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| {{Other uses|Laws of motion (disambiguation){{!}}Laws of motion}}
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| {{pp-semi-vandalism|small=yes}}
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| [[Image:Newtons laws in latin.jpg|thumb|right|200px|Newton's First and Second laws, in Latin, from the original 1687 ''[[Philosophiæ Naturalis Principia Mathematica|Principia Mathematica]]''.]]
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| {{Classical mechanics}}
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| '''Newton's laws of motion''' are three [[physical law]]s that together laid the foundation for [[classical mechanics]]. They describe the relationship between a body and the [[force]]s acting upon it, and its [[motion (physics)|motion]] in response to said forces. They have been expressed in several different ways over nearly three centuries,<ref>For explanations of Newton's laws of motion by [[Isaac Newton|Newton]] in the early 18th century, by the physicist [[William Thomson, 1st Baron Kelvin|William Thomson (Lord Kelvin)]] in the mid-19th century, and by a modern text of the early 21st century, see:-
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| *Newton's "Axioms or Laws of Motion" starting on [http://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA19#v=onepage&q=&f=false page 19 of volume 1 of the 1729 translation] of the "[[Mathematical Principles of Natural Philosophy|Principia]]";
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| *[http://books.google.com/books?id=wwO9X3RPt5kC&pg=PA178 Section 242, ''Newton's laws of motion''] in [[#tho1867|Thomson, W (Lord Kelvin), and Tait, P G, (1867)]], ''Treatise on natural philosophy'', volume 1; and
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| *[[#cro2000|Benjamin Crowell (2000), ''Newtonian Physics'']].</ref> and can be summarized as follows:
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| # '''First law''': When viewed in an [[inertial reference frame]], an object either is at rest or moves at a constant [[velocity]], unless acted upon by an external [[force]].<ref name=first-law-shaums>{{Cite book| last = Browne| first =Michael E.| title =Schaum's outline of theory and problems of physics for engineering and science| publisher = McGraw-Hill Companies| date =July 1999| format =Series: Schaum's Outline Series| pages =58| url =http://books.google.com/?id=5gURYN4vFx4C&pg=PA58&dq=newton's+first+law+of+motion&q=newton's%20first%20law%20of%20motion| isbn =978-0-07-008498-8}}</ref><ref name=first-law-dmmy>{{Cite book| last = Holzner| first = Steven | title =Physics for Dummies| publisher =Wiley, John & Sons, Incorporated| date =December 2005| pages =64| url =http://books.google.com/?id=FrRNO6t51DMC&pg=PA64&dq=Newton's+laws+of+motion&cd=8#v=onepage&q=Newton's%20laws%20of%20motion| isbn =978-0-7645-5433-9}}</ref>
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| # '''Second law''': The [[vector sum]] of the forces on an object is equal to the total mass of that object multiplied by the acceleration of the object. In more technical terms, the [[acceleration]] of a body is directly proportional to, and in the same direction as, the [[net force]] acting on the body, and inversely proportional to its [[mass]]. Thus, '''F''' = ''m'''''a''', where '''F''' is the net force acting on the object, ''m'' is the mass of the object and '''a''' is the acceleration of the object.<!-- Beware! Both the acceleration and momentum formulations of Newton's second law are valid ''only'' for constant-mass systems. This is covered in the discussion below and in multiple references given. --> Force and acceleration are both vectors (as denoted by the bold type). This means that they have both a magnitude (size) and a direction relative to some reference frame.
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| # '''Third law''': When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.
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| The three laws of motion were first compiled by [[Isaac Newton]] in his ''[[Philosophiæ Naturalis Principia Mathematica]]'' (''Mathematical Principles of Natural Philosophy''), first published in 1687.<ref name=Principia>See the ''Principia'' on line at [http://ia310114.us.archive.org/2/items/newtonspmathema00newtrich/newtonspmathema00newtrich.pdf Andrew Motte Translation]</ref> Newton used them to explain and investigate the motion of many physical objects and systems.<ref name=Motte>[http://members.tripod.com/~gravitee/axioms.htm Andrew Motte translation of Newton's ''Principia'' (1687) ''Axioms or Laws of Motion'']</ref> For example, in the third volume of the text, Newton showed that these laws of motion, combined with his [[Newton's law of universal gravitation|law of universal gravitation]], explained [[Kepler's laws of planetary motion]].
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| ==Overview==
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| [[File:Sir Isaac Newton (1643-1727).jpg|thumb|150px|left|Isaac Newton (1643-1727), the physicist who formulated the laws]]Newton's laws are applied to objects which are idealized as single point masses,<ref>''[...]while Newton had used the word 'body' vaguely and in at least three different meanings, Euler realized that the statements of Newton are generally correct only when applied to masses concentrated at isolated points;''{{Cite book| last1 = Truesdell | first1 = Clifford A.| last2 = Becchi| first2 = Antonio| last3 = Benvenuto| first3 = Edoardo| title = Essays on the history of mechanics: in memory of Clifford Ambrose Truesdell and Edoardo Benvenuto| publisher = Birkhäuser| year = 2003| location = New York| page = 207| url = http://books.google.com/?id=6LO_U6T-HvsC&printsec=frontcover&dq=essays+in+the+History&cd=9#v=snippet&q=%22isolated%20points%22| isbn = 3-7643-1476-1}}</ref> in the sense that the size and shape of the object's body are neglected in order to focus on its motion more easily. This can be done when the object is small compared to the distances involved in its analysis, or the [[deformation (mechanics)|deformation]] and rotation of the body are of no importance. In this way, even a planet can be idealized as a particle for analysis of its orbital motion around a star.
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| In their original form, Newton's laws of motion are not adequate to characterize the motion of [[rigid bodies]] and [[deformable bodies]]. [[Leonhard Euler]] in 1750 introduced a generalization of Newton's laws of motion for rigid bodies called the [[Euler's laws of motion]], later applied as well for deformable bodies assumed as a [[Continuum mechanics|continuum]]. 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.<ref>{{cite book| last = Lubliner| first = Jacob| title = Plasticity Theory (Revised Edition)| publisher = Dover Publications| year = 2008| url = http://www.ce.berkeley.edu/~coby/plas/pdf/book.pdf| isbn = 0-486-46290-0}}</ref>
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| Newton's laws hold only with respect to a certain set of [[frames of reference]] called [[Inertial reference frame|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 only holds 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.<ref name=tseitlin>{{cite journal |url= http://www.springerlink.com/content/j42866672t863506/ |title= Newton's First Law: Text, Translations, Interpretations and Physics Education |journal= Science & Education | author= Galili, I.; Tseitlin, M. |volume= 12 |issue= 1 |year= 2003 |pages= 45–73 |doi= 10.1023/A:1022632600805 |bibcode = 2003Sc&Ed..12...45G }}</ref><ref>{{cite book |url= http://www.lightandmatter.com/html_books/1np/ch04/ch04.html |title= Newtonian Physics |author= Benjamin Crowell |chapter= 4. Force and Motion |isbn= 0-9704670-1-X }}</ref> The explicit concept of an inertial frame of reference was not developed until long after Newton's death.
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| In the given interpretation [[mass]], [[acceleration]], [[momentum]], and (most importantly) [[force]] are assumed to be externally defined quantities. This is the most common, but not the only interpretation of the way one can consider the laws to be a definition of these quantities.
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| Newtonian mechanics has been superseded by [[special relativity]], but it is still useful as an approximation when the speeds involved are much slower than the [[speed of light]].<ref>In making a modern adjustment of the second law for (some of) the effects of relativity, ''m'' would be treated as the [[relativistic mass]], producing the relativistic expression for momentum, and the third law might be modified if possible to allow for the finite signal propagation speed between distant interacting particles.</ref>
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| ==Newton's first law==
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| [[File:first law.ogg|300px|thumb|Explanation of Newton's first law and reference frames. <small>([http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-6/ MIT Course 8.01])</small><ref>
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| {{cite AV media
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| | people = [[Walter Lewin]] | date = September 20, 1999
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| | title = Newton’s First, Second, and Third Laws. MIT Course 8.01: Classical Mechanics, Lecture 6.
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| | url = http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-6/
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| | format = ogg | medium = videotape | publisher = [[MIT OpenCourseWare|MIT OCW]] | location = Cambridge, MA USA
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| | accessdate = December 23, 2010 | time = 0:00–6:53 | ref =lewin1
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| }}</ref> ]]
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| The first law states that if the [[net force]] (the [[vector sum]] of all forces acting on an object) is zero, then the [[velocity]] of the object is constant. Velocity is a [[Euclidean vector|vector]] quantity which expresses both the object's [[speed]] and the direction of its motion; therefore, the statement that the object's velocity is constant is a statement that both its speed and the direction of its motion are constant.
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| The first law can be stated mathematically as
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| :<math>
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| \sum \mathbf{F} = 0\; \Rightarrow\; \frac{\mathrm{d} \mathbf{v} }{\mathrm{d}t} = 0.
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| </math>
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| Consequently,
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| * An object that is at rest will stay at rest unless an external force acts upon it.
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| * An object that is in motion will not change its velocity unless an external force acts upon it.
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| This is known as ''uniform motion''. An object ''continues'' to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest (demonstrated when a tablecloth is skillfully whipped from under dishes on a tabletop and the dishes remain in their initial state of rest). If an object is moving, it continues to move without turning or changing its speed. This is evident in space probes that continually move in outer space. Changes in motion must be imposed against the tendency of an object to retain its state of motion. In the absence of net forces, a moving object tends to move along a straight line path indefinitely.
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| Newton placed the first law of motion to establish [[frames of reference]] for which the other laws are applicable. The first law of motion postulates the existence of at least one [[frame of reference]] called a Newtonian or [[inertial reference frame]], relative to which the motion of a particle not subject to forces is a straight line at a constant speed.<ref name=tseitlin/><ref name=Woodhouse>{{cite book |url=http://books.google.com/?id=ggPXQAeeRLgC&printsec=frontcover&dq=isbn=1852334266#PPA6,M1 |title=Special relativity |page=6 |author=NMJ Woodhouse |publisher=Springer |year=2003 |isbn=1-85233-426-6 |location=London/Berlin}}</ref> Newton's first law is often referred to as the ''[[Inertia|law of inertia]]''. Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net [[force]] acting on it is zero. In this sense, the first law can be restated as:
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| {{quote|''In every material universe, the motion of a particle in a preferential reference frame Φ is determined by the action of forces whose total vanished for all times when and only when the velocity of the particle is constant in Φ. That is, a particle initially at rest or in uniform motion in the preferential frame Φ continues in that state unless compelled by forces to change it.''<ref>{{cite book |author=Beatty, Millard F.|year=2006|title=Principles of engineering mechanics Volume 2 of Principles of Engineering Mechanics: Dynamics-The Analysis of Motion, |page=24| publisher =Springer|isbn=0-387-23704-6|url=http://books.google.com/?id=wr2QOBqOBakC&lpg=PP1&pg=PA24#v=onepage&q}}</ref>}}
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| Newton's laws are valid only in an [[inertial reference frame]]. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame, i.e. [[Galilean invariance]] or the [[principle of relativity|principle of Newtonian relativity]].<ref>{{cite book |author=Thornton, Marion|year=2004|title=Classical dynamics of particles and systems|page=53| publisher = Brooks/Cole| edition=5th|
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| isbn=0-534-40896-6|url=http://books.google.com/?id=HOqLQgAACAAJ&dq=classical%20dynamics%20of%20particles%20and%20systems}}</ref>
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| ==Newton's second law== <!-- [Newton's second law] -->
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| [[File:secondlaw.ogg|320px|thumb|right|Explanation of Newton's second law, using gravity as an example. <span style="font-size:80%">([http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-6/ MIT OCW])</span><ref>[[Walter Lewin|Lewin]], [http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-6/ Newton’s First, Second, and Third Laws], Lecture 6. (6:53–11:06)</ref> ]]
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| The second law states that the [[net force]] on an object is equal to the rate of change (that is, the ''[[derivative]]'') of its [[Momentum|linear momentum]] '''p''' in an [[inertial reference frame]]:
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| :<math>\mathbf{F} = \frac{\mathrm{d}\mathbf{p}}{\mathrm{d}t} = \frac{\mathrm{d}(m\mathbf v)}{\mathrm{d}t}.</math>
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| The second law can also be stated in terms of an object's acceleration. The mass can be taken outside the [[Derivative|differentiation]] operator by the [[constant factor rule in differentiation]]. Thus,
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| :<math>\mathbf{F} = m\,\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t} = m\mathbf{a},</math>
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| where '''F''' is the net force applied, ''m'' is the mass of the body, and '''a''' is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it. This form of Newton's second law is valid for constant-mass systems.<ref name="plastino">{{cite journal|last=Plastino|first=Angel R. |coauthors=Muzzio, Juan C.|year=1992|title=On the use and abuse of Newton's second law for variable mass problems|journal=Celestial Mechanics and Dynamical Astronomy|publisher=Kluwer Academic Publishers|location=Netherlands|volume= 53|issue= 3|pages=227–232|issn=0923-2958|bibcode=1992CeMDA..53..227P|doi=10.1007/BF00052611}} "We may conclude emphasizing that Newton's second law is valid for constant mass only. When the mass varies due to accretion or ablation, [an alternate equation explicitly accounting for the changing mass] should be used."</ref><ref name=Halliday>{{cite book|last=Halliday|coauthors=Resnick|title=Physics|volume=1|pages=199|quote=It is important to note that we ''cannot'' derive a general expression for Newton's second law for variable mass systems by treating the mass in '''F''' = ''d'''''P'''/''dt'' = ''d''(''M'''''v''') as a ''variable''. [...] We ''can'' use '''F''' = ''d'''''P'''/''dt'' to analyze variable mass systems ''only'' if we apply it to an ''entire system of constant mass'' having parts among which there is an interchange of mass.|isbn=0-471-03710-9}} [Emphasis as in the original]</ref><ref name=Kleppner>
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| {{cite book|last=Kleppner|first=Daniel|coauthors=Robert Kolenkow|title=An Introduction to Mechanics|publisher=McGraw-Hill|year=1973|pages=133–134|isbn=0-07-035048-5|quote=Recall that '''F''' = ''d'''''P'''/''dt'' was established for a system composed of a certain set of particles[. ... I]t is essential to deal with the same set of particles throughout the time interval[. ...] Consequently, the mass of the system can not change during the time of interest.}}</ref>
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| Consistent with the [[Newton's laws of motion#Newton's first law|first law]], the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude; such is the case with [[uniform circular motion]]. The relationship also implies the [[conservation of momentum]]: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum.
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| Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see [[#Variable-mass_systems|below]]).
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| Newton's second law requires modification if the effects of [[special relativity]] are to be taken into account, because at high speeds the approximation that momentum is the product of rest mass and velocity is not accurate.
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| ===Impulse===
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| An [[Impulse (physics)|impulse]] '''J''' occurs when a force '''F''' acts over an interval of time Δ''t'', and it is given by<ref>Hannah, J, Hillier, M J, ''Applied Mechanics'', p221, Pitman Paperbacks, 1971</ref><ref name=Serway>{{cite book |title=College Physics |page=161 |author=Raymond A. Serway, Jerry S. Faughn |url=http://books.google.com/?id=wDKD4IggBJ4C&pg=PA247&dq=impulse+momentum+%22rate+of+change%22 |isbn=0-534-99724-4 |year=2006 |publisher=Thompson-Brooks/Cole |location=Pacific Grove CA }}</ref>
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| :<math> \mathbf{J} = \int_{\Delta t} \mathbf F \,\mathrm{d}t .</math>
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| Since force is the time derivative of momentum, it follows that
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| :<math>\mathbf{J} = \Delta\mathbf{p} = m\Delta\mathbf{v}.</math>
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| This relation between impulse and momentum is closer to Newton's wording of the second law.<ref name=Harman>{{cite book |title=The investigation of difficult things: essays on Newton and the history of the exact sciences in honour of D.T. Whiteside |page=353 |author=I Bernard Cohen (Peter M. Harman & Alan E. Shapiro, Eds) |url=http://books.google.com/?id=oYZ-0PUrjBcC&pg=PA353&dq=impulse+momentum+%22rate+of+change%22+-angular+date:2000-2009 |isbn=0-521-89266-X |year=2002 |publisher=Cambridge University Press |location=Cambridge UK }}</ref>
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| Impulse is a concept frequently used in the analysis of collisions and impacts.<ref name=Stronge>{{cite book |title=Impact mechanics |page=12 ff |publisher=Cambridge University Press |year=2004 |location=Cambridge UK |author= WJ Stronge|url=http://books.google.com/?id=nHgcS0bfZ28C&pg=PA12&dq=impulse+momentum+%22rate+of+change%22+-angular+date:2000-2009 |isbn=0-521-60289-0}}</ref>
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| ===Variable-mass systems===
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| {{main|Variable-mass system}}
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| Variable-mass systems, like a rocket burning fuel and ejecting spent gases, are not [[closed system|closed]]. Therefore one must consider opposite forces such as that produced onto the ejecting mass {{math|'''F'''<sub>gas</sub>}} and onto other external bodies {{math|'''F'''<sub>other</sub>}}. The net external force on the body is:
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| :<math>\mathbf{F}_{ext} = -\left(\mathbf{F}_{gas} + \mathbf{F}_{other}\right).</math>
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| Let {{math|'''V'''}} be the velocity of the variable mass, and let be {{math|'''v<sub>e</sub>'''}} be the velocity of the ejecting mass, where {{math|'''V'''}} and {{math|'''v<sub>e</sub>'''}} are evaluated in the same inertial frame of reference:
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| :<math> \mathbf{F}_{ext} = \frac{\mathrm{d}}{\mathrm{d}t}\big[m_{rocket}(t)\mathbf{V}(t)\big]</math>
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| :<math> \mathbf{F}_{ext} = m_{rocket}(t) \frac{\mathrm{d}\mathbf{V}}{\mathrm{d}t} + \mathbf{V}(t) \frac{\mathrm{d}m_{rocket}}{\mathrm{d}t}</math>
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| :<math> \mathbf{F}_{ext} = -\left(\frac{\mathrm{d}}{\mathrm{d}t}\big[m_{gas}(t)\mathbf{v_e}(t)\big] + F_{other}(t)\right)</math>
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| :<math> \mathbf{F}_{ext} = -\left(m_{gas}(t) \frac{\mathrm{d}\mathbf{v_e}}{\mathrm{d}t} + \mathbf{v_e}(t) \frac{\mathrm{d}m_{gas}}{\mathrm{d}t} + F_{other}(t)\right).</math>
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| If we assume that the ejecting mass transfers momentum to the rocket instantaneously (i.e., via an [[Orbital maneuver#impulsive maneuvers|impulsive maneuver]]) and thus lacks a device, such as a [[Rocket engine nozzle|nozzle]], that would ''otherwise'' allow differential propellant {{math|d''m''}} to transfer momentum to the rocket over a significant displacement, then:
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| :<math>m_{gas}(t) \frac{\mathrm{d}\mathbf{v_e}}{\mathrm{d}t}=0</math>
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| In which case, this term within {{math|'''F'''<sub>ext</sub>}} may be dropped, and thus:
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| :<math>\mathbf{F}_{ext} = m_{rocket}(t) \frac{\mathrm{d}\mathbf{V}}{\mathrm{d}t} + \mathbf{V}(t) \frac{\mathrm{d}m_{rocket}}{\mathrm{d}t} = - \left(\mathbf{v_e}(t) \frac{\mathrm{d}m_{gas}}{\mathrm{d}t} + F_{other}(t)\right).</math>
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| From the frame of reference of the body ''only'', where {{math|'''V'''{{=}}0}}, {{math|'''v'''<sub>e</sub>}} becomes {{math|'''v'''<sub>rel</sub>}}, the relative velocity of the gas with respect to the rocket, and one may use the following equation:
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| :<math>m_{rocket}(t) \frac{\mathrm{d}\mathbf{V}}{\mathrm{d}t} = -\left(\mathbf{v_{rel}}(t) \frac{\mathrm{d}m_{gas}}{\mathrm{d}t} + F_{other}(t)\right).</math>
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| If there are no other forces except those on the immediate propellant and the body, then the force equation in the frame of reference of the body simplifies to:
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| :<math>m_{rocket}(t) \frac{\mathrm{d}\mathbf{V}}{\mathrm{d}t} = -\mathbf{v_{rel}}(t) \frac{\mathrm{d}m_{gas}}{\mathrm{d}t}.</math>
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| It is important to stress that although this simplified formula agrees with the derivation of the [[Tsiolkovsky rocket equation]], both require that all forces are impulsive (i.e. involve instantaneous transfers of momenta).
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| Note that an accreting mass may push the object in the same direction as would an explusing mass do, in which both {{math|'''v'''<sub>rel</sub>}} and {{math|d''m''<sub>gas</sub>/d''t''}} switch sign.
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| ==Newton's third law==
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| [[Image:Skaters showing newtons third law.svg|thumb|right|250px|An illustration of Newton's third law in which two skaters push against each other. The first skater on the left exerts a normal force N<sub>12</sub> on the second skater directed towards the right, and the second skater exerts a normal force N<sub>21</sub> on the first skater directed towards the left. <br>The magnitude of both forces are equal, but they have opposite directions, as dictated by Newton's third law.]]
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| [[File:thirdlaw.ogg|250px|thumb|left| A description of Newton's third law and contact forces<ref>[[Walter Lewin|Lewin]], [http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-6/ Newton’s First, Second, and Third Laws], Lecture 6. (14:11–16:00)</ref> ]]
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| The third law states that all forces exist in pairs: if one object ''A'' exerts a force '''F'''<sub>''A''</sub> on a second object ''B'', then ''B'' simultaneously exerts a force '''F'''<sub>''B''</sub> on ''A'', and the two forces are equal and opposite: '''F'''<sub>''A''</sub> = −'''F'''<sub>''B''</sub>.<ref name="resnick83">{{cite book|last1=Resnick|last2=Halliday|last3=Krane|title=Physics, Volume 1|edition=4th|page=83|year=1992}}</ref> The third law means that all forces are ''[[interaction]]s'' between different bodies,<ref>{{cite journal
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| | title = Newton’s third law revisited
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| | author = C Hellingman
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| | journal = Phys. Educ.
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| | volume = 27
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| | year = 1992
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| | issue = 2
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| | pages = 112–115
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| | quote = Quoting Newton in the ''Principia'': It is not one action by which the Sun attracts Jupiter, and another by which Jupiter attracts the Sun; but it is one action by which the Sun and Jupiter mutually endeavour to come nearer together.
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| | doi = 10.1088/0031-9120/27/2/011|bibcode = 1992PhyEd..27..112H }}</ref><ref>{{cite web
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| | title = Physics
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| | author = Resnick and Halliday
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| | edition = Third
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| | publisher = John Wiley & Sons
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| | year = 1977
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| | pages = 78–79
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| | quote = Any single force is only one aspect of a mutual interaction between ''two'' bodies.}}</ref> and thus that there is no such thing as a unidirectional force or a force that acts on only one body. This law is sometimes referred to as the ''[[Reaction (physics)|action-reaction law]]'', with '''F'''<sub>''A''</sub> called the "action" and '''F'''<sub>''B''</sub> 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.<ref name="resnick83" />
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| 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).
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| 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.<ref>Hewitt (2006), p. 75</ref>
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| ==History==
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| ===Newton's 1st Law===
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| From the original [[Latin]] of Newton's ''Principia'':
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| {{Cquote|''Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.''}}
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| Translated to English, this reads:
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| {{Cquote|Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.<ref>Isaac Newton, ''The Principia'', A new translation by I.B. Cohen and A. Whitman, University of California press, Berkeley 1999.</ref>}}
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| The ancient [[Greeks|Greek]] [[philosophy|philosopher]] [[Aristotle]] 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 to continually propel it, otherwise it would stop moving. [[Galileo Galilei]], however, realized that a force is necessary to change the velocity of a body, i.e., acceleration, but no force is needed to maintain its velocity. In other words, 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 Galileo 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.
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| The law of inertia apparently occurred to several different natural philosophers and scientists independently, including [[Thomas Hobbes]] in his ''[[Leviathan (book)|Leviathan]]''.<ref>Thomas Hobbes wrote in ''[[Leviathan (book)|Leviathan]]'': {{quote|That when a thing lies still, unless somewhat else stir it, it will lie still forever, is a truth that no man doubts. But [the proposition] that when a thing is in motion it will eternally be in motion unless somewhat else stay it, though the reason be the same (namely that nothing can change itself), is not so easily assented to. For men measure not only other men but all other things by themselves. And because they find themselves subject after motion to pain and lassitude, [they] think every thing else grows weary of motion and seeks repose of its own accord, little considering whether it be not some other motion wherein that desire of rest they find in themselves, consists.}}</ref> The 17th century philosopher and mathematician [[René Descartes]] also formulated the law, although he did not perform any experiments to confirm it.{{citation needed|date=May 2013}}
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| ===Newton's 2nd Law===
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| Newton's original Latin reads:
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| {{Cquote|''Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur''.}}
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| This was translated quite closely in Motte's 1729 translation as:
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| {{Cquote|Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.}}
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| According to modern ideas of how Newton was using his terminology,<ref>According to Maxwell in ''Matter and Motion'', Newton meant by ''motion'' "''the quantity of matter moved as well as the rate at which it travels" and by ''impressed force'' he meant "the time during which the force acts as well as the intensity of the force''". See Harman and Shapiro, cited below.</ref> this is understood, in modern terms, as an equivalent of:
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| ''{{quote|The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.}}''
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| Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading:
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| ''{{quote|If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.}}''
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| The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton's formulation and modern formulations.<ref>See for example (1) I Bernard Cohen, "Newton’s Second Law and the Concept of Force in the Principia", in "The Annus Mirabilis of Sir Isaac Newton 1666–1966" (Cambridge, Massachusetts: The MIT Press, 1967), pages 143–185; (2) Stuart Pierson, "'Corpore cadente. . .': Historians Discuss Newton’s Second Law", Perspectives on Science, 1 (1993), pages 627–658; and (3) Bruce Pourciau, "Newton's Interpretation of Newton's Second Law", Archive for History of Exact Sciences, vol.60 (2006), pages 157–207; also an online discussion by G E Smith, in [http://plato.stanford.edu/entries/newton-principia/index.html#NewLawMot 5. Newton's Laws of Motion], s.5 of "Newton's Philosophiae Naturalis Principia Mathematica" in (online) Stanford Encyclopedia of Philosophy, 2007.</ref>
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| ===Newton's 3rd Law===
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| {{Cquote|''Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.''}}
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| {{Cquote|Law III: To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.}}
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| A more direct translation than the one just given above is:
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| {{quote|LAW III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. — Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinges upon another, and by its force changes the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of the bodies; that is to say, if the bodies are not hindered by any other impediments. For, as the motions are equally changed, the changes of the velocities made toward contrary parts are reciprocally proportional to the bodies. This law takes place also in attractions, as will be proved in the next scholium.<ref>This translation of the third law and the commentary following it can be found in the "[[Mathematical Principles of Natural Philosophy|Principia]]" on [http://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA20#v=onepage&q=&f=false page 20 of volume 1 of the 1729 translation].</ref>}}
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| In the above, as usual, ''motion'' is Newton's name for momentum, hence his careful distinction between motion and velocity.
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| Newton used the third law to derive the law of [[momentum#Conservation|conservation of momentum]];<ref>Newton, ''Principia'', Corollary III to the laws of motion</ref> however from a deeper perspective, conservation of momentum is the more fundamental idea (derived via [[Noether's theorem]] from [[Galilean invariance]]), and holds in cases where Newton's third law appears to fail, for instance when [[force field (physics)|force fields]] as well as particles carry momentum, and in [[quantum mechanics]]. <!-- In force fields I do not think the violation is a necessity; we could easily remodel the fields perhaps as interaction between particles at the quantum level and still have the 3rd law holding. I think the 3rd law breakdown is just a consequence of the model used -->
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| ==Importance and range of validity==
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| 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]] and the mathematical techniques of [[calculus]], provided for the first time a unified quantitative explanation for a wide range of physical phenomena.
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| 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]]) are inappropriate for use in certain circumstances, most notably at very small scales, very high speeds (in [[special relativity]], the [[Lorentz factor]] must be included in the expression for momentum along with [[rest mass]] and velocity) or very strong gravitational fields. Therefore, the laws cannot be used to explain phenomena such as conduction of electricity in a [[semiconductor]], optical properties of substances, errors in non-relativistically corrected [[GPS]] systems and [[superconductivity]]. Explanation of these phenomena requires more sophisticated physical theories, including [[general relativity]] and [[quantum field theory]].
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| In [[quantum mechanics]] concepts such as force, momentum, and position are defined by linear [[Operator (physics)|operators]] that operate on the [[quantum state]]; at speeds that are much lower than the speed of light, Newton's laws are just as exact for these operators as they are for classical objects. At speeds comparable to the speed of light, the second law holds in the original form '''F''' = d'''p'''/d''t'', where '''F''' and '''p''' are [[four-vector]]s.
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| ==Relationship to the conservation laws==
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| In modern physics, the [[conservation law|laws of conservation]] of [[momentum]], [[energy]], and [[angular momentum]] are of more general validity than Newton's laws, since they apply to both light and matter, and to both classical and non-classical physics.
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| This can be stated simply, "Momentum, energy and angular momentum cannot be created or destroyed."
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| Because force is the time derivative of momentum, the concept of force is redundant and subordinate to the conservation of momentum, and is not used in fundamental theories (e.g., [[quantum mechanics]], [[quantum electrodynamics]], [[general relativity]], etc.). The [[standard model]] explains in detail how the three fundamental forces known as [[Gauge theory|gauge forces]] originate out of exchange by [[virtual particles]]. Other forces such as [[Gravitation|gravity]] and [[Pauli exclusion principle#Consequences|fermionic degeneracy pressure]] also arise from the momentum conservation. Indeed, the conservation of [[4-momentum]] in inertial motion via [[curved space-time]] results in what we call [[gravitational force]] in [[general relativity]] theory. Application of space derivative (which is a [[momentum operator]] in quantum mechanics) to overlapping [[wave functions]] of pair of [[fermion]]s (particles with half-integer [[spin (physics)|spin]]) results in shifts of maxima of compound wavefunction away from each other, which is observable as "repulsion" of fermions.
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| Newton stated the third law within a world-view that assumed instantaneous action at a distance between material particles. However, he was prepared for philosophical criticism of this [[Action at a distance (physics)|action at a distance]], and it was in this context that he stated the famous phrase "[[Hypotheses non fingo|I feign no hypotheses]]". In modern physics, action at a distance has been completely eliminated, except for subtle effects involving [[quantum entanglement]].{{citation needed|date=August 2012}} However in modern engineering in all practical applications involving the motion of vehicles and satellites, the concept of action at a distance is used extensively.
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| The discovery of the [[Second Law of Thermodynamics]] by Carnot in the 19th century showed that every physical quantity is not conserved over time, thus disproving the validity of inducing the opposite metaphysical view from Newton's laws. Hence, a "steady-state" worldview based solely on Newton's laws and the conservation laws does not take [[entropy]] into account.
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| ==See also==
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| {{Wikipedia books|Isaac Newton}}
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| * [[Euler's laws]]
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| * [[Galilean invariance]]
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| * [[Hamiltonian mechanics]]
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| * [[Lagrangian mechanics]]
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| * [[List of scientific laws named after people]]
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| * [[Mercury (planet)#Orbit and rotation|Mercury, orbit of]]
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| * [[Modified Newtonian dynamics]]
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| * [[Newton's law of universal gravitation]]
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| * [[Principle of least action]]
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| * [[Reaction (physics)]]
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| ==References and notes==
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| {{reflist|colwidth=30em}}
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| ==Further reading and works referred to==
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| *<cite id=cro2000>Crowell, Benjamin, (2011), [http://www.lightandmatter.com/lm/ ''Light and Matter''], (2011, Light and Matter), especially at Section [http://www.lightandmatter.com/html_books/lm/ch04/ch04.html#Section4.2 '''4.2, Newton's First Law'''], Section [http://www.lightandmatter.com/html_books/lm/ch04/ch04.html#Section4.3 '''4.3, Newton's Second Law'''], and Section [http://www.lightandmatter.com/html_books/lm/ch05/ch05.html#Section5.1 '''5.1, Newton's Third Law'''].</cite>
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| *<cite id=fey2005>{{cite book|last1=Feynman|first1=R. P.|author1-link=Richard Feynman|last2=Leighton|first2=R. B.|last3=Sands|first3=M.|year=2005|title=The Feynman Lectures on Physics|volume=Vol. 1|edition=2nd|publisher=Pearson/Addison-Wesley|isbn=0-8053-9049-9}}</cite>
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| *<cite id=fow1999>{{cite book|last1=Fowles|first1=G. R.|last2=Cassiday|first2=G. L.|year=1999|title=Analytical Mechanics|edition=6th|publisher=Saunders College Publishing|isbn=0-03-022317-2}}</cite>
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| *<cite id=lik1973>{{cite book|last=Likins|first=Peter W.|authorlink=Peter Likins|year=1973|title=Elements of Engineering Mechanics|publisher=McGraw-Hill Book Company|isbn=0-07-037852-5}}</cite>
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| *<cite id=mar1995>{{cite book|last=Marion|first1=Jerry|last2=Thornton|first2=Stephen|year=1995|title=Classical Dynamics of Particles and Systems|publisher=Harcourt College Publishers|isbn=0-03-097302-3}}</cite>
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| *<cite id=new1729v1>Newton, Isaac, "[[Mathematical Principles of Natural Philosophy]]", 1729 English translation based on 3rd Latin edition (1726), [http://books.google.com/books?id=Tm0FAAAAQAAJ volume 1, containing Book 1], especially at the section [http://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA19 '''Axioms or Laws of Motion''' starting page 19].</cite>
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| *<cite id=new1729v2>Newton, Isaac, "[[Mathematical Principles of Natural Philosophy]]", 1729 English translation based on 3rd Latin edition (1726), [http://books.google.com/books?id=6EqxPav3vIsC volume 2, containing Books 2 & 3].</cite>
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| *<cite id=tho1867>Thomson, W (Lord Kelvin), and Tait, P G, (1867), [http://books.google.com/books?id=wwO9X3RPt5kC ''Treatise on natural philosophy''], volume 1, especially at [http://books.google.com/books?id=wwO9X3RPt5kC&pg=PA178 Section 242, '''Newton's laws of motion'''].</cite>
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| *<cite id=woo2003>{{cite book |url=http://books.google.com/?id=ggPXQAeeRLgC&printsec=frontcover&dq=isbn=1852334266#PPA6,M1 |title=Special relativity |page=6 |author=NMJ Woodhouse |publisher=Springer |year=2003 |isbn=1-85233-426-6 |location=London/Berlin}}</cite>
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| ==External links==
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| * [http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/Video-Segment-Index-for-L-6.htm MIT Physics video lecture] on Newton's three laws
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| * [http://www.lightandmatter.com/lm/ Light and Matter] – an on-line textbook
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| *[http://phy.hk/wiki/englishhtm/firstlaw.htm Simulation on Newton's first law of motion]
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| *"[http://demonstrations.wolfram.com/NewtonsSecondLaw/ Newton's Second Law]" by Enrique Zeleny, [[Wolfram Demonstrations Project]].
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| *[http://www.youtube.com/watch?v=9gFMObYCccU Newton's 3rd Law demonstrated in a vacuum]
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| {{DEFAULTSORT:Newton's Laws Of Motion}}
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