Inertia#Rotational inertia

Joseph Needham<-->Professor John H. Lienhard points out the Mozi – based on a Chinese text from the Warring States period (475–221 BCE) – as having given the first description of inertia.{{cite web|url=http://www.uh.edu/engines/epi2080.htm|title=No. 2080 The Survival of Invention|website=www.uh.edu}} 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 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.{{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...}}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}} Aristotle said that all moving objects (on Earth) eventually come to rest unless an external power (force) continued to move them.{{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] 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.Aristotle, Physics, 8.10, 267a1–21; [http://etext.library.adelaide.edu.au/a/aristotle/a8ph/]<--> [http://www.documentacatholicaomnia.eu/03d/-384_-322,_Aristoteles,_02_Physics,_EN.pdf Aristotle, Physics, trans. by R. P. Hardie and R. K. Gaye, 'projectile'] {{webarchive|url=https://web.archive.org/web/20070129111002/http://etext.library.adelaide.edu.au/a/aristotle/a8ph/ |date=2007-01-29 }}.

Despite its general acceptance, Aristotle's concept of motion{{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}} 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).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, 'all must move'] 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.{{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}}{{cite encyclopedia |url=http://plato.stanford.edu/entries/philoponus/#2.1 |encyclopedia=Stanford Encyclopedia of Philosophy |title=John Philoponus |date=8 June 2007 |access-date=26 July 2012}} This view was strongly opposed by Averroes and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the 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.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.]

{{Main|Theory of impetus}}

{{See also|Conatus}}

In the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named impetus, dissipated spontaneously. Buridan's position was that a moving object would be arrested by the resistance of the air and the weight of the body which would oppose its impetus.Jean Buridan: Quaestiones on Aristotle's Physics (quoted at [https://web.archive.org/web/20110720105959/http://brahms.phy.vanderbilt.edu/a203/impetus_theory.html Impetus Theory]) Buridan also maintained that impetus increased with speed; thus, his initial idea of impetus was similar in many ways to the modern concept of momentum. Despite the obvious similarities to more modern ideas of inertia, Buridan saw his theory as only a modification to Aristotle's basic philosophy, maintaining many other peripatetic views, including the belief that there was still a fundamental difference between an object in motion and an object at rest. Buridan also believed that impetus could be not only linear but also circular in nature, causing objects (such as celestial bodies) to move in a circle. Buridan's theory was followed up by his pupil Albert of Saxony (1316–1390) and the Oxford Calculators, who performed various experiments which further undermined the Aristotelian model. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of illustrating the laws of motion with graphs.

Shortly before Galileo's theory of inertia, Giambattista Benedetti modified the growing theory of impetus to involve linear motion alone:

{{quote|[Any] portion of corporeal matter which moves by itself when an impetus has been impressed on it by any external motive force has a natural tendency to move on a rectilinear, not a curved, path.Giovanni Benedetti, selection from Speculationum, in Stillman Drake and I. E. Drabkin, Mechanics in Sixteenth-Century Italy University of Wisconsin Press, 1969, p. 156.{{Failed verification|date=October 2022|reason=The citation for this passage appears to be incorrect. It is not on p. 156 of Drake and Drabkin, and apparently not anywhere in the book.}}<-->Stillman Drake. Essays on Galileo etc. Vol 3. [https://books.google.com/books?id=dKEqrYdQ0I0C&q=%22Fourth,%20any%20portion%22 p. 285.]}}

Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion.

According to science historian Charles Coulston Gillispie, inertia "entered science as a physical consequence of Descartes' geometrization of space-matter, combined with the immutability of God."{{cite book |last=Gillispie |first=Charles Coulston |author-link1=Charles Coulston Gillispie |title=The Edge of Objectivity: An Essay in the History of Scientific Ideas |url=https://archive.org/details/edgeofobjectivit00char/page/367 |url-access=registration |year=1960 |publisher=Princeton University Press |isbn=0-691-02350-6 |pages=[https://archive.org/details/edgeofobjectivit00char/page/367 367–68] }} The first physicist to completely break away from the Aristotelian model of motion was Isaac Beeckman in 1614.{{Citation| last = van Berkel| first = Klaas| title = Isaac Beeckman on Matter and Motion: Mechanical Philosophy in the Making| publisher = Johns Hopkins University Press| year = 2013| url = https://books.google.com/books?id=D3WTX-23UVEC&pg=PA105| pages= 105–110| isbn = 9781421409368}}

The term "inertia" was first introduced by Johannes Kepler in his Epitome Astronomiae CopernicanaeLawrence Nolan (ed.), The Cambridge Descartes Lexicon, Cambridge University Press, 2016, "Inertia.", p. 405 (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 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.{{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 }}

The principle of inertia, as formulated by Aristotle for "motions in a void",7th paragraph of section 8, book 4 of Physica includes that a mundane object tends to resist a change in motion. 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.Nicholas Copernicus, [http://www.webexhibits.org/calendars/year-text-Copernicus.html#:~:text=revolution%20around%20the%20sun The Revolutions of the Heavenly Spheres], 1543File:Portrait of Sir Isaac Newton, 1689.jpgFile:Galileo.arp.300pix.jpg

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:

A body moving on a level surface will continue in the same direction at a constant speed unless disturbed.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}}.<-->

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."{{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}}

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.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]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] For Galileo, a motion is "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."{{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}}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" [http://www.physics.oregonstate.edu/~mcintyre/COURSES/ph429_S06/slides.pdf Using great circles] It is also worth noting that 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 reference to compare it against.Galileo, Dialogue Concerning the Two Chief World Systems, 1632 ([http://www.webexhibits.org/calendars/year-text-Galileo.html#:~:text=moving%20or%20nonmoving full text]). 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 laws of motion (first published in Newton's work, Philosophiæ Naturalis Principia Mathematica, in 1687):

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.Andrew Motte's English translation:{{Citation| last = Newton| first = Isaac| title = Newton's Principia : the mathematical principles of natural philosophy| publisher = Daniel Adee| year = 1846| location = New York| url = https://archive.org/details/newtonspmathema00newtrich/page/n87/mode/2up| pages= 83}} This usual statement of Newton's law from the Motte-Cajori translation, is however misleading giving the impression that 'state' refers only to rest and not motion whereas it refers to both. So the comma should come after 'state' not 'rest' (Koyre: Newtonian Studies London 1965 Chap III, App A)

<-->

Despite having defined the concept in his laws of motion, Newton did not actually use the term "inertia.” In fact, he originally viewed the respective phenomena as being caused by "innate forces" inherent in matter which resist any acceleration. Given this perspective, and borrowing from Kepler, Newton conceived of "inertia" as "the innate force possessed by an object which resists changes in motion", thus defining "inertia" to mean the cause of the phenomenon, rather than the phenomenon itself.

However, Newton's original ideas of "innate resistive force" were ultimately problematic for a variety of reasons, and thus most physicists no longer think in these terms. As no alternate mechanism has been readily accepted, and it is now generally accepted that there may not be one that we can know, the term "inertia" has come to mean simply the phenomenon itself, rather than any inherent mechanism. Thus, ultimately, "inertia" in modern classical physics has come to be a name for the same phenomenon as described by Newton's first law of motion, and the two concepts are now considered to be equivalent.

File:Inertial-vs-gravitational-mass-experiment.svg

Albert Einstein's theory of special relativity, as proposed in his 1905 paper entitled "On the Electrodynamics of Moving Bodies", was built on the understanding of inertial reference frames developed by Galileo, Huygens and Newton. While this revolutionary theory did significantly change the meaning of many Newtonian concepts such as mass, energy, and distance, Einstein's concept of inertia remained at first unchanged from Newton's original meaning. However, this resulted in a limitation inherent in special relativity: the principle of relativity could only apply to inertial reference frames. To address this limitation, Einstein developed his general theory of relativity ("The Foundation of the General Theory of Relativity", 1916), which provided a theory including noninertial (accelerated) reference frames.Alfred Engel English Translation:{{Citation| last = Einstein| first = Albert| title = The Foundation of the General Theory of Relativity| publisher = Princeton University Press| year = 1997| location = New Jersey| url = http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdf| access-date = 30 May 2014| archive-date = 15 November 2015| archive-url = https://web.archive.org/web/20151115215202/http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdf| url-status = dead}}

In general relativity, the concept of inertial motion got a broader meaning. Taking into account general relativity, inertial motion is any movement of a body that is not affected by forces of electrical, magnetic, or other origin, but that is only under the influence of gravitational masses.{{cite book|title=Einstein's Theory of Relativity|author1=Max Born |author2=Günther Leibfried |url=https://archive.org/details/einsteinstheory000born|url-access=registration|quote=inertial motion.|isbn=0-486-60769-0|publisher=Courier Dover Publications|location=New York|year=1962|page=[https://archive.org/details/einsteinstheory000born/page/315 315]}}{{cite web|url=https://archive.org/details/einsteinstheoryo00born/page/252/mode/2up?view=theater|title=Einstein's Theory of Relativity - inertial motion, p. 252|author=Max Born|year=1922 |publisher=New York, E. P. Dutton and company, publishers }} Physically speaking, this happens to be exactly what a properly functioning three-axis accelerometer is indicating when it does not detect any proper acceleration.

The term inertia comes from the Latin word iners, meaning idle or sluggish.{{Cite web |title=inertia {{!}} Etymology, origin and meaning of inertia by etymonline |url=https://www.etymonline.com/word/inertia |access-date=2023-10-01 |website=www.etymonline.com |language=en}}

A quantity related to inertia is rotational inertia (→ moment of inertia), the property that a rotating rigid body maintains its state of uniform rotational motion. Its angular momentum remains unchanged unless an external torque is applied; this is called conservation of angular momentum. Rotational inertia is often considered in relation to a rigid body. For example, a gyroscope uses the property that it resists any change in the axis of rotation.

{{cols|colwidth=16em}}

• Flywheel energy storage devices which may also be known as an Inertia battery
• General relativity
• Vertical and horizontal
• Inertial navigation system
• Inertial response of synchronous generators in an electrical grid
• Kinetic energy
• List of moments of inertia
• Mach's principle
• Newton's laws of motion
• Classical mechanics
• Special relativity
• Parallel axis theorem

{{colend}}

{{clear}}

{{Reflist|35em}}

{{refbegin}}

• Butterfield, H (1957), The Origins of Modern Science, {{ISBN|0-7135-0160-X}}.
• Clement, J (1982), "Students' preconceptions in introductory mechanics", American Journal of Physics vol 50, pp 66–71
• Crombie, A C (1959), Medieval and Early Modern Science, vol. 2.
• McCloskey, M (1983), "Intuitive physics", Scientific American, April, pp. 114–123.
• McCloskey, M & Carmazza, A (1980), "Curvilinear motion in the absence of external forces: naïve beliefs about the motion of objects", Science vol. 210, pp. 1139–1141.
• {{cite book |last1= Pfister |first1= Herbert| last2 = King | first2 = Markus | title = Inertia and Gravitation. The Fundamental Nature and Structure of Space-Time | publisher = Springer | location = Heidelberg | year=2015 |volume=The Lecture Notes in Physics. Volume 897|doi =10.1007/978-3-319-15036-9| isbn=978-3-319-15035-2}}
• {{Cite journal

|last=Ragep

|first=F. Jamil

|date=2001a

|title=Tusi and Copernicus: The Earth's Motion in Context

|journal=Science in Context

|volume=14

|issue=1–2

|pages=145–163

|publisher=Cambridge University Press

|doi=10.1017/S0269889701000060

|s2cid=145372613

}}

• {{Cite journal

|last=Ragep

|first=F. Jamil

|date=2001b

|title=Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science

|journal=Osiris |series=2nd Series

|volume=16

|issue=Science in Theistic Contexts: Cognitive Dimensions

|pages=49–64 & 66–71

|bibcode = 2001Osir...16...49R

|doi=10.1086/649338|s2cid=142586786

|url=http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=156332

}}

{{refend}}

• {{wikiquote-inline}}
• [https://www.youtube.com/watch?v=TQxeutcYP6I Why Does the Earth Spin? (YouTube)]

{{Isaac Newton}}

{{Physics-footer}}

{{Authority control}}

Category:Classical mechanics

Category:Gyroscopes

Category:Mass

Category:Velocity

Category:Articles containing video clips