TheInfoList

Inertia is the resistance of any physical
object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Entity, something that is tangible and within the grasp of the senses ** Object (abstract), an object which does not exist at any particular time or pl ...
to any change in its
velocity The velocity of an object is the Time derivative, rate of change of its Position (vector), position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction ...

. This includes changes to the object's
speed In everyday use and in kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, bodies (objects), and systems of bodies (groups of objects) without considerin ...

, or
direction Direction may refer to: *Relative direction, for instance left, right, forward, backwards, up, and down ** Anatomical terms of location for those used in anatomy *Cardinal direction Mathematics and science *Direction vector, a unit vector that ...
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
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

s act upon them. Inertia comes from the Latin word, ''iners'', meaning idle, sluggish. Inertia is one of the primary manifestations of
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
, which is a quantitative property of
physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environment. The environment is ignored except ...
s.
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

defined inertia as a force, before his first law in the monumental ''
Philosophiæ Naturalis Principia Mathematica (from Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republic, it bec ...
''. There, one reads: After some other definitions, Newton states (at page 83) his first law of motion: 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 In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

, 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 In classical mechanics, Newton's laws of motion are three Scientific law, laws that describe the relationship between the motion of an object and the forces acting on it. The first law states that an object either remains at rest or continues ...
, stated above, according to which an object will continue moving at its current
velocity The velocity of an object is the Time derivative, rate of change of its Position (vector), position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction ...

until some force causes its speed or direction to change. On the surface of the Earth, inertia is often masked by
gravity Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate'' toward) one another. , gravity gives to s, and the causes the s of the oceans. The gravitational attracti ...

and the effects of
friction Friction is the force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related en ...

and
air resistance In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding f ...
, both of which tend to decrease the speed of moving objects (commonly to the point of rest). This misled the philosopher
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental quest ...

to believe that objects would move only as long as force was applied to them. The principle of inertia is one of the fundamental principles in
classical physics Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the ...
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 Noel Joseph Terence Montgomery Needham (; 9 December 1900 – 24 March 1995) was a British biochemist, historian and sinologist Sinology or Chinese studies, is an academic discipline that focuses on the study of China China, officially t ...
credits The Mozi (a Chinese text from the
Warring States The Warring States period () was an era in characterized by warfare, as well as bureaucratic and military reforms and consolidation. It followed the and concluded with the that saw the annexation of all other contender states, which ultimate ...
period (475–221 BCE) as the first description of inertia. Before the European
Renaissance The Renaissance ( , ) , from , with the same meanings. is a period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in ...

the prevailing theory of motion in
western philosophy Western philosophy encompasses the philosophical Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical or mental reality ...
was that of
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental quest ...

(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. 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. Despite its general acceptance, Aristotle's concept of motion was disputed on several occasions by notable philosophers over nearly two
millennia A millennium (plural millennia or millenniums) is a period of one thousand year A year is the orbital period of a planetary body, for example, the Earth, moving in Earth's orbit, its orbit around the Sun. Due to the Earth's axial tilt, the ...
. For example,
Lucretius Titus Lucretius Carus ( , ; 99 – c. 55 BC) was a Ancient Rome, Roman Roman literature, poet and Ancient Roman philosophy, philosopher. His only known work is the philosophical poem ''De rerum natura'', a didactic work about the tenets and ...
(following, presumably,
Epicurus Epicurus, ''Epíkouros'', "ally, comrade" (341–270 BC) was an and who founded , a highly influential school of . He was born on the Greek island of to parents. Influenced by , , , and possibly the , he turned against the of his day and e ...

) stated that the "default state" of the matter was motion, not stasis. In the 6th century,
John Philoponus John Philoponus (; ; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Byzantine Alexandrian philologist, commentaries on Aristotle, Aristotelian commentator and Christian theologian, author of a considerable number ...
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. This view was strongly opposed by
Averroes Ibn Rushd ( ar, ; full name Image:FML names-2.png, 300px, First/given, middle and last/family/surname with John Fitzgerald Kennedy as example. This shows a structure typical for the Anglosphere, among others. Other cultures use other struc ...

and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the
Islamic world The terms Muslim world and Islamic world commonly refer to the Islamic Islam (; ar, اَلْإِسْلَامُ, al-’Islām, "submission o God Oh God may refer to: * An exclamation; similar to "oh no", "oh yes", "oh my", "aw goodne ...
, where Philoponus had several supporters who further developed his ideas. In the 11th century, Persian
polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific prob ...

Ibn Sina Ibn Sina ( fa, ابن سینا), also known as Abu Ali Sina (), Pur Sina (), and often known in the West as Avicenna (;  – June 1037), was a Persian Persian may refer to: * People and things from Iran, historically called ''Persia'' ...
(Avicenna) claimed that a projectile in a vacuum would not stop unless acted upon.

## Theory of impetus

In the 14th century,
Jean Buridan Jean Buridan (; Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman ...
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. 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 en, Frederick Augustus Albert Anthony Ferdinand Joseph Charles Maria Baptist Nepomuk William Xavier George Fidelis , image = Albert of Saxony by Nicola Perscheid c1900.jpg , image_size = , caption = Albert of Saxony by Nicola P ...
(1316–1390) and the
Oxford Calculators The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College Merton College (in full: The House or College of Scholars of Merton in the University of Oxford) is one of the constituent colleges of th ...
, who performed various experiments which further undermined the Aristotelian model. Their work in turn was elaborated by
Nicole Oresme Nicole Oresme (; c. 1320–1325 – July 11, 1382), also known as Nicolas Oresme, Nicholas Oresme, or Nicolas d'Oresme, was a significant philosopher A philosopher is someone who practices philosophy. The term ''philosopher'' comes from the g ...
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: 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 Charles Coulston Gillispie (; August 6, 1918 – October 6, 2015) was an American historian of science. He was the Dayton-Stockton Professor of History of Science, Emeritus at Princeton University. He was succeeded by Arno J. Mayer. Life The son of ...
, inertia "entered science as a physical consequence of ' geometrization of space-matter, combined with the immutability of God." The principle of inertia, which originated with Aristotle for "motions in a void", 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 Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate'' toward) one another. , gravity gives to s, and the causes the s of the oceans. The gravitational attracti ...

,
friction Friction is the force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related en ...

, 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 Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, link=no, Niclas Koppernigk, modern: ''Nikolaus Kopernikus''; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic Church, Ca ...

in the 16th century, who argued that the Earth is never at rest, but is actually in constant motion around the Sun.
Galileo Galileo di Vincenzo Bonaiuti de' Galilei ( , ; 15 February 1564 – 8 January 1642), commonly referred to as Galileo, was an astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific qu ...

, in his further development of the
Copernican model Copernican heliocentrism is the name given to the astronomical scientific modeling, model developed by Nicolaus Copernicus and published in 1543. This model positioned the Sun at the center of the Universe, motionless, with Earth and the other plan ...
, 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.
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." 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. For Galileo, a motion is "" 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." 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. This observation ultimately came to be the basis for
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

to develop the theory of
special relativity In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
. The first physicist to completely break away from the Aristotelian model of motion was
Isaac Beeckman Isaac Beeckman (10 December 1588 – 19 May 1637) was a Dutch philosopher and scientist, who, through his studies and contact with leading natural philosophers, may have "virtually given birth to modern atomism Atomism (from Greek , ''atomon'', ...
in 1614. Concepts of inertia in Galileo's writings would later come to be refined, modified and codified by
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

as the first of his
Laws of MotionIn physics, a number of noted theories of the motion of objects have developed. Among the best known are: * Classical mechanics ** Newton's laws of motion ** Euler's laws of motion ** Cauchy momentum equation, Cauchy's equations of motion ** Kepler's ...
(first published in Newton's work, ''
Philosophiae Naturalis Principia Mathematica Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical reality Reality is the sum or aggregate of all that is real or existen ...
'', 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.
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 Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of eve ...

known as classical mechanics. The term "inertia" was first introduced by
Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe as ...

in his ''
Epitome Astronomiae Copernicanae The ''Epitome Astronomiae Copernicanae'' was an astronomy book on the heliocentric system published by Johannes Kepler in the period 1618 to 1621. The first volume (books I–III) was printed in 1618, the second (book IV) in 1620, and the third ...
'' (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. 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 Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

's theory of
special relativity In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
, as proposed in his 1905 paper entitled "
On the Electrodynamics of Moving Bodies 200px, Einstein in 1904 or 1905, about the time he wrote the ''Annus Mirabilis'' papers The ''Annus mirabilis'' papers (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European l ...
," was built on the understanding of
inertial reference frames In classical physics and special relativity, an inertial frame of reference is a frame of reference that is not undergoing acceleration. In an inertial frame of reference, a physical object with zero net force acting on it moves with a constan ...
developed by Galileo and Newton. While this revolutionary theory did significantly change the meaning of many Newtonian concepts such as
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
,
energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

, and
distance Distance is a numerical measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or eve ...

, 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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...
could only apply to inertial reference frames. To address this limitation, Einstein developed his
general theory of relativity General relativity, also known as the general theory of relativity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern ph ...
("The Foundation of the General Theory of Relativity", 1916), which provided a theory including ''noninertial'' (accelerated) reference frames.Alfred Engel English Translation:

# Rotational inertia

A quantity related to inertia is ''rotational inertia'' (→
moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body In physics Physics is the natural science that studies matter, its ...

), the property that a rotating rigid body maintains its state of uniform
rotation A rotation is a circular movement of an object around a center (or point) of rotation. The plane (geometry), geometric plane along which the rotation occurs is called the ''rotation plane'', and the imaginary line extending from the center an ...

al motion. Its
angular momentum In , angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of . It is an important quantity in physics because it is a —the total angular momentum of a closed system remains constant. In three , the ...

remains unchanged, unless an external
torque In physics and mechanics, torque is the rotational equivalent of linear force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the na ...

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 A gyroscope (from Ancient Greek Ancient Greek includes the forms of the used in and the from around 1500 BC to 300 BC. It is often roughly divided into the following periods: (), Dark Ages (), the period (), and the period (). ...

uses the property that it resists any change in the axis of rotation.

*
Flywheel energy storage Flywheel energy storage (FES) works by accelerating a rotor (flywheel) to a very high speed and maintaining the energy in the system as rotational energy. When energy is extracted from the system, the flywheel's rotational speed is reduced as a co ...
devices which may also be known as an ''Inertia battery'' *
General relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
*
Horizontal and vertical In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mat ...

*
Inertial guidance system An inertial navigation system (INS) is a navigation Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation i ...
*
Inertial responseInertial response is a property of large Synchronization (alternating current), synchronous generators, which contain large synchronous rotating masses, and which acts to overcome the immediate imbalance between power supply and demand for electric p ...
of synchronous generators in an electrical grid *
Kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
*
List of moments of inertia Moment of inertia, denoted by , measures the extent to which an object resists rotational acceleration about a Rotation around a fixed axis, particular axis, and is the rotational analogue to mass (which determines an object's resistance to Linear a ...
*
Mach's principle In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist A physicist is a scientist A sc ...
*
Newton's laws of motion Newton's laws of motion are three law Law is a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its ...
* Newtonian physics *
Special relativity In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
* Steiner theorem