Newton's Laws of Motion - Glenn Research Center

Newton's Third Law: Action & Reaction Skiptomaincontent Home>BeginnersGuidetoAeronautics SirIsaacNewton’slawsofmotionexplaintherelationshipbetweenaphysicalobjectandtheforcesactinguponit.Understandingthisinformationprovidesuswiththebasisofmodernphysics. Onthispage: WhatareNewton’sLawsofMotion? Anobjectatrestremainsatrest,andanobjectinmotionremainsinmotionatconstantspeedandinastraightlineunlessactedonbyanunbalancedforce. Theaccelerationofanobjectdependsonthemassoftheobjectandtheamountofforceapplied. Wheneveroneobjectexertsaforceonanotherobject,thesecondobjectexertsanequalandoppositeonthefirst. SirIsaacNewtonworkedinmanyareasofmathematicsandphysics.Hedevelopedthetheoriesofgravitationin1666whenhewasonly23yearsold.In1686,hepresentedhisthreelawsofmotioninthe“PrincipiaMathematicaPhilosophiaeNaturalis.” Bydevelopinghisthreelawsofmotion,Newtonrevolutionizedscience.Newton’slawstogetherwithKepler’sLawsexplainedwhyplanetsmoveinellipticalorbitsratherthanincircles. BelowisashortmoviefeaturingOrvilleandWilburWrightandadiscussionabouthowNewton’sLawsofMotionappliedtotheflightoftheiraircraft. Newton’sFirstLaw:Inertia Anobjectatrestremainsatrest,andanobjectinmotionremainsinmotionatconstantspeedandinastraightlineunlessactedonbyanunbalancedforce. Newton’sfirstlawstatesthateveryobjectwillremainatrestorinuniformmotioninastraightlineunlesscompelledtochangeitsstatebytheactionofanexternalforce.Thistendencytoresistchangesinastateofmotionis inertia.Ifalltheexternalforcescanceleachotherout,thenthereisnonetforceactingontheobject. Ifthereisnonetforceactingontheobject,thentheobjectwillmaintainaconstantvelocity. Ifthatvelocityiszero,thentheobjectremainsatrest.Ifanexternalforceactsonanobject,thevelocitywillchangebecauseoftheforce. Examplesofinertiainvolvingaerodynamics: Themotionofanairplanewhenapilotchangesthethrottlesettingofanengine. Themotionofaballfallingdownthroughtheatmosphere. Amodelrocketbeinglaunchedupintotheatmosphere. Themotionofakitewhenthewindchanges. Newton’sSecondLaw:Force Theaccelerationofanobjectdependsonthemassoftheobjectandtheamountofforceapplied. Hissecondlawdefinesa force tobeequaltochangein momentum (masstimesvelocity)perchangeintime. Momentumisdefinedtobethemass m ofanobjecttimesits velocity V. Letusassumethatwehaveanairplaneatapoint“0”definedbyitslocation X0 andtime t0.Theairplanehasamass m0 andtravelsatvelocity V0.AnexternalforceFtotheairplaneshownabovemovesittopoint“1”.Theairplane’snewlocationisX1andtimet1. Themassandvelocityoftheairplanechangeduringtheflighttovalues m1 and V1.Newton’ssecondlawcanhelpusdeterminethenewvaluesof V1 and m1,ifweknowhowbigtheforce F is.Letusjusttakethedifferencebetweentheconditionsatpoint“1”andtheconditionsatpoint“0”. F=(m1*V1–m0*V0)/(t1–t0) Newton’ssecondlawtalksaboutchangesinmomentum(m*V).Soatthispoint,wecan’tseparateouthowmuchthemasschangedandhowmuchthevelocitychanged.Weonlyknowhowmuchproduct(m*V)changed. Letusassumethatthemassstaysataconstantvalueequaltom.Thisassumptionisrathergoodforanairplanebecausetheonlychangeinmasswouldbeforthefuelburnedbetweenpoint“1”andpoint“0”.Theweightofthefuelisprobablysmallrelativetotheweightoftherestoftheairplane,especiallyifweonlylookatsmallchangesintime.Ifwewerediscussingtheflightofabaseball, thencertainlythemassremainsaconstant.Butifwewerediscussingtheflightofa bottlerocket,thenthemassdoesnotremainaconstantandwecanonlylookatchangesinmomentum.Foraconstantmass m,Newton’ssecondlawlookslike: F=m*(V1–V0)/(t1–t0) Thechangeinvelocitydividedbythechangeintimeisthedefinitionoftheacceleration a.Thesecondlawthenreducestothemorefamiliarproductofamassandanacceleration: F=m*a Rememberthatthisrelationisonlygoodforobjectsthathaveaconstantmass.Thisequationtellsusthatanobjectsubjectedtoanexternalforcewillaccelerateandthattheamountoftheaccelerationisproportionaltothesizeoftheforce.Theamountofaccelerationisalsoinverselyproportionaltothemassoftheobject;forequalforces,aheavierobjectwillexperiencelessaccelerationthanalighterobject.Consideringthemomentumequation,aforcecausesachangeinvelocity;andlikewise,achangeinvelocitygeneratesaforce.Theequationworksbothways. Thevelocity,force,acceleration,andmomentumhavebotha magnitude anda direction associatedwiththem.Scientistsandmathematicianscallthisa vectorquantity.Theequationsshownhereareactuallyvectorequationsandcanbeappliedineachofthe componentdirections.Wehaveonlylookedatonedirection,and,ingeneral,anobjectmovesinallthreedirections(up-down,left-right,forward-back). Exampleofforceinvolvingaerodynamics: Anaircraft’s motionresultingfrom aerodynamicforces,aircraft weight,and thrust. Newton’sThirdLaw:Action&Reaction Wheneveroneobjectexertsaforceonasecondobject,thesecondobjectexertsanequalandoppositeforceonthefirst. Histhirdlawstatesthatforeveryaction(force)innaturethereisanequalandoppositereaction.IfobjectAexertsaforceonobjectB,objectBalsoexertsanequalandoppositeforceonobjectA.Inotherwords,forcesresultfrominteractions. Examplesofactionandreactioninvolvingaerodynamics: Themotionofliftfromanairfoil,theairisdeflecteddownwardbytheairfoil’saction,andinreaction,thewingispushedupward. Themotionofa spinningball,theairisdeflectedtooneside,andtheballreactsbymovingintheopposite Themotionofajetengineproduces thrustandhotexhaustgasesflowoutthebackoftheengine,andathrustingforceisproducedintheoppositedirection. ReviewNewton’sLawsofMotion 1.Newton’sFirstLawofMotion(Inertia) Anobjectatrestremainsatrest,andanobjectinmotionremainsinmotionatconstantspeedandinastraightlineunlessactedonbyanunbalancedforce. 2.Newton’sSecondLawofMotion(Force) Theaccelerationofanobjectdependsonthemassoftheobjectandtheamountofforceapplied. 3.Newton’sThirdLawofMotion(Action&Reaction) Wheneveroneobjectexertsaforceonanotherobject,thesecondobjectexertsanequalandoppositeonthefirst. 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