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AnIntroductiontoMechanics For40years,KleppnerandKolenkow’sclassictexthasintroducedstu- dents to the principles of mechanics. Now brought up-to-date, this re- vised and improved Second Edition is ideal for classical mechanics coursesforfirst-andsecond-yearundergraduateswithfoundationskills inmathematics. Thebookretainsallthefeaturesofthefirstedition,includingnumer- ousworkedexamples,challengingproblems,andextensiveillustrations, andhasbeenrestructuredtoimprovetheflowofideas.Itnowfeatures • Newexamplestakenfromrecentdevelopments,suchaslaserslowing ofatoms,exoplanets,andblackholes • A “Hints, Clues, and Answers” section for the end-of-chapter prob- lemstosupportstudentlearning • Asolutionsmanualforinstructorsatwww.cambridge.org/kandk daniel kleppner is Lester Wolfe Professor of Physics, Emeritus, at MassachusettsInstituteofTechnology.Forhiscontributionstoteaching he has been awarded the Oersted Medal by the American Association of Physics Teachers and the Lilienfeld Prize of the American Physical Society.HehasalsoreceivedtheWolfPrizeinPhysicsandtheNational MedalofScience. robert kolenkow was Associate Professor of Physics at Mas- sachusettsInstituteofTechnology.Renownedforhisskillsasateacher, KolenkowwasawardedtheEverettMooreBakerAwardforOutstanding Teaching. AN Daniel Kleppner Robert Kolenkow INTRODUCTION TO MECHANICS SECOND EDITION UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom CambridgeUniversityPressisapartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9780521198110 (cid:2)c D.KleppnerandR.Kolenkow2014 ThiseditionisnotforsaleinIndia. Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. FirsteditionpreviouslypublishedbyMcGraw-HillEducation1973 FirstpublishedbyCambridgeUniversityPress2010 Reprinted2012 SecondeditionpublishedbyCambridgeUniversityPress2014 PrintedintheUnitedStatesbySheridanInc. AcataloguerecordforthispublicationisavailablefromtheBritishLibrary ISBN978-0-521-19811-0Hardback Additionalresourcesforthispublicationatwww.cambridge.org/kandk CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication, anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. CONTENTS PREFACE pagexi TOTHETEACHER xv LISTOFEXAMPLES xvii 1 VECTORSANDKINEMATICS 1 1.1 Introduction 2 1.2 Vectors 2 1.3 TheAlgebraofVectors 3 1.4 MultiplyingVectors 4 1.5 ComponentsofaVector 8 1.6 BaseVectors 11 1.7 ThePositionVectorrandDisplacement 12 1.8 VelocityandAcceleration 14 1.9 FormalSolutionofKinematicalEquations 19 1.10 MoreabouttheTimeDerivativeofaVector 22 1.11 MotioninPlanePolarCoordinates 26 Note1.1 ApproximationMethods 36 Note1.2 TheTaylorSeries 37 Note1.3 SeriesExpansionsofSomeCommon Functions 38 Note1.4 Differentials 39 Note1.5 SignificantFiguresandExperimental Uncertainty 40 Problems 41 vi CONTENTS 2 NEWTON’SLAWS 47 2.1 Introduction 48 2.2 NewtonianMechanicsandModernPhysics 48 2.3 Newton’sLaws 49 2.4 Newton’sFirstLawandInertialSystems 51 2.5 Newton’sSecondLaw 51 2.6 Newton’sThirdLaw 54 2.7 BaseUnitsandPhysicalStandards 59 2.8 TheAlgebraofDimensions 63 2.9 ApplyingNewton’sLaws 64 2.10 DynamicsUsingPolarCoordinates 72 Problems 77 3 FORCESANDEQUATIONSOFMOTION 81 3.1 Introduction 82 3.2 TheFundamentalForcesofPhysics 82 3.3 Gravity 83 3.4 SomePhenomenologicalForces 89 3.5 ADigressiononDifferentialEquations 95 3.6 Viscosity 98 3.7 Hooke’sLawandSimpleHarmonicMotion 102 Note3.1 TheGravitationalForceofaSphericalShell 107 Problems 110 4 MOMENTUM 115 4.1 Introduction 116 4.2 DynamicsofaSystemofParticles 116 4.3 CenterofMass 119 4.4 CenterofMassCoordinates 124 4.5 ConservationofMomentum 130 4.6 ImpulseandaRestatementoftheMomentum Relation 131 4.7 MomentumandtheFlowofMass 136 4.8 RocketMotion 138 4.9 MomentumFlowandForce 143 4.10 MomentumFlux 145 Note4.1 CenterofMassofTwo-and Three-dimensionalObjects 151 Problems 155 5 ENERGY 161 5.1 Introduction 162 5.2 IntegratingEquationsofMotioninOneDimension 162 5.3 WorkandEnergy 166 5.4 TheConservationofMechanicalEnergy 179 5.5 PotentialEnergy 182 5.6 WhatPotentialEnergyTellsUsaboutForce 185 CONTENTS vii 5.7 EnergyDiagrams 185 5.8 Non-conservativeForces 187 5.9 EnergyConservationandtheIdealGasLaw 189 5.10 ConservationLaws 192 5.11 WorldEnergyUsage 194 Note5.1 CorrectiontothePeriodofaPendulum 199 Note5.2 Force,PotentialEnergy,andtheVector Operator∇ 200 Problems 205 6 TOPICSINDYNAMICS 211 6.1 Introduction 212 6.2 SmallOscillationsinaBoundSystem 212 6.3 Stability 217 6.4 NormalModes 219 6.5 CollisionsandConservationLaws 225 Problems 233 7 ANGULARMOMENTUMANDFIXEDAXISROTATION 239 7.1 Introduction 240 7.2 AngularMomentumofaParticle 241 7.3 FixedAxisRotation 245 7.4 Torque 250 7.5 TorqueandAngularMomentum 252 7.6 DynamicsofFixedAxisRotation 260 7.7 PendulumMotionandFixedAxisRotation 262 7.8 MotionInvolvingTranslationandRotation 267 7.9 TheWork–EnergyTheoremandRotational Motion 273 7.10 TheBohrAtom 277 Note7.1 Chasles’Theorem 280 Note7.2 ASummaryoftheDynamicsofFixedAxis Rotation 282 Problems 282 8 RIGIDBODYMOTION 291 8.1 Introduction 292 8.2 TheVectorNatureofAngularVelocityand AngularMomentum 292 8.3 TheGyroscope 300 8.4 ExamplesofRigidBodyMotion 304 8.5 ConservationofAngularMomentum 310 8.6 RigidBodyRotationandtheTensorofInertia 312 8.7 AdvancedTopicsinRigidBodyDynamics 320 Note8.1 FiniteandInfinitesimalRotations 329 Note8.2 MoreaboutGyroscopes 331 Problems 337 viii CONTENTS 9 NON-INERTIALSYSTEMSANDFICTITIOUSFORCES 341 9.1 Introduction 342 9.2 GalileanTransformation 342 9.3 UniformlyAcceleratingSystems 344 9.4 ThePrincipleofEquivalence 347 9.5 PhysicsinaRotatingCoordinateSystem 356 Note9.1 TheEquivalencePrincipleandthe GravitationalRedShift 368 Problems 370 10 CENTRALFORCEMOTION 373 10.1 Introduction 374 10.2 CentralForceMotionasaOne-bodyProblem 374 10.3 UniversalFeaturesofCentralForceMotion 376 10.4 TheEnergyEquationandEnergyDiagrams 379 10.5 PlanetaryMotion 386 10.6 SomeConcludingCommentsonPlanetary Motion 402 Note10.1 IntegratingtheOrbitIntegral 403 Note10.2 PropertiesoftheEllipse 405 Problems 407 11 THEHARMONICOSCILLATOR 411 11.1 Introduction 412 11.2 SimpleHarmonicMotion:Review 412 11.3 TheDampedHarmonicOscillator 414 11.4 TheDrivenHarmonicOscillator 421 11.5 TransientBehavior 425 11.6 ResponseinTimeandResponseinFrequency 427 Note11.1 ComplexNumbers 430 Note11.2 SolvingtheEquationofMotionforthe DampedOscillator 431 Note11.3 SolvingtheEquationofMotionforthe DrivenHarmonicOscillator 434 Problems 435 12 THESPECIALTHEORYOFRELATIVITY 439 12.1 Introduction 440 12.2 ThePossibilityofFlawsinNewtonianPhysics 440 12.3 TheMichelson–MorleyExperiment 442 12.4 TheSpecialTheoryofRelativity 445 12.5 Transformations 447 12.6 SimultaneityandtheOrderofEvents 450 12.7 TheLorentzTransformation 451 12.8 RelativisticKinematics 454 12.9 TheRelativisticAdditionofVelocities 463 12.10 TheDopplerEffect 466