TheInfoList

Newton's laws of motion are three
law Law is a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its bounda ...
s of classical mechanics that describe the relationship between the
motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon in which an object changes its position (mathematics), position over time. Motion is mathematically described in terms of Displacem ...

of an object and the
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

s acting on it. These laws can be paraphrased as follows: ''Law 1''. A body continues in its state of rest, or in uniform motion in a straight line, unless acted upon by a force. ''Law 2''. A body acted upon by a force moves in such a manner that the time rate of change of
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

equals the force. ''Law 3''. If two bodies exert forces on each other, these forces are equal in magnitude and opposite in direction. The three laws of motion were first stated by
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

in his ''
Philosophiæ Naturalis Principia Mathematica (from Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republic, it bec ...
'' (''Mathematical Principles of Natural Philosophy''), first published in 1687.See the ''Principia'' on line a
Andrew Motte Translation
/ref> Newton used them to explain and investigate the motion of many physical objects and systems, which laid the foundation for Newtonian mechanics.

# Laws

## First law

Newton's first law, also called the "law of
inertia Inertia is the resistance of any physical object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Entity, something that is tangible and within the grasp of the senses ** Object (abstract), an ob ...

", states that an object at rest remains at rest, and an object that is moving will continue to move straight and with constant
velocity The velocity of an object is the rate of change of its position with respect to a frame of reference In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical scie ...

,
if and only if In logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents st ...
there is no
net force In mechanics Mechanics (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximate ...

acting on that object. If any number of different external forces $\mathbf_1, \mathbf_2, \ldots$ are being applied to an object, then the net force $F_$ is the
vector sum In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

of those forces, so $F_ = \mathbf_1 + \mathbf_2 + \cdots$. If that net force is zero, then the object's velocity must not be changing. Conversely, if the object's velocity is not changing, then it must have a net force of zero. Mathematically, $\mathbf_ = 0\; \Leftrightarrow\; \frac = 0$ Newton's first law describes objects that are in two different situations: objects that are stationary, and objects that are moving straight at a constant speed. Newton observed that objects in both situations will only change their speed if a net force is applied to them. An object which is undergoing a net force of zero is said to be at
mechanical equilibrium In classical mechanics, a particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can be ascribed several physical property, phys ...
, and Newton's first law suggests two different types of mechanical equilibrium: an object which has net forces of zero and which is not moving is at mechanical equilibrium, but an object that is moving in a straight line and with constant velocity is also at mechanical equilibrium. Newton's first law is valid only in an
inertial reference frame In classical physics Classical physics is a group of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies mat ...
.

## Second law

Newton's second law describes a simple relationship between the
acceleration In mechanics Mechanics (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approx ...

of an object with mass , and the
net force In mechanics Mechanics (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximate ...

acting on that object: $\mathbf_ = m\mathbf$ The net force and the object's acceleration are both vectors, and they point in the same direction. This version of the law applies to an object with a fixed mass $m$. mphasis as in the original/ref> This relationship says that the net force applied to a body produces a proportional acceleration. It also means that if a body is accelerating, then a net force is being applied to it. The law is also commonly stated in terms of the object's
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

, since and . So, Newton's second law is also written as: $\mathbf = \frac$ Some textbooks use Newton's second law as a ''definition'' of force, but this has been disparaged in other textbooks.

## Variable-mass systems

Variable-mass systems, like a rocket burning fuel and ejecting spent gases, are not closed and cannot be directly treated by making mass a function of time in the second law; the equation of motion for a body whose mass varies with time by either ejecting or accreting mass is obtained by applying the second law to the entire, constant-mass system consisting of the body and its ejected or accreted mass. The result is $\mathbf F + \mathbf \frac = m$ where is the
exhaust velocity Specific impulse (usually abbreviated ) is a measure of how efficiently a reaction mass engine (a rocket A rocket (from it, rocchetto, , bobbin/spool) is a projectile that spacecraft, aircraft An aircraft is a vehicle that is able to ...
of the escaping or incoming mass relative to the body. From this equation one can derive the equation of motion for a varying mass system, for example, the
Tsiolkovsky rocket equation The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself usi ...

. Under some conventions, the quantity on the left-hand side, which represents the
advection In the field of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy ...
of
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

, is defined as a force (the force exerted on the body by the changing mass, such as rocket exhaust) and is included in the quantity . Then, by substituting the definition of acceleration, the equation becomes .

## Third law

The third law states that all forces between two objects exist in equal magnitude and opposite direction: if one object ''A'' exerts a force F''A'' on a second object ''B'', then ''B'' simultaneously exerts a force F''B'' on ''A'', and the two forces are equal in magnitude and opposite in direction: F''A'' = −F''B''. The third law means that all forces are ''
interaction Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way causal effect. Closely related terms are interac ...

s'' between different bodies, or different regions within one body, and thus that there is no such thing as a force that is not accompanied by an equal and opposite force. In some situations, the magnitude and direction of the forces are determined entirely by one of the two bodies, say Body ''A''; the force exerted by Body ''A'' on Body ''B'' is called the "action", and the force exerted by Body ''B'' on Body ''A'' is called the "reaction". This law is sometimes referred to as the '' action-reaction law'', with F''A'' called the "action" and F''B'' the "reaction". In other situations the magnitude and directions of the forces are determined jointly by both bodies and it isn't necessary to identify one force as the "action" and the other as the "reaction". The action and the reaction are simultaneous, and it does not matter which is called the ''action'' and which is called ''reaction''; both forces are part of a single interaction, and neither force exists without the other. The two forces in Newton's third law are of the same type (e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing backward on the road). From a conceptual standpoint, Newton's third law is seen when a person walks: they push against the floor, and the floor pushes against the person. Similarly, the tires of a car push against the road while the road pushes back on the tires—the tires and road simultaneously push against each other. In swimming, a person interacts with the water, pushing the water backward, while the water simultaneously pushes the person forward—both the person and the water push against each other. The reaction forces account for the motion in these examples. These forces depend on friction; a person or car on ice, for example, may be unable to exert the action force to produce the needed reaction force. Newton used the third law to derive the law of
conservation of momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a direction. If is an object's ma ...
; from a deeper perspective, however, conservation of momentum is the more fundamental idea (derived via
Noether's theorem Noether's theorem or Noether's first theorem states that every differentiable In calculus (a branch of mathematics), a differentiable function of one Real number, real variable is a function whose derivative exists at each point in its Domai ...
from
Galilean invariance Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frame In classical physics Classical physics is a group of physics Physics (from grc, φυσική (ἐπιστήμη), physik ...
), and holds in cases where Newton's third law appears to fail, for instance when
force fields In speculative fiction, a force field, sometimes known as an energy shield, force shield, force bubble, defence shield or deflector shield, is a barrier made of things like energy, negative energy, dark energy, electromagnetic fields, gravitationa ...
as well as particles carry momentum, and in
quantum mechanics Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...
.

# History

The ancient Greek philosopher
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questio ...

had the view that all objects have a natural place in the universe: that heavy objects (such as rocks) wanted to be at rest on the Earth and that light objects like smoke wanted to be at rest in the sky and the stars wanted to remain in the heavens. He thought that a body was in its natural state when it was at rest, and for the body to move in a straight line at a constant speed an external agent was needed continually to propel it, otherwise it would stop moving.
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei ( , ; 15 February 1564 – 8 January 1642), commonly referred to as Galileo, was an astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific q ...

, however, realised that a force is necessary to change the velocity of a body but no force is needed to maintain its velocity. Galileo stated that, in the ''absence'' of a force, a moving object will continue moving. (The tendency of objects to resist changes in motion was what
Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe as ...

had called ''inertia''.) This insight was refined by Newton, who made it into his first law, also known as the "law of inertia"—no force means no acceleration, and hence the body will maintain its velocity. As Newton's first law is a restatement of the law of inertia which Galileo had already described, Newton appropriately gave credit to Galileo.

# Importance and range of validity

Newton's laws were verified by experiment and observation for over 200 years, and they are excellent approximations at the scales and speeds of everyday life. Newton's laws of motion, together with his law of
universal gravitation Newton's law of universal gravitation is usually stated as that every particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can ...

and the mathematical techniques of
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations ...

, provided for the first time a unified quantitative explanation for a wide range of physical phenomena. For example, in the third volume of the ''Principia'', Newton showed that his laws of motion, combined with the
law of universal gravitation Newton's law of universal gravitation is usually stated as that every particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can ...
, explained
Kepler's laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the Copernican heliocentrism, heliocentric theory of Nicolaus Copernicus, repl ...
. Newton's laws are applied to bodies which are idealised as single point masses, in the sense that the size and shape of the body are neglected to focus on its motion more easily. This can be done when the
line of action In physics, the line of action (also called line of application) of a force ''F'' is a geometric representation of how the force is applied. It is the line (mathematics), line through the point at which the force is applied in the same direction ...

of the resultant of all the external forces acts through the center of mass of the body. In this way, even a planet can be idealised as a particle for analysis of its orbital motion around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of
rigid bodies In physics, a rigid body (also known as a rigid object ) is a solid body Body may refer to: In science * Physical body, an object in physics that represents a large amount, has mass or takes up space * Body (biology), the physical material of ...

and
deformable bodies In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
.
Leonhard Euler Leonhard Euler ( ; ; 15 April 170718 September 1783) was a Swiss mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ) ...

in 1750 introduced a generalisation of Newton's laws of motion for rigid bodies called Euler's laws of motion, later applied as well for deformable bodies assumed as a
continuum Continuum may refer to: * Continuum (measurement) Continuum theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities. In contrast, categorical theories or models explain variatio ...
. If a body is represented as an assemblage of discrete particles, each governed by Newton's laws of motion, then Euler's laws can be derived from Newton's laws. Euler's laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure. Newton's laws hold only with respect to a certain set of
frames of reference In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...
called Newtonian or inertial reference frames. Some authors interpret the first law as defining what an inertial reference frame is; from this point of view, the second law holds only when the observation is made from an inertial reference frame, and therefore the first law cannot be proved as a special case of the second. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed until long after Newton's death. These three laws hold to a good approximation for macroscopic objects under everyday conditions. However, Newton's laws (combined with universal gravitation and
classical electrodynamics Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charge Electric charge is the physical property of matter that causes it to experience a force when place ...
) are inappropriate for use in certain circumstances, most notably at very small scales, at very high speeds, or in very strong gravitational fields. Therefore, the laws cannot be used to explain phenomena such as conduction of electricity in a
semiconductor A semiconductor material has an electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric curre ...
, optical properties of substances, errors in non-relativistically corrected
GPS The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government The federal government of the United States (U.S. federal government) is the national ...

systems and
superconductivity Superconductivity is a set of physical properties observed in certain materials where electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current An electric current is a st ...

. Explanation of these phenomena requires more sophisticated physical theories, including
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
and
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
. In
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
, the second law holds in the original form F = dp/d''t'', where F and p are
four-vector In special relativity In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in oth ...
s. Special relativity reduces to Newtonian mechanics when the speeds involved are much less than the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
. Some also describe a fourth law that is assumed but was never stated by Newton, which states that forces add like vectors, that is, that forces obey the principle of superposition.

* Euler's laws of motion *
Hamiltonian mechanics Hamiltonian mechanics is a mathematically sophisticated formulation of classical mechanics. Historically, it contributed to the formulation of statistical mechanics and quantum mechanics. Hamiltonian mechanics was first formulated by William Rowan ...
*
Lagrangian mechanics Introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia
*
List of scientific laws named after people This is a list of scientific laws named after people ( eponymous laws). For other lists of eponyms, see eponym An eponym is a person, place, or thing after whom or which someone or something is, or is believed to be, named. The adjectives deri ...
* Orbit of Mercury *
Modified Newtonian dynamics Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's laws In classical mechanics, Newton's laws of motion are three law Law is a system A system is a group of Interaction, interacting or inter ...
*
Newton's law of universal gravitation Newton's law of universal gravitation is usually stated as that every particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can ...
*
Principle of least action :''This article discusses the history of the principle of least action. For the application, please refer to action (physics) In physics, action is an attribute of the dynamics (physics), dynamics of a physical system from which the equations ...

*
Principle of relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...
*
Reaction (physics)As described by the third of Newton's laws of motion of classical mechanics, all forces occur in pairs such that if one object exerts a force on another object, then the second object exerts an equal and opposite reaction force on the first. The thi ...

# Sources

## Citations

* * * * * * ;Historical For explanations of Newton's laws of motion by Newton in the early 18th century and by the physicist William Thomson (Lord Kelvin) in the mid-19th century, see the following: * * *