Inertia
Encyclopedia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. 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. Isaac Newton
defined inertia as his first law in his Philosophiæ Naturalis Principia Mathematica, which states:
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.
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.
the most generally accepted theory of motion in Western philosophy
was based on Aristotle
(around 335 BC to 322 BC) who stated 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. Aristotle concluded that such violent motion in a void was impossible.
Despite its general acceptance, Aristotle's concept of motion was disputed on several occasions by notable philosophers over nearly 2 millennia. For example Lucretius
(following, presumably, Epicurus
) stated that the 'default state' of matter was motion not stasis. 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. 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.
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. 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 maintained 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:
Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion.
, 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. 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:
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. 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):
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 branch of physics
known as 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 considered to be equivalent.
'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 space-time, 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.
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
of the body at given velocity 
; it is a proportionality factor in the formula:
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:
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
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.
Gravitational mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass. This is typically done with some sort of balance. The beauty of this method is that no matter where, or on what planet you are, the masses will always balance out because the gravitational field present for each object will be the same. As long as there is a gravitational field, a balance will yield a reliable mass measurement. This does break down near supermassive objects such as black holes and neutron stars due to the steep gradient of the gravitational field around such objects. It also breaks down in weightless environments, because no matter what objects are compared, it will yield a balanced reading.
Inertial mass is found by applying a known net force to an unknown mass, measuring the resulting acceleration, and applying Newton's Second Law, m = F/a. This gives an accurate value for mass, limited only by the accuracy of the measurements. When astronauts need to be measured in the weightlessness of free fall, they actually find their inertial mass in a special chair called a body mass measurement device (BMMD).
The interesting thing is that, physically, no difference has been found between gravitational and inertial mass. Many experiments have been performed to check the values and the experiments always agree to within the margin of error for the experiment. 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. Dennis Sciama later showed that the reaction force produced by the combined gravity of all matter in the universe upon an accelerating object is mathematically equal to the object's inertia http://physics.fullerton.edu/~jimw/general/inertia/index.htm, but this would only be a workable physical explanation if by some mechanism the gravitational effects operated instantaneously.
Since Einstein used inertial mass to describe special relativity
, inertial mass is closely related to relativistic mass and is therefore different from rest mass.
In an inertial frame all the observers in uniform (non-accelerating) motion will observe the same laws of physics. However observers in another inertial frame can make a simple, and intuitively obvious, transformation (the Galilean transformation
), to convert their observations. Thus, an observer from outside the moving train could deduce that the dropped ball within the carriage fell vertically downwards.
However, in frames which are experiencing acceleration (non-inertial frames), objects appear to be affected by fictitious force
s. For example, if the railway carriage were accelerating, the ball would not fall vertically within the carriage but would appear to an observer to be deflected because the carriage and the ball would not be traveling at the same speed while the ball was falling. Other examples of fictitious forces occur in rotating frames such as the earth. For example, a missile at the North Pole could be aimed directly at a location and fired southwards. An observer would see it apparently deflected away from its target by a force (the Coriolis force
) but in reality the southerly target has moved because earth has rotated while the missile is in flight. Because the earth is rotating, a useful inertial frame of reference is defined by the stars, which only move imperceptibly during most observations.The law of inertia is also known as Isaac Newton's first law of motion.
In summary, the principle of inertia is intimately linked with the principles of conservation of energy
and conservation of momentum.
(see Mach's principle
), Albert Einstein, D Sciama
, and Bernard Haisch
have all run into significant criticisms from more recent theorists.
), which refers to the fact that a rotating rigid body maintains its state of uniform rotation
al 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.
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
. The principle of inertia is one of the fundamental principles of classical physics
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
which are used to describe the motion
Motion (physics)
In physics, motion is a change in position of an object with respect to time. Change in action is the result of an unbalanced force. Motion is typically described in terms of velocity, acceleration, displacement and time . An object's velocity cannot change unless it is acted upon by a force, as...
of matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
and how it is affected by applied forces. Inertia comes from the Latin word, iners, meaning idle, or lazy. Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
defined inertia as his first law in his Philosophiæ Naturalis Principia Mathematica, which states:
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
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
, 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
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
; 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
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
until some force causes its speed or direction to change.
On the surface of the Earth inertia is often masked by the effects of friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types 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
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
, who believed that objects would move only as long as force was applied to them.
Early understanding of motion
Prior to the RenaissanceRenaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...
the most generally accepted theory of motion in Western philosophy
Western philosophy
Western philosophy is the philosophical thought and work of the Western or Occidental world, as distinct from Eastern or Oriental philosophies and the varieties of indigenous philosophies....
was based on Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
(around 335 BC to 322 BC) who stated 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. Aristotle concluded that such violent motion in a void was impossible.
Despite its general acceptance, Aristotle's concept of motion was disputed on several occasions by notable philosophers over nearly 2 millennia. For example Lucretius
Lucretius
Titus Lucretius Carus was a Roman poet and philosopher. His only known work is an epic philosophical poem laying out the beliefs of Epicureanism, De rerum natura, translated into English as On the Nature of Things or "On the Nature of the Universe".Virtually no details have come down concerning...
(following, presumably, Epicurus
Epicurus
Epicurus was an ancient Greek philosopher and the founder of the school of philosophy called Epicureanism.Only a few fragments and letters remain of Epicurus's 300 written works...
) stated that the 'default state' of matter was motion not stasis. In the 6th century John Philoponus
John Philoponus
John Philoponus , also known as John the Grammarian or John of Alexandria, was a Christian and Aristotelian commentator and the author of a considerable number of philosophical treatises and theological works...
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. This view was strongly opposed by Averroes
Averroes
' , better known just as Ibn Rushd , and in European literature as Averroes , was a Muslim polymath; a master of Aristotelian philosophy, Islamic philosophy, Islamic theology, Maliki law and jurisprudence, logic, psychology, politics, Arabic music theory, and the sciences of medicine, astronomy,...
and by many scholastic
Scholasticism
Scholasticism is a method of critical thought which dominated teaching by the academics of medieval universities in Europe from about 1100–1500, and a program of employing that method in articulating and defending orthodoxy in an increasingly pluralistic context...
philosophers who supported Aristotle. However this view did not go unchallenged in the Islamic world
Islamic Golden Age
During the Islamic Golden Age philosophers, scientists and engineers of the Islamic world contributed enormously to technology and culture, both by preserving earlier traditions and by adding their own inventions and innovations...
, where Philoponus did have several supporters who further developed his ideas.
Theory of impetus
In the 14th century, Jean BuridanJean Buridan
Jean Buridan was a French priest who sowed the seeds of the Copernican revolution in Europe. Although he was one of the most famous and influential philosophers of the late Middle Ages, he is today among the least well known...
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. 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
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
. 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 maintained 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
Albert of Saxony (philosopher)
Albert of Saxony was a German philosopher known for his contributions to logic and physics...
(1316–1390) and the Oxford Calculators
Oxford Calculators
The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford, who took a strikingly logico-mathematical approach to philosophical problems....
, 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
Giambattista Benedetti
Giambattista Benedetti was an Italian mathematician from Venice who was also interested in physics, mechanics, the construction of sundials, and the science of music.-Science of motion:...
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 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, frictionFriction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of 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
Nicolaus Copernicus
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....
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. This observation ultimately came to be the basis for Einstein to develop the theory of Special Relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
.
Galileo's concept of inertia would later come to be refined and codified by Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
as the first of his Laws of Motion
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
(first published in Newton's work, Philosophiae Naturalis Principia Mathematica
Philosophiae Naturalis Principia Mathematica
Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726...
, 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 branch of physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
known as classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
.
The actual term "inertia" was first introduced by Johannes Kepler
Johannes Kepler
Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...
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 considered to be equivalent.
Relativity
Albert EinsteinAlbert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
's theory of Special Relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
, 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
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
, and distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical 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
Principle of relativity
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....
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
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
("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 space-time, 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.
Mass and inertia
PhysicsPhysics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
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
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
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
of the body at given velocity ; it is a proportionality factor in the formula: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:
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
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.
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. This is typically done with some sort of balance. The beauty of this method is that no matter where, or on what planet you are, the masses will always balance out because the gravitational field present for each object will be the same. As long as there is a gravitational field, a balance will yield a reliable mass measurement. This does break down near supermassive objects such as black holes and neutron stars due to the steep gradient of the gravitational field around such objects. It also breaks down in weightless environments, because no matter what objects are compared, it will yield a balanced reading.
Inertial mass is found by applying a known net force to an unknown mass, measuring the resulting acceleration, and applying Newton's Second Law, m = F/a. This gives an accurate value for mass, limited only by the accuracy of the measurements. When astronauts need to be measured in the weightlessness of free fall, they actually find their inertial mass in a special chair called a body mass measurement device (BMMD).
The interesting thing is that, physically, no difference has been found between gravitational and inertial mass. Many experiments have been performed to check the values and the experiments always agree to within the margin of error for the experiment. 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. Dennis Sciama later showed that the reaction force produced by the combined gravity of all matter in the universe upon an accelerating object is mathematically equal to the object's inertia http://physics.fullerton.edu/~jimw/general/inertia/index.htm, but this would only be a workable physical explanation if by some mechanism the gravitational effects operated instantaneously.
Since Einstein used inertial mass to describe special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
, 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 (as seen by an observer in the carriage) would behave as it would if it were dropped in a stationary carriage. The ball would simply descend vertically. It is possible to ignore the motion of the carriage by defining it as an inertial frame. In a moving but non-accelerating frame, the ball behaves normally because the train and its contents continue to move at a constant velocity. 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 observers in another inertial frame can make a simple, and intuitively obvious, transformation (the Galilean transformation
Galilean transformation
The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. This is the passive transformation point of view...
), to convert their observations. Thus, an observer from outside the moving train could deduce that the dropped ball within the carriage fell vertically downwards.
However, in frames which are experiencing acceleration (non-inertial frames), objects appear to be affected by fictitious force
Fictitious force
A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame....
s. For example, if the railway carriage were accelerating, the ball would not fall vertically within the carriage but would appear to an observer to be deflected because the carriage and the ball would not be traveling at the same speed while the ball was falling. Other examples of fictitious forces occur in rotating frames such as the earth. For example, a missile at the North Pole could be aimed directly at a location and fired southwards. An observer would see it apparently deflected away from its target by a force (the Coriolis force
Coriolis effect
In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right...
) but in reality the southerly target has moved because earth has rotated while the missile is in flight. Because the earth is rotating, a useful inertial frame of reference is defined by the stars, which only move imperceptibly during most observations.The law of inertia is also known as Isaac Newton's first law of motion.
In summary, the principle of inertia is intimately linked with the principles of conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
and conservation of momentum.
Source of inertia
There is no single accepted theory that explains the source of inertia. Various efforts by notable physicists such as Ernst MachErnst Mach
Ernst Mach was an Austrian physicist and philosopher, noted for his contributions to physics such as the Mach number and the study of shock waves...
(see Mach's principle
Mach's principle
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....
), Albert Einstein, D Sciama
Dennis William Sciama
Dennis William Siahou Sciama FRS was a British physicist who, through his own work and that of his students, played a major role in developing British physics after the Second World War. He is considered as one of the fathers of modern cosmology.-Life:Sciama was born in Manchester, England...
, and Bernard Haisch
Bernard Haisch
Bernard Haisch is a German-born American astrophysicist who has done research in solar-stellar astrophysics and stochastic electrodynamics. He has developed with Alfonso Rueda a speculative theory that the non-zero lowest energy state of the vacuum, as predicted by quantum mechanics, might provide...
have all run into significant criticisms from more recent theorists.
Rotational inertia
Another form of inertia is rotational inertia (→ moment of inertiaMoment of inertia
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...
), which refers to the fact that a rotating rigid body maintains its state of uniform rotation
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...
al motion. Its angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
is unchanged, unless an external torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
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
Gyroscope
A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation...
uses the property that it resists any change in the axis of rotation.
See also
- General relativityGeneral relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
- Inertial guidance system
- Kinetic EnergyKinetic energyThe kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
- List of moments of inertia
- Mach's principleMach's principleIn 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....
- Newton's laws of motionNewton's laws of motionNewton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
- Newtonian physics
- Special relativitySpecial relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
- Steiner theorem
External links
Books and papers
- Butterfield, H (1957) The Origins of Modern Science ISBN 0-7135-0160-X
- Clement, J (1982) "Students' preconceptions in introductory mechanics", American Journal of PhysicsAmerican Journal of PhysicsThe American Journal of Physics is a monthly, peer-reviewed scientific journal published by the American Association of Physics Teachers and the American Institute of Physics. The editor is Jan Tobochnik of Kalamazoo College.-Aims and scope:...
vol 50, pp 66–71 - Crombie, A C (1959) Medieval and Early Modern Science, vol 2
- McCloskey, M (1983) "Intuitive physics", Scientific American, April, pp 114–123
- McCloskey, M & Carmazza, A (1980) "Curvilinear motion in the absence of external forces: naïve beliefs about the motion of objects", Science vol 210, pp1139–1141