Inertia
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Inertia

Inertia is the resistance of any physical object to a change in its velocity. This includes changes to the object's speed, or direction of motion. An aspect of this property is the tendency of objects to keep moving in a straight line at a constant speed when no forces act upon them.

Inertia comes from the Latin word, iners, meaning idle, sluggish. Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. Isaac Newton defined inertia as a force, before his first law in the monumental Philosophiæ Naturalis Principia Mathematica. There, one reads:

DEFINITION III. The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest or of moving uniformly forward in a right line.[1]

After some other definitions, Newton states (at page 83) his first law of motion:

LAW I. 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.

Note that Newton makes use of the active verbal form "to persevere", rather than other passive forms such as "to continue", or "to remain", commonly found in modern textbooks. This follows from some changes in Newton's original mechanics (as stated in the Principia) made by Euler, d'Alembert, and other Cartesians.

In common usage, the term "inertia" may refer to an object's "amount of resistance to change in velocity" or for simpler terms, "resistance to a change in motion" (which is quantified by its mass), or sometimes to its momentum, depending on the context. The term "inertia" is more properly understood as shorthand for "the principle of inertia" as described by Newton in his first law of motion, stated above, according to which an object will continue moving at its current velocity until some force causes its speed or direction to change.

On the surface of the Earth, inertia 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.[2][3]

The principle of inertia is one of the fundamental principles in classical physics that are still used today to describe the motion of objects and how they are affected by the applied forces on them.

## History and development of the concept

### Early understanding of motion

The sinologist Joseph Needham credits The Mozi (a Chinese text from the Warring States period (475-221 BCE) as the first description of inertia.[4] Before the European Renaissance the prevailing theory of motion in western philosophy was that of Aristotle (335 BCE to 322 BCE). Aristotle said that all moving objects (on Earth) eventually come to rest unless an external power (force) continued to move them.[5] 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.[6]

Despite its general acceptance, Aristotle's concept of motion 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.[7] 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.[8][9][10] 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.[11]

### Theory of impetus

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.[12] 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 thought 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:

"...[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."[13]

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

### Classical inertia

According to historian of science Charles Coulston Gillispie, inertia "entered science as a physical consequence of Descartes' geometrization of space-matter, combined with the immutability of God."[14]

Galileo Galilei

The principle of inertia, which originated with Aristotle for "motions in a void",[15] states that an 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.[16] 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.[17]

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 movement towards the west (for example), it will maintain itself in that movement."[18] This notion which is termed "circular inertia" or "horizontal circular inertia" by historians of science, is a precursor to, but distinct from, Newton's notion of rectilinear inertia.[19][20] 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."[21][22]

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.[23] This observation ultimately came to be the basis for Albert Einstein to develop the theory of special relativity.

The first physicist to completely break away from the Aristotelian model of motion was Isaac Beeckman in 1614.[24]

The effect of inertial mass: if pulled slowly, the upper thread breaks (a). If pulled quickly, the lower thread breaks (b)

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, Philosophiae 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.[25]

Since initial publication, Newton's Laws of Motion (and by inclusion, this first law) have come to form the basis for the branch of physics known as classical mechanics.[26]

The term "inertia" was first introduced by Johannes Kepler in his Epitome Astronomiae Copernicanae[27] (published in three parts from 1617-1621); 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 a resistance to movement, once again based on the presumption 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 these concepts as it is today.[28]

Nevertheless, despite defining the concept so elegantly in his laws of motion, even Newton did not actually use the term "inertia" to refer to his First Law. In fact, Newton originally viewed the phenomenon he described in his First Law of Motion as being caused by "innate forces" inherent in matter, which resisted any acceleration. Given this perspective, and borrowing from Kepler, Newton attributed the term "inertia" to mean "the innate force possessed by an object which resists changes in motion"; thus, Newton defined "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 which 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 described by Newton's First Law of Motion, and the two concepts are now considered to be equivalent.

### Relativity

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 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 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.[29]

## Rotational inertia

rotational inertia

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 also 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.

## References

1. ^ Andrew Motte's English translation:Newton, Isaac (1846), Newton's Principia: the mathematical principles of natural philosophy (3rd edition), New York: Daniel Adee, p. 73
2. ^ Aristotle: Minor works (1936), Mechanical Problems (Mechanica), University of Chicago Library: Loeb Classical Library Cambridge (Mass.) and London, p. 407, ...it [a body] stops when the force which is pushing the travelling object has no longer power to push it along...
3. ^ Pages 2 to 4, Section 1.1, "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
4. ^ "No. 2080 The Survival of Invention". www.uh.edu.
5. ^ Byrne, Christopher (2018). Aristotle's Science of Matter and Motion. University of Toronto Press. p. 21. ISBN 978-1-4875-0396-3. Extract of page 21
6. ^ Aristotle, Physics, 8.10, 267a1-21; Aristotle, Physics, trans. by R. P. Hardie and R. K. Gaye Archived 2007-01-29 at the Wayback Machine.
7. ^ Lucretius, On the Nature of Things (London: Penguin, 1988), pp. 60-65
8. ^ Sorabji, Richard (1988). Matter, space and motion : theories in antiquity and their sequel (1st ed.). Ithaca, N.Y.: Cornell University Press. pp. 227-228. ISBN 978-0801421945.
9. ^ "John Philoponus". Stanford Encyclopedia of Philosophy. 8 June 2007. Retrieved 2012.
10. ^ Darling, David (2006). Gravity's arc: the story of gravity, from Aristotle to Einstein and beyond. John Wiley and Sons. pp. 17, 50. ISBN 978-0-471-71989-2.
11. ^ Espinoza, Fernando. "An Analysis of the Historical Development of Ideas About Motion and its Implications for Teaching". Physics Education. Vol. 40(2).
12. ^ Jean Buridan: Quaestiones on Aristotle's Physics (quoted at Impetus Theory)
13. ^ Giovanni Benedetti, selection from Speculationum, in Stillman Drake and I. E. Drabkin, Mechanics in Sixteenth-Century Italy University of Wisconsin Press, 1969, p. 156.
14. ^ Gillispie, Charles Coulston (1960). The Edge of Objectivity: An Essay in the History of Scientific Ideas. Princeton University Press. pp. 367-68. ISBN 0-691-02350-6.
15. ^ 7th paragraph of section 8, book 4 of Physica
16. ^ Nicholas Copernicus, The Revolutions of the Heavenly Spheres, 1543
17. ^ For a detailed analysis concerning this issue, 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, ISBN 0792320859.
18. ^ Drake, S. Discoveries and Opinions of Galileo, Doubleday Anchor, New York, 1957, pp. 113-114
19. ^ 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.
20. ^ Dijksterhuis E.J. The Mechanisation of the World Picture, Oxford University Press, Oxford, 1961, p. 352
21. ^ Galileo, Letters on Sunspots, 1613 quoted in Drake, S. Discoveries and Opinions of Galileo, Doubleday Anchor, New York, 1957, pp. 113-114.
22. ^ 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, 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" Using great circles
23. ^ Galileo, Dialogue Concerning the Two Chief World Systems, 1632 (full text).
24. ^ van Berkel, Klaas (2013), Isaac Beeckman on Matter and Motion: Mechanical Philosophy in the Making, Johns Hopkins University Press, pp. 105-110, ISBN 9781421409368
25. ^ Andrew Motte's English translation:Newton, Isaac (1846), Newton's Principia : the mathematical principles of natural philosophy, New York: Daniel Adee, p. 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)
26. ^ Dourmaskin, Peter (December 2013). "Classical Mechanics: MIT 8.01 Course Notes". MIT Physics 8.01. Retrieved 2016.
27. ^ Lawrence Nolan (ed.), The Cambridge Descartes Lexicon, Cambridge University Press, 2016, "Inertia."
28. ^ Biad, Abder-Rahim (2018-01-26). Restoring the Bioelectrical Machine. Lulu Press, Inc. ISBN 9781365447709.
29. ^ Alfred Engel English Translation:Einstein, Albert (1997), The Foundation of the General Theory of Relativity (PDF), New Jersey: Princeton University Press, p. 57, retrieved 2014