# Inertia

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Inertia is the resistance of any physical object to any 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.

## Contents

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 Mozi, which was an ancient philosophical text from China during the Warring States period, was the first to describe the idea of inertia as reported in the findings of sinologist Joseph Needham. [4] In the west before the Renaissance, the most generally accepted theory of motion in Western philosophy was based on Aristotle who around about 335 BC to 322 BC said that, in the absence of an external motive power, all objects (on Earth) would come to rest and that moving objects only continue to move so long as there is a power inducing them to do so. [5] Aristotle explained the continued motion of projectiles, which are separated from their projector, by the action of the surrounding medium, which continues to move the projectile in some way. [6] Aristotle concluded that such violent motion in a void was impossible. [7]

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 matter was motion, not stasis. [8] 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. [9] [10] [11] 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 did have 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. [12]

### 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. [13] 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 that further undermined the classical, Aristotelian view. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of demonstrating laws of motion in the form of 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." [14]

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." [15]

The principle of inertia, which originated with Aristotle for "motions in a void", [16] 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. [17] 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. [18]

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." [19] 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. [20] [21] 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." [22] [23]

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. [24] 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. [25]

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. [26]

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. [27]

The term "inertia" was first introduced by Johannes Kepler in his Epitome Astronomiae Copernicanae [28] (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. [29]

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. [30]

## 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.

## Related Research Articles

In physics, a force is any influence that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newton (N). Force is represented by the symbol F.

Physics is a branch of science whose primary objects of study are matter and energy. Discoveries of physics find applications throughout the natural sciences and in technology. Physics today may be divided loosely into classical physics and modern physics.

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 constant velocity —or, equivalently, it is a frame of reference in which Newton's first law of motion holds. An inertial frame of reference can be defined in analytical terms as a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. Conceptually, the physics of a system in an inertial frame have no causes external to the system. An inertial frame of reference may also be called an inertial reference frame, inertial frame, Galilean reference frame, or inertial space.

Mass is both a property of a physical body and a measure of its resistance to acceleration when a net force is applied. An object's mass also determines the strength of its gravitational attraction to other bodies.

Mechanics is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in displacements, or changes of an object's position relative to its environment. This branch of physics has its origins in Ancient Greece with the writings of Aristotle and Archimedes. During the early modern period, scientists such as Galileo, Kepler, and Newton laid the foundation for what is now known as classical mechanics. It is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as a branch of science which deals with the motion of and forces on bodies not in the quantum realm. The field is today less widely understood in terms of quantum theory.

In classical mechanics, Newton's laws of motion are three 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 to move at a constant velocity, unless it is acted upon by an external force. The second law states that the rate of change of momentum of an object is directly proportional to the force applied, or, for an object with constant mass, that the net force on an object is equal to the mass of that object multiplied by the acceleration. The third law states that when one object exerts a force on a second object, that second object exerts a force that is equal in magnitude and opposite in direction on the first object.

The following is a timeline of classical mechanics:

In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.

In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.

Jean Buridan was an influential 14th century French philosopher.

In theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The purpose of the hypothesis was to attempt to explain how rotating objects maintain a frame of reference, such as gyroscopes and spinning celestial bodies. The idea is that the existence of absolute rotation is determined by the large-scale distribution of matter, as exemplified by this anecdote:

You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?

In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

Absolute space and time is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame.

John Philoponus, also known as John the Grammarian or John of Alexandria, was a Byzantine Greek philologist, Aristotelian commentator, Christian theologian and an author of a considerable number of philosophical treatises and theological works. He was born in Alexandria. A rigorous, sometimes polemical writer and an original thinker who was controversial in his own time, John Philoponus broke from the Aristotelian–Neoplatonic tradition, questioning methodology and eventually leading to empiricism in the natural sciences. He was one of the first to propose a "theory of impetus" similar to the modern concept of inertia over Aristotelian dynamics.

In physics, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation since ancient times. The first extant sources discussing such theories are found in ancient Greek philosophy. This work was furthered by ancient Indian and medieval Islamic physicists, before gaining great strides during the Renaissance and Scientific Revolution, culminating in the formulation of Newton's law of gravity. This was superseded by Albert Einstein's theory of relativity in the early 20th century.

In early philosophies of psychology and metaphysics, conatus is an innate inclination of a thing to continue to exist and enhance itself. This "thing" may be mind, matter, or a combination of both. Over the millennia, many different definitions and treatments have been formulated, including seventeenth-century philosophers René Descartes, Baruch Spinoza, Gottfried Leibniz, and Thomas Hobbes who had made significant contributions. The conatus may refer to the instinctive "will to live" of living organisms or to various metaphysical theories of motion and inertia. Often the concept is associated with God's will in a pantheist view of Nature. The concept may be broken up into separate definitions for the mind and body and split when discussing centrifugal force and inertia.

Aristotelian physics is the form of natural science described in the works of the Greek philosopher Aristotle. In his work Physics, Aristotle intended to establish general principles of change that govern all natural bodies, both living and inanimate, celestial and terrestrial – including all motion, quantitative change, qualitative change, and substantial change. To Aristotle, 'physics' was a broad field that included subjects that would now be called the philosophy of mind, sensory experience, memory, anatomy and biology. It constitutes the foundation of the thought underlying many of his works.

The theory of impetus was an auxiliary or secondary theory of Aristotelian dynamics, put forth initially to explain projectile motion against gravity. It was introduced by John Philoponus in the 6th century, and elaborated by Nur ad-Din al-Bitruji at the end of the 12th century. The theory was modified by Avicenna in the 11th century and Hibat Allah Abu'l-Barakat al-Baghdaadi in the 12th century, before it was later established in Western scientific thought by Jean Buridan in the 14th century. It is the intellectual precursor to the concepts of inertia, momentum and acceleration in classical mechanics.

The natural sciences saw various advancements during the Golden Age of Islam, adding a number of innovations to the Transmission of the Classics. During this period, Islamic theology was encouraging of thinkers to find knowledge. Thinkers from this period included Al-Farabi, Abu Bishr Matta, Ibn Sina, al-Hassan Ibn al-Haytham and Ibn Bajjah. These works and the important commentaries on them were the wellspring of science during the medieval period. They were translated into Arabic, the lingua franca of this period.

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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
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8. Lucretius, On the Nature of Things (London: Penguin, 1988), pp. 60–65
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14. Giovanni Benedetti, selection from Speculationum, in Stillman Drake and I. E. Drabkin, Mechanics in Sixteenth-Century Italy University of Wisconsin Press, 1969, p. 156.
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16. 7th paragraph of section 8, book 4 of Physica
17. Nicholas Copernicus, The Revolutions of the Heavenly Spheres, 1543
18. 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.
19. Drake, S. Discoveries and Opinions of Galileo, Doubleday Anchor, New York, 1957, pp. 113–114
20. 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.
21. Dijksterhuis E.J. The Mechanisation of the World Picture, Oxford University Press, Oxford, 1961, p. 352
22. Galileo, Letters on Sunspots, 1613 quoted in Drake, S. Discoveries and Opinions of Galileo, Doubleday Anchor, New York, 1957, pp. 113–114.
23. 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
24. Galileo, Dialogue Concerning the Two Chief World Systems , 1632 (full text).
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27. Dourmaskin, Peter (December 2013). "Classical Mechanics: MIT 8.01 Course Notes". MIT Physics 8.01. Retrieved September 9, 2016.
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29. Biad, Abder-Rahim (2018-01-26). Restoring the Bioelectrical Machine. Lulu Press, Inc. ISBN   9781365447709.
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