# 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.

The velocity of an object is the rate of change of its 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 of motion. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

In everyday use and in kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.

The most common relative directions are left, right, forward(s), backward(s), up, and down. No absolute direction corresponds to any of the relative directions. This is a consequence of the translational invariance of the laws of physics: nature, loosely speaking, behaves the same no matter what direction one moves. As demonstrated by the Michelson-Morley null result, there is no absolute inertial frame of reference. There are definite relationships between the relative directions, however. left and right, forward and backward, and up and down are three pairs of complementary directions, each pair orthogonal to both of the others. Relative directions are also known as egocentric coordinates.

## 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 his first law in his Philosophiæ Naturalis Principia Mathematica , which states:

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.

In physics, a physical system is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment. The environment is ignored except for its effects on the system.

Sir Isaac Newton was an English mathematician, physicist, astronomer, theologian, and author who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

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 preserve its present state, whether it be of rest or of moving uniformly forward in a straight line. [1]

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: an object not subject to any net external force moves at a constant velocity. Thus, an object will continue moving at its current velocity until some force causes its speed or direction to change.

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If m is an object's mass and v is the velocity, then the momentum is

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]

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing, forming stars—and for the stars to group together into galaxies—so gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become increasingly weaker on farther objects.

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:

In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag forces depend on velocity. Drag force is proportional to the velocity for a laminar flow and the squared velocity for a turbulent flow. Even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent of viscosity.

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.

Classical physics refers to theories of physics 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 previous theories, or new theories based on the older paradigm, will often be referred to as belonging to the realm of "classical physics".

## History and development of the concept

### Early understanding of motion

Prior to 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. 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. [4] Aristotle concluded that such violent motion in a void was impossible. [5]

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. [6] 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. [7] [8] [9] 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.

### 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. [10] 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." [11]

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." [12]

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, 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. [13] 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. [14]

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." [15] 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. [16] [17] For Galileo, a motion is "horizontal" if it does not carry the moving body towards or away from the centre 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." [18] [19]

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. [20] This observation ultimately came to be the basis for 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. [21]

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):

Unless acted upon by a net unbalanced force, an object will maintain a constant velocity.

Note that "velocity" in this context is defined as a vector, thus Newton's "constant velocity" implies both constant speed and constant direction (and also includes the case of zero speed, or no motion). 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. [22]

The term "inertia" was first introduced by Johannes Kepler in his Epitome Astronomiae Copernicanae [23] (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. [24]

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. [25]

## Rotational inertia

Another form of inertia is rotational inertia (→ moment of inertia), the property that a rotating rigid body maintains its state of uniform rotational motion. Its angular momentum is unchanged, unless an external torque is applied; this is also called conservation of angular momentum. Rotational inertia depends on the object remaining structurally intact as a rigid body, and also has practical consequences. For example, a gyroscope uses the property that it resists any change in the axis of rotation.

## Example

If you had a tablecloth, with food on it, and you pull it quickly, most likely, the objects won't move. That's inertia.

## Related Research Articles

In physics, a force is any interaction 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 newtons and 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, since matter and energy are the basic constituents of the natural world. Some other domains of study—more limited in their scope—may be considered branches that have split off from physics to become sciences in their own right. Physics today may be divided loosely into classical physics and modern physics.

An inertial frame of reference in classical physics and special relativity possesses the property that in this frame of reference a body with zero net force acting upon it does not accelerate; that is, such a body is at rest or moving at a constant velocity. 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.

Mechanics is the area of science concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The scientific discipline 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 objects. The field is yet less widely understood in terms of quantum theory.

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a quantitative measure of the force, and the third asserts that a single isolated force doesn't exist. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows:

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 acceleration 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 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 Alexandrian philologist, Aristotelian commentator and Christian theologian, author of a considerable number of philosophical treatises and theological works. 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. Greek philosopher Aristotle believed that objects tend toward a point due to their inner gravitas (heaviness). Vitruvius understood that objects fall based on their specific gravity. 5th/6th-century AD Indian mathematician Aryabhata developed a geocentric model incorporating gravity; in the 7th century, Brahmagupta spoke of gravity as an attractive force.

Aristotelian physics is the form of natural science described in the works of the Greek philosopher Aristotle (384–322 BCE). 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.

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

## References

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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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6. Lucretius, On the Nature of Things (London: Penguin, 1988), pp. 60–65
7. 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.
8. "John Philoponus". Stanford Encyclopedia of Philosophy. 8 June 2007. Retrieved 26 July 2012.
9. 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.
10. Jean Buridan: Quaestiones on Aristotle's Physics (quoted at Impetus Theory)
11. Giovanni Benedetti, selection from Speculationum, in Stillman Drake and I. E. Drabkin, Mechanics in Sixteenth Century Italy University of Wisconsin Press, 1969, p. 156.
12. 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.
13. Nicholas Copernicus, The Revolutions of the Heavenly Spheres, 1543
14. For a detailed analysis concerning this issue, see Alan Chalmers article "Galliean Relativity and Galileo's Relativity", in Correspondence, Invariance and Heuristics: Essays in Hounour of Heinz Post, eds. Steven French and Harmke Kamminga, Kluwer Academic Publishers, Dordrecht, 1991, ISBN   0792320859.
15. Drake, S. Discoveries and Opinions of Galileo, Doubleday Anchor, New York, 1957, pp. 113–114
16. See Alan Chalmers article "Galliean Relativity and Galileo's Relativity", in Correspondence, Invariance and Heuristics: Essays in Hounour 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.
17. Dijksterhuis E.J. The Mechanisation of the World Picture, Oxford University Press, Oxford, 1961, p. 352
18. Galileo, Letters on Sunspots, 1613 quoted in Drake, S. Discoveries and Opinions of Galileo, Doubleday Anchor, New York, 1957, pp. 113–114.
19. According to Newtonian mechanics, if a projectile on a smooth spherical planet is given an initial horizontal impetus, it will not remain on the surface of the earth. Various curves are possible depending on the initial speed and the height of 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
20. Galileo, Dialogue Concerning the Two Chief World Systems , 1632 (full text).
21. van Berkel, Klaas (2013), Isaac Beeckman on Matter and Motion: Mechanical Philosophy in the Making, Johns Hopkins University Press, pp. 105–110, ISBN   9781421409368
22. Dourmaskin, Peter (December 2013). "Classical Mechanics: MIT 8.01 Course Notes". MIT Physics 8.01. Retrieved September 9, 2016.
23. Lawrence Nolan (ed.), The Cambridge Descartes Lexicon, Cambridge University Press, 2016, "Inertia."
24. Biad, Abder-Rahim (2018-01-26). Restoring the Bioelectrical Machine. Lulu Press, Inc. ISBN   9781365447709.
25. Alfred Engel English Translation:Einstein, Albert (1997), The Foundation of the General Theory of Relativity (PDF), New Jersey: Princeton University Press, p. 57, retrieved 30 May 2014