The reluctance of a massive object to change its motion. Inherent to mass, it is present in the absence of gravity. Newton's first law is sometimes called the law of inertia, and is equivalent to ascribing the property of inertia to objects.
This article is about inertia as it applies to local motion. For other uses, see Inertia (disambiguation).The principle of inertia is one of the fundamental laws of classical physics which are used to describe the motion of matter and how it is affected by applied forces. Inertia is the property of an object to resist changes in velocity unless acted upon by an outside force. Inertia is dependent upon the mass and shape of the object. The concept of inertia is today most commonly defined using Sir Isaac Newton's First Law of Motion, which states:
Every body perseveres in its state of being at rest or of moving uniformly straight ahead, except insofar as it is compelled to change its state by forces impressed. [Cohen & Whitman 1999 translation]
The description of inertia presented by Newton's law is still considered the standard for classical physics. In common usage, however, people may also use the term "inertia" to refer qualitatively to an object's "amount of resistance to change in velocity" (which is determined by its mass), and sometimes its momentum, depending on context (e.g. The term "inertia" is more properly understood as a shorthand for "the principle of inertia as described by Newton in his First Law."
In simple terms we can say that "In an isolated system, a body at rest will remain at rest and a body moving with constant velocity will continue to do so, unless disturbed by an unbalanced force"History and development of the concept
Early understanding of motion
Prior to the Renaissance in the 15th century, the generally accepted theory of motion in western philosophy was that proposed by Aristotle (around 335 BC to 322 BC), which stated that in the absence of an external motive power, all objects (on earth) would naturally come to rest in a state of no movement, and that moving objects only continue to move so long as there is a power inducing them to do so.
Despite its remarkable success and general acceptance, Aristotle's concept of motion was disputed on several occasions by notable philosophers over the nearly 2 millennia of its reign. Philoponus proposed that motion was not maintained by the action of the surrounding medium but by some property implanted in the object when it was set in motion. This was not the modern concept of inertia, for there was still the need for a power to keep a body in motion.
Theory of impetus
In the 14th century Jean Buridan rejected the notion that this motion-generating property, which he named impetus, dissipated spontaneously. 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.
Shortly before Galileo's theory of inertia, Giovanni 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
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 (and everything on it) was in fact never "at rest", but was actually in constant motion around the sun. 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.
It is also worth noting that Galileo later went on to conclude 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.
Galileo's concept of inertia would later come to be refined 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 an 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).
The actual term "inertia" was first introduced by Johannes Kepler in his Epitome Astronomiae Copernicanae (published in three parts from 1618-1621); 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. Given this perspective, and borrowing from Kepler, Newton actually attributed the term "inertia" to mean "the innate force possessed by an object which resists changes in motion"; 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 basically equivalent.
Relativity
Albert Einstein's theory of Special Relativity, as proposed in his 1905 paper, "On the Electrodynamics of Moving Bodies," built on the understanding of inertia and 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 (in fact the entire theory was based on Newton's definition of inertia).
As a result of this redefinition, Einstein also redefined the concept of "inertia" in terms of geodesic deviation instead, with some subtle but significant additional implications. The result of this is that according to General Relativity, when dealing with very large scales, the traditional Newtonian idea of "inertia" does not actually apply, and cannot necessarily be relied upon.
Another profound, perhaps the most well-known, conclusion of the theory of Special Relativity was that energy and mass are not separate things, but are, in fact, interchangeable. The logical conclusion of Special Relativity was that if mass exhibits the principle of inertia, then inertia must also apply to energy as well.
Interpretations
According to Isaac Asimov
According to Isaac Asimov in "Understanding Physics": "This tendency for motion (or for rest) to maintain itself steadily unless made to do otherwise by some interfering force can be viewed as a kind of "laziness," a kind of unwillingness to make a change. And indeed, [Newton's] first law of motion is referred to as the principle of inertia, from a Latin word meaning "idleness" or "laziness."
As Isaac Asimov goes on to explain, "Newton's laws of motion represent assumptions and definitions and are not subject to proof.
Mass and 'inertia'
Physics and mathematics appear to be less inclined to use the original concept of inertia as "a tendency to maintain momentum" and instead favor the mathematically useful definition of inertia as the measure of a body's resistance to changes in momentum or simply a body's inertial mass.
This was clear in the beginning of the 20th century, when the theory of relativity was not yet created. And at the same time mass was the quantitative measure of inertia of a body.
The mass of a body determines the momentum P of the body at given velocity v; it is a proportionality factor in the formula:
P = mv
The factor m is referred to as inertial mass.
But mass as related to 'inertia' of a body can be defined also by the formula:
F = ma
By this formula, the greater its mass, the less a body accelerates under given force.
This meaning of a body's inertia therefore is altered from the original meaning as "a tendency to maintain momentum" to a description of the measure of how difficult it is to change the momentum of a body.
Inertial mass
The only difference there appears to be between inertial mass and gravitational mass is the method used to determine them.
Gravitational mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass.
Inertial mass is found by applying a known force to an unknown mass, measuring the acceleration, and applying Newton's Second Law, m = F/a.
The interesting thing is that, physically, no difference has been found between gravitational and inertial mass. Einstein used the fact that gravitational and inertial mass were equal to begin his Theory of General Relativity in which he postulated that gravitational mass was the same as inertial mass, and that the acceleration of gravity is a result of a 'valley' or slope in the space-time continuum that masses 'fell down' much as pennies spiral around a hole in the common donation toy at a chain store.
Since Einstein used inertial mass to describe Special Relativity, inertial mass is closely related to relativistic mass and is therefore different from rest mass.
Inertial frames
In a location such as a steadily moving railway carriage, a dropped ball would behave as it would if it were dropped in a stationary carriage. Before being dropped, the ball was traveling with the train at the same speed, and the ball's inertia ensured that it continued to move in the same speed and direction as the train, even while dropping. Note that, here, it is inertia which ensured that, not its mass.
In an inertial frame all the observers in uniform (non-accelerating) motion will observe the same laws of physics.
However, in frames which are experiencing acceleration (non-inertial frames), objects appear to be affected by fictitious forces.
In summary, the principle of inertia is intimately linked with the principles of conservation of energy and conservation of momentum.
Rotational inertia
Another form of inertia is rotational inertia, which refers to the fact that a rotating rigid body maintains its state of uniform rotational motion. Carmazza, A (1980) "Curvilinear motion in the absence of external forces: naïve beliefs about the motion of objects", Science vol 210, pp1139-1141 Masreliez, C.J., Motion, Inertia and Special Relativity – a Novel Perspective, Physica Scripta, accepted (Oct 2006)
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