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Inertia is the resistance of any physical object to a change in its state of motion or rest. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to describe the motion of matter and how it is affected by applied forces. Inertia comes from the Latin word, iners, meaning idle, or lazy. Sir Isaac Newton defined inertia in Definition 3 of his Philosophiæ Naturalis Principia Mathematica, which states:^[1]

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.

In common usage the term "inertia" may refer to an object's "amount of resistance to change in velocity" (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; that 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. An object that is not in motion (velocity = zero) will remain at rest until some force causes it to move.
On the surface of the Earth inertia is often masked by the effects of friction and gravity, both of which tend to decrease the speed of moving objects (commonly to the point of rest). This misled classical theorists such as Aristotle, who believed that objects would move only as long as force was applied to them.




Classical inertia

The law of inertia states that it is the tendency of an object to resist a change in motion. According to Newton's words, an object will stay at rest or stay in motion unless acted on by a net external force, whether it results from gravity, friction, contact, or some other source. 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.^[10] 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.^[11] This observation ultimately came to be the basis for Einstein to develop the theory of Special Relativity.
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 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 extension this first law) have come to form the basis for the almost universally accepted branch of physics now termed classical mechanics.
The actual term "inertia" was first introduced by Johannes Kepler in his Epitome Astronomiae Copernicanae (published in three parts from 1618–1621); 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 actually 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 basically equivalent.

Relativity

Albert Einstein's theory of Special Relativity, as proposed in his 1905 paper, "On the Electrodynamics of Moving Bodies," was 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). However, this resulted in a limitation inherent in Special Relativity that the principle of relativity could only apply to reference frames that were inertial in nature (meaning when no acceleration was present). In an attempt to address this limitation, Einstein proceeded to develop his theory of General Relativity ("The Foundation of the General Theory of Relativity," 1916), which ultimately provided a unified theory for both inertial and noninertial (accelerated) reference frames. However, in order to accomplish this, in General Relativity Einstein found it necessary to redefine several fundamental concepts (such as gravity) in terms of a new concept of "curvature" of spacetime, instead of the more traditional system of forces understood by Newton.
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. Luckily, for sufficiently small regions of spacetime, the Special Theory can still be used, in which inertia still means the same (and works the same) as in the classical model.
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. This new relationship, however, also carried with it new implications for the concept of inertia. The logical conclusion of Special Relativity was that if mass exhibits the principle of inertia, then inertia must also apply to energy as well. This theory, and subsequent experiments confirming some of its conclusions, have also served to radically expand the definition of inertia in some contexts to apply to a much wider context including energy as well as matter.

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 laws of motion, as Asimov goes on to explain, "represent assumptions and definitions and are not subject to proof. In particular, the notion of 'inertia' is as much an assumption as Aristotle's notion of 'natural place'.... To be sure, the new relativistic view of the universe advanced by Einstein makes it plain that in some respects Newton's laws of motion are only approximations.... At ordinary velocities and distance, however, the approximations are extremely good."

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. Mass, m, denoted something like amount of substance or quantity of matter. 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

Here, F is force, m is mass, and a is acceleration.
By this formula, the greater its mass, the less a body accelerates under given force. Masses m defined by formula (1) and (2) are equal because formula (2) is a consequence of formula (1) if mass does not depend on time and velocity. Thus, "mass is the quantitative or numerical measure of body’s inertia, that is of its resistance to being accelerated".
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.

Rotational inertia

Another form of inertia is rotational inertia (→ moment of inertia), which refers to the fact 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 hidden practical consequences ^. For example, a gyroscope uses the property that it resists any change in the axis of rotation