# Inertia

Inertia is the resistance of any physical object to any change in its state of motion. This includes changes to the object's speed, direction, or state of rest. The term "inertia" is also understood as shorthand for "the principle of inertia" as defined by Isaac Newton (translated by Andrew Motte) in his first law of the Philosophiæ Naturalis Principia Mathematica:

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.

## Quotes

• [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.
• Giambattista Benedetti, Diversarum speculationum mathematicarum et physicarum liber (1585) as translated in Stillman Drake, I. E. Drabkin, Mechanics in Sixteenth Century Italy (1969) p. 156.
• Special relativity has this in common with Newtonian mechanics: The laws of both theories are supposed to hold only with respect to certain coordinate sys­tems: those known as "inertial systems. " An inertial system is a system in a state of motion such that "force-free" material points within it are not accelerated with respect to the coordinate system. How­ever, this definition is empty if there is no independent means for recognizing the absence of forces. But such a means of recognition does not exist if gravitation is considered as a "field."
• [O]ne of the most interesting aspects in Fabri's physics is the wholehearted adoption of the important principle of conservation of rectilinear motion (...CRM) - a direct result of an impetus which... tends to conserve itself in the absence of obstacles or hindrences, and the possibility of motion in a vacuum... CRM is often referred to as "inertia", but this problematic term is both anachronistic and misleading. The word... (...meaning "laziness") was first utilized in a physical sense by Johannes Kepler, to mean a tendency of bodies to come to rest once they are set in motion... It was subsequently used, in a different sense - meaning the reluctance of of bodies in rest to be set in motion - by Descartes... and even by Fabri himself. This notion, as... expressed in Newton's first law... could be regarded merely as a "less important aspect of inertia" than in his second law... it is also clear that the classical (or Newtonian) concept cannot be fully expressed and understood without Newton's third law and his concept of force...
• Michael Elazar, Honoré Fabri and the Concept of Impetus: A Bridge between Conceptual Frameworks (2011) Boston Studies in the Philosophy of Science.
• The law of inertia has no known origin.
• One other test of gravity... is the question of whether the pull is exactly proportional to the mass... and changes in velocity are inversely proportional to the mass... That means that two objects of different mass will change their velocity in the same manner in a gravitational field. ...That is Galileo's old experiment from the Leaning Tower of Pisa. ...How accurate is it? It was measured in an experiment by ...Eötvös in 1909 and ...by Dicke, and is known to one part in 10,000,000,000. ...[S]uppose you wanted to know whether the pull is exactly proportional to the inertia. The earth is going around the sun, so the things are thrown out by inertia. But they are attracted by the sun to the extent that they have mass... So if they are attracted to the sun in a different proportion from that thrown out by inertia, one will be pulled towards the sun, and the other away from it, and so, hanging them on opposite ends of a rod on another Cavendish quartz fiber, the thing will twist towards the sun. It does not twist at this accuracy, so we know that the sun's attraction to two objects is exactly proportional to its coefficient of inertia; in other words, its mass.
• The situation of everyday life which Kant used as an analogy to the inertia of matter is the contrast between matter itself and the artisan who operates on the material... The characteristic feature of matter is its complete passivity... responsible for its inertia. ...Although this introduction of the concept of "life" into physical science does make it more "human," it certainly has little to do with the actual law of inertia in mechanics. It even gives the misleading impression that for living organisms the law of inertia would not be valid.
• Phillip Frank, Philosophy of Science: The Link Between Science and Philosophy (1957)
• I tell you that if natural bodies have it from Nature to be moved by any movement, this can only be circular motion, nor is it possible that Nature has given to any of its integral bodies a propensity to be moved by straight motion. I have many confirmations of this proposition, but for the present one alone suffices, which is this. I suppose the parts of the universe to be in the best arrangement, so that none is out of its place, which is to say that Nature and God have perfectly arranged their structure. This being so, it is impossible for those parts to have it from Nature to be moved in straight, or in other than circular motion, because what moves straight changes place, and if it changes place naturally, then it was at first in a place preternatural to it, which goes against the supposition. Therefore, if the parts of the world are well ordered, straight motion is superfluous and not natural, and they can only have it when some body is forcibly removed from its natural place, to which it would then return by a straight line, for thus it appears that a part of the earth does [move] when separated from its whole. I said "it appears to us," because I am not against thinking that not even for such an effect does Nature make use of straight line motion.
• I mentally conceive of some moveable [sphere] projected on a horizontal plane, all impediments being put aside. Now it is evident... that equable motion on this plane would be perpetual if the plane were of infinite extent, but if we assume it to be ended, and [situated] on high, the movable, driven to the end of this plane and going on further, adds on to its previous equable and indelible motion, that downward tendency which it has from its heaviness. Thus, there emerges a certain motion, compounded...
• Galileo Galilei, Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638) Stillman Drake translation (1974) Author, Day Four, On the Motion of Projectiles, p. 268.
• It seems to me proper to adorn the Author's thought here with its conformity to a conception of Plato's regarding the determination of the various speeds of equable motion in the celestial motions of revolution. ...he said that God, after having created the movable celestial bodies, in order to assign to them those speeds with which they must be moved perpetually in equable circular motion, made them depart from rest and move through determinate spaces in that natural straight motion in which we sensibly see our moveables to be moved from the state of rest, successively accelerating. And he added that these having been made to gain that degree [of speed] which it pleased God that they should maintain forever, He turned their straight motion into circulation, the only kind [of motion] that is suitable to be conserved equably, turning always without retreat from or approach toward any pre-established goal desired by them. The conception is truly worthy of Plato, and it is to be more esteemed to the extent that its foundations, of which Plato remained silent, but which were discovered by our Author in removing their poetical mask or semblance, show it the guise of a true story.
• Galileo Galilei, Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638) Sagredo, Day Four, Stillman Drake translation (1974) pp.283-284.
• Second law of mechanics.—All change of matter has an external cause. (Every body remains in its state of rest or motion in the same direction and with the same velocity, if not compelled by an external cause to forsake this state.)
Demonstration.
(From universal metaphysics the proposition that all change has a cause, is laid at the foundation; here it only remains to be proved of matter, that its change must always have an external cause. ... this cause cannot be internal for matter has no absolutely internal determinations and grounds of determination. ...
Observation.
This mechanical law can only be called the law of inertia (lex inertiæ)...
• Immanuel Kant, Metaphysische Anfangsgründe der Naturwissenschaft (1786) as translated in Metaphysical Foundations of Natural Science (1883) Tr. Ernest Belfort Bax, Third Division: Metaphysical Foundations of Mechanics, Proposition 3, p. 222.
• The inertia of matter is and means nothing but its lifelessness, as matter in itself. Life means the capacity of a substance, to act from an internal principle, determining a finite substance to change, and a material substance to rest or motion, as change of its state. ...Thus all matter as such is lifeless. The proposition of inertia says so much and no more. If we seek the cause of any change of matter whatsoever in life, we shall have to seek it at once in another substance, distinct from matter, although bound up with it.
• Immanuel Kant, Metaphysische Anfangsgründe der Naturwissenschaft (1786) Tr. Ernest Belfort Bax, as translated in Metaphysical Foundations of Natural Science (1883) Third Division: Metaphysical Foundations of Mechanics, Proposition 3, pp. 222-223.
• On the law of inertia (next to that of the permanence of substance) the possibility of a natural science proper entirely rests. The opposite of the first, and therefore the death of all natural philosophy, would be hylozoism. From the same conception of inertia as that of mere lifelessness, it follows... that it does not signify a positive effort to maintain its state. Only living beings can be termed inert in this latter sense, inasmuch as they have a conception of another state, which they dread and strive against with all their might.
• Immanuel Kant, Metaphysische Anfangsgründe der Naturwissenschaft (1786) Tr. Ernest Belfort Bax as translated in Metaphysical Foundations of Natural Science (1883) Third Division: Metaphysical Foundations of Mechanics, Proposition 3, p. 223.
• Law I. Every body perseveres in its state of rest or of moving uniformly in a straight line, except in so far as it is made to change that state by external forces. ...the motion of a cannon ball is retarded, but this arises from an action between the projectile and the air which surrounds it, whereby the ball experiences a force in the direction opposite to its relative motion, while the air, pushed forward by an equal force, is itself set in motion... But our conviction of the truth of this law may be greatly strengthened by considering what is involved in a denial of it. ...Let us in the first place suppose the law to be that the velocity diminishes at a certain [extremely slow] rate... The velocity referred to in this hypothetical law can only be the velocity referred to a point absolutely at rest... the point of reference. ...If, when referred to a certain point, the body appears to be moving northward with diminishing velocity, we have only to refer it to another point moving northward with a uniform velocity greater than that of the body, and it will appear to be moving southward with increasing velocity.
Hence the hypothetical law is without meaning unless we admit the possibility of defining absolute rest and absolute velocity.
Even if we admit this as a possibility, the hypothetical law, if found to be true, might be interpreted, not as a contradiction of Newton's law, but as evidence of the resisting action of some medium in space.
To take another case. Suppose the law to be that a body, not acted on by any force, ceases at once to move. This is not only contradicted by experience, but it leads to a definition of absolute rest as the state which a body assumes as soon as it is freed from the action of external forces.
It may thus be shown that the denial of Newton's law is in contradiction to the only system of consistent doctrine about space and time which the human mind has been able to form.
• The idea that inertia is an acquired property is old, generally going under the name of “Mach’s principle”. According to it, inertia is due to the interaction of bodies with some omnipresent medium. Ideas along this line differ on what the medium is, and on the nature of the interaction. But if indeed such is the origin of inertia, then inertia is not some property of ultimate fundamentality, but can take different forms depending on where we are in parameter space of the body with respect to signposts and boundary stones defined by the characteristics of the medium.
• The old Greek philosophy, which in Europe in the later middle ages was synonymous with the works of Aristotle, considered motion as a thing for which a cause must be found: a velocity required a force to produce and to maintain it. The great discovery of Galileo was that not velocity, but acceleration requires a force.
• As related by Archimedes in the "sand-counter", Aristarchus advanced the bold hypothesis that the earth rotates in a circle about the sun. Most astronomers rejected this... as Archimedes tells us also. [I]n view of the status of mechanics at the time, there are weighty arguments against the motion of the earth... already found in Aristotle and, developed more fully, in Ptolemy. If the earth had such an enormously rapid motion, says Ptolemy, then everything that was not clinched to and riveted to the earth, would fall behind and would therefore appear to fly off in the opposite direction. Clouds... would be overtaken by the rotation of the earth and would lag behind. ...[T]here is nothing to be said against this since the Greeks did not know the law of inertia and required a force to account for every motion. If the earth does not drag the clouds along, they have to lag behind. We do not know how Aristarchus met these arguments.