic physical principle: | ||
<blockquote>A body moving on a level surface will continue in the same direction at a constant speed unless disturbed.<!--><ref>For a detailed analysis concerning this issue, see Alan Chalmers's article "Galilean Relativity and Galileo's Relativity", in ''Correspondence, Invariance and Heuristics: Essays in Honour of Heinz Post'', eds. Steven French and Harmke Kamminga, Kluwer Academic Publishers, Dordrecht, 1991, {{ISBN|0792320859}}.</ref><--> </blockquote> | <blockquote>A body moving on a level surface will continue in the same direction at a constant speed unless disturbed.<!--><ref>For a detailed analysis concerning this issue, see Alan Chalmers's article "Galilean Relativity and Galileo's Relativity", in ''Correspondence, Invariance and Heuristics: Essays in Honour of Heinz Post'', eds. Steven French and Harmke Kamminga, Kluwer Academic Publishers, Dordrecht, 1991, {{ISBN|0792320859}}.</ref><--> </blockquote> | ||
Galileo writes that "all external impediments removed, a heavy body on a spherical surface concentric with the earth will maintain itself in that state in which it has been; if placed in a movement towards the west (for example), it will maintain itself in that movement."<ref>{{cite web|last=Drake|first=Stillman|url=https://archive.org/details/B-001-001-741/page/n125/mode/2up?view=theater|title=Galilei's presentation of his principle of inertia, p. 113|access-date=2022-07-31}}</ref><!--<ref>Drake, S. ''Discoveries and Opinions of Galileo'', Doubleday Anchor, New York, 1957, pp. 113–114</ref> --> This notion, which is termed "circular inertia" or "horizontal circular inertia" by historians of science, is a precursor to, but is distinct from, Newton's notion of rectilinear inertia.<ref>See Alan Chalmers article "Galilean Relativity and Galileo's Relativity", in ''Correspondence, Invariance and Heuristics: Essays in Honour of Heinz Post'', eds. Steven French and Harmke Kamminga, Kluwer Academic Publishers, Dordrecht, 1991, pp. 199–200, {{ISBN|0792320859}}. Chalmers does not, however, believe that Galileo's physics had a general principle of inertia, circular or otherwise. [https://books.google.com/books?id=QyMyBwAAQBAJ&pg=PA199 page 199]</ref><ref>Dijksterhuis E.J. ''The Mechanisation of the World Picture'', Oxford University Press, Oxford, 1961, [https://archive.org/details/e.j.dijksterhuisthemechanizationoftheworldpictureoxforduniversitypress1961/page/n357/mode/2up p. 352]</ref> For Galileo, a motion is "[[horizontal and vertical|horizontal]]" if it does not carry the moving body towards or away from the center of the Earth, and for him, "a ship, for instance, having once received some impetus through the tranquil sea, would move continually around our globe without ever stopping."<ref>{{cite web|last=Drake|first=Stillman|url=https://archive.org/details/B-001-001-741/page/n125/mode/2up?view=theater|title=Discoveries and Opinions of Galileo, p. 113-114|access-date=2022-07-31}}</ref><!--<ref>Galileo, ''Letters on Sunspots'', 1613 quoted in Drake, S. ''Discoveries and Opinions of Galileo'', Doubleday Anchor, New York, 1957, pp. 113–114.</ref>--><ref>According to Newtonian mechanics, if a projectile on a smooth spherical planet is given an initial horizontal velocity, it will not remain on the surface of the planet. Various curves are possible depending on the initial speed and the height of the launch. See Harris Benson ''University Physics'', New York 1991, [https://archive.org/details/universityphysic0000bens/page/268/mode/2up page 268]. If constrained to remain on the surface, by being sandwiched, say, in between two concentric spheres, it will follow a great circle on the surface of the earth, i.e. will only maintain a westerly direction if fired along the equator. See "Using great circles" [ | Galileo writes that "all external impediments removed, a heavy body on a spherical surface concentric with the earth will maintain itself in that state in which it has been; if placed in a movement towards the west (for example), it will maintain itself in that movement."<ref>{{cite web|last=Drake|first=Stillman|url=https://archive.org/details/B-001-001-741/page/n125/mode/2up?view=theater|title=Galilei's presentation of his principle of inertia, p. 113|access-date=2022-07-31}}</ref><!--<ref>Drake, S. ''Discoveries and Opinions of Galileo'', Doubleday Anchor, New York, 1957, pp. 113–114</ref> --> This notion, which is termed "circular inertia" or "horizontal circular inertia" by historians of science, is a precursor to, but is distinct from, Newton's notion of rectilinear inertia.<ref>See Alan Chalmers article "Galilean Relativity and Galileo's Relativity", in ''Correspondence, Invariance and Heuristics: Essays in Honour of Heinz Post'', eds. Steven French and Harmke Kamminga, Kluwer Academic Publishers, Dordrecht, 1991, pp. 199–200, {{ISBN|0792320859}}. Chalmers does not, however, believe that Galileo's physics had a general principle of inertia, circular or otherwise. [https://books.google.com/books?id=QyMyBwAAQBAJ&pg=PA199 page 199]</ref><ref>Dijksterhuis E.J. ''The Mechanisation of the World Picture'', Oxford University Press, Oxford, 1961, [https://archive.org/details/e.j.dijksterhuisthemechanizationoftheworldpictureoxforduniversitypress1961/page/n357/mode/2up p. 352]</ref> For Galileo, a motion is "[[horizontal and vertical|horizontal]]" if it does not carry the moving body towards or away from the center of the Earth, and for him, "a ship, for instance, having once received some impetus through the tranquil sea, would move continually around our globe without ever stopping."<ref>{{cite web|last=Drake|first=Stillman|url=https://archive.org/details/B-001-001-741/page/n125/mode/2up?view=theater|title=Discoveries and Opinions of Galileo, p. 113-114|access-date=2022-07-31}}</ref><!--<ref>Galileo, ''Letters on Sunspots'', 1613 quoted in Drake, S. ''Discoveries and Opinions of Galileo'', Doubleday Anchor, New York, 1957, pp. 113–114.</ref>--><ref>According to Newtonian mechanics, if a projectile on a smooth spherical planet is given an initial horizontal velocity, it will not remain on the surface of the planet. Various curves are possible depending on the initial speed and the height of the launch. See Harris Benson ''University Physics'', New York 1991, [https://archive.org/details/universityphysic0000bens/page/268/mode/2up page 268]. If constrained to remain on the surface, by being sandwiched, say, in between two concentric spheres, it will follow a great circle on the surface of the earth, i.e. will only maintain a westerly direction if fired along the equator. See "Using great circles" [https://www.physics.oregonstate.edu/~mcintyre/COURSES/ph429_S06/slides.pdf Using great circles]</ref> Galileo later (in 1632) concluded that based on this initial premise of inertia, it is impossible to tell the difference between a moving object and a stationary one without some outside [[Inertial frame of reference|reference]] to compare it against.<ref>Galileo, ''[[Dialogue Concerning the Two Chief World Systems]]'', 1632 ([https://www.webexhibits.org/calendars/year-text-Galileo.html#:~:text=moving%20or%20nonmoving full text]).</ref> This observation ultimately came to be the basis for [[Albert Einstein]] to develop the theory of [[special relativity]]. | ||
Concepts of inertia in Galileo's writings would later come to be refined, modified, and codified by [[Isaac Newton]] as the first of his [[Newton's laws of motion|laws of motion]] (first published in Newton's work, ''[[Philosophiæ Naturalis Principia Mathematica]]'', in 1687): | Concepts of inertia in Galileo's writings would later come to be refined, modified, and codified by [[Isaac Newton]] as the first of his [[Newton's laws of motion|laws of motion]] (first published in Newton's work, ''[[Philosophiæ Naturalis Principia Mathematica]]'', in 1687): | ||
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*[[General relativity]] | *[[General relativity]] | ||
*[[Vertical and horizontal]] | *[[Vertical and horizontal]] | ||
*[[Inertial force]] | |||
*[[Inertial navigation system]] | *[[Inertial navigation system]] | ||
*[[Inertial response]] of synchronous generators in an electrical grid | *[[Inertial response]] of synchronous generators in an electrical grid | ||