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W. W. Norton & Company, Inc. • www.NortonEbooks.com PHYSICS Hans C. Ohanian, John T. Markert THIRD EDITION FOR ENGINEERS AND SCIENTISTS Volume One Physics_Vol-2-FM.qxd 07/02/2007 7:43 AM Page vi PMAC-291 27B:GK023:Chapters:FM-Vol2: TechBooks [PPG -QUARK] Physics for Engineers and Scientists Third Edition W • W • NORTON & COMPANY B NEW YORK • LONDON Volume1 (Chapters 1–21) MOTION, FORCE, AND ENERGY OSCILLATIONS, WAVES, AND FLUIDS TEMPERATURE, HEAT, AND THERMODYNAMICS Physics_FM.qxd 7/10/06 12:28 PM Page i PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] Physics_FM.qxd 7/10/06 12:28 PM Page ii PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] Physics for Engineers and Scientists Third Edition H A N S C . O H A N I A N , U N I V E R S I T Y O F V E R M O N T J O H N T. M A R K E R T, U N I V E R S I T Y O F T E X A S A T A U S T I N W • W • NORTON & COMPANY B NEW YORK • LONDON Volume1 (Chapters 1–21) MOTION, FORCE, AND ENERGY OSCILLATIONS, WAVES, AND FLUIDS TEMPERATURE, HEAT, AND THERMODYNAMICS Physics_FM.qxd 7/10/06 12:29 PM Page iii PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] To Susan Ohanian, writer, who gently tried to teach me some of her craft.—H.C.O. To Frank D. Markert, a printer by trade; to Christiana Park, for her thirst for new knowledge; and to Erin, Ryan, Sean, and Gwen, for their wonder and clarity.—J.T.M. Copyright © 2007 by W.W. Norton & Company, Inc. All rights reserved Printed in the United States of America Third Edition Composition: Techbooks Manufacturing: RR Donnelley & Sons Company Editor: Leo A. W. Wiegman Media Editor: April E. Lange Director of Manufacturing—College: Roy Tedoff Senior Project Editor: Christopher Granville Photo Researcher: Kelly Mitchell Editorial Assistant: Lisa Rand, Sarah L. Mann Copy Editor: Richard K. Mickey Book designer: Sandy Watanabe Layout artist: Paul Lacy Illustration Studio: JB Woolsey Arts, Inc. Cover Illustration: John Belcher, inter alia. Cover Design: Joan Greenfield Library of Congress Cataloging-in-Publication Data has been applied for. ISBN 978-0-393-11101-9 (ebook) W. W. Norton & Company, Inc., 500 Fifth Avenue, New York, N.Y. 10110 www.wwnorton.com W. W. Norton & Company Ltd., Castle House, 75/76 Wells Street, London W1T 3QT 1234567890 W.W. Norton & Company has been independent since its founding in 1923, when William Warder Norton and Mary D. Herter Norton first published lectures delivered at the People’s Institute, the adult education division of New York City’s Cooper Union.The Nortons soon expanded their program beyond the Institute, publishing books by celebrated academics from America and abroad. By mid-century, the two major pillars of Norton’s publishing program—trade books and college texts— were firmly established. In the 1950s, the Norton family transferred control of the company to its employees, and today—with a staff of four hundred and a comparable number of trade, college, and professional titles published each year—W. W. Norton & Company stands as the largest and oldest publishing house owned wholly by its employees. Physics_FM.qxd 7/10/06 12:29 PM Page iv PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] Brief Contents PREFACE xiii OWNER’S MANUAL xxv PRELUDE: THE WORLD OF PHYSICS xxxv PART I MOTION, FORCE, AND ENERGY 1 1. SPACE, TIME, AND MASS 2 2. MOTION ALONG A STRAIGHT LINE 28 3. VECTORS 69 4. MOTION IN TWO AND THREE DIMENSIONS 94 5. NEWTON’S LAWS OF MOTION 130 6. FURTHER APPLICATIONS OF NEWTON’S LAWS 173 7. WORK AND ENERGY 204 8. CONSERVATION OF ENERGY 235 9. GRAVITATION 271 10. SYSTEMS OF PARTICLES 305 11. COLLISIONS 338 12. ROTATION OF A RIGID BODY 365 13. DYNAMICS OF A RIGID BODY 394 14. STATICS AND ELASTICITY 429 PART II OSCILLATIONS, WAVES, AND FLUIDS 466 15. OSCILLATIONS 468 16. WAVES 507 17. SOUND 536 18. FLUID MECHANICS 565 PART III TEMPERATURE, HEAT, AND THERMODYNAMICS 600 19. THE IDEAL GAS 602 20. HEAT 628 21. THERMODYNAMICS 661 v PART IV ELECTRICITY AND MAGNETISM 22. ELECTRIC FORCE AND ELECTRIC CHARGE 23. THE ELECTRIC FIELD 24. GAUSS’ LAW 25. ELECTROSTATIC POTENTIAL AND ENERGY 26. CAPACITORS AND DIELECTRICS 27. CURRENTS AND OHM’S LAW 28. DIRECT CURRENT CIRCUITS 29. MAGNETIC FORCE AND FIELD 30. CHARGES AND CURRENTS IN MAGNETIC FIELDS 31. ELECTROMAGNETIC INDUCTION 32. ALTERNATING CURRENT CIRCUITS PART V WAVES AND OPTICS 33. ELECTROMAGNETIC WAVES 34. REFLECTION, REFRACTION, AND OPTICS 35. INTERFERENCE AND DIFFRACTION PART VI RELATIVITY, QUANTA, AND PARTICLES 36. THE THEORY OF SPECIAL RELATIVITY 37. QUANTA OF LIGHT 38. SPECTRAL LINES, BOHR’S THEORY, AND QUANTUM MECHANICS 39. QUANTUM STRUCTURE OF ATOMS, MOLECULES, AND SOLIDS 40. NUCLEI 41. ELEMENTARY PARTICLES AND COSMOLOGY APPENDICES A-1 Chapters 1–21 appear in Volume 1; Chapters 22–36 appear in Volume 2; Chapters 37–41 appear in Volume 3. Physics_FM.qxd 7/10/06 12:29 PM Page v PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] Physics_FM.qxd 7/10/06 12:29 PM Page vi PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] Table of Contents PREFACE xiii OWNER’S MANUAL xxv PRELUDE: THE WORLD OF PHYSICS xxxv PART I MOTION, FORCE, AND ENERGY 1 1. SPACE, TIME, AND MASS 2 1.1 Coordinates and Reference Frames 3 1.2 The Unit of Length 5 1.3 The Unit of Time 9 1.4 The Unit of Mass 11 1.5 Derived Units 13 1.6 Significant Figures; Consistency of Units and Conversion of Units 14 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 20 2. MOTION ALONG A STRAIGHT LINE 28 2.1 Average Speed 29 2.2 Average Velocity for Motion along a Straight Line 32 2.3 Instantaneous Velocity 35 2.4 Acceleration 39 2.5 Motion with Constant Acceleration 42 2.6 The Acceleration of Free Fall 49 2.7* Integration of the Equations of Motion 54 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 57 3. VECTORS 69 3.1 The Displacement Vector and Other Vectors 70 3.2 Vector Addition and Subtraction 72 3.3 The Position Vector; Components of a Vector 76 3.4 Vector Multiplication 81 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 87 4. MOTION IN TWO AND THREE DIMENSIONS 94 4.1 Components of Velocity and Acceleration 95 4.2 The Velocity and Acceleration Vectors 98 4.3 Motion with Constant Acceleration 102 4.4 The Motion of Projectiles 104 4.5 Uniform Circular Motion 112 4.6 The Relativity of Motion and the Addition of Velocities 115 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 118 5. NEWTON’S LAWS OF MOTION 130 5.1 Newton’s First Law 131 5.2 Newton’s Second Law 133 5.3 The Combination of Forces 138 5.4 Weight; Contact Force and Normal Force 141 5.5 Newton’s Third Law 144 5.6 Motion with a Constant Force 151 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 159 6. FURTHER APPLICATIONS OF NEWTON’S LAWS 173 6.1 Friction 174 6.2 Restoring Force of a Spring; Hooke’s Law 182 6.3 Force for Uniform Circular Motion 184 6.4* The Four Fundamental Forces 191 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 192 vii Chapters 1–21 appear in Volume 1; Chapters 22–36 appear in Volume 2; and Chapters 37–41 appear in Volume 3. Physics_FM.qxd 7/10/06 12:29 PM Page vii PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] 7. WORK AND ENERGY 204 7.1 Work 205 7.2 Work for a Variable Force 211 7.3 Kinetic Energy 214 7.4 Gravitational Potential Energy 218 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 224 8. CONSERVATION OF ENERGY 235 8.1 Potential Energy of a Conservative Force 236 8.2 The Curve of Potential Energy 244 8.3 Other Forms of Energy 248 8.4* Mass and Energy 251 8.5 Power 253 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 259 9. GRAVITATION 271 9.1 Newton’s Law of Universal Gravitation 272 9.2 The Measurement of G 277 9.3 Circular Orbits 278 9.4 Elliptical Orbits; Kepler’s Laws 282 9.5 Energy in Orbital Motion 288 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 293 10. SYSTEMS OF PARTICLES 305 10.1 Momentum 306 10.2 Center of Mass 313 10.3 The Motion of the Center of Mass 323 10.4 Energy of a System of Particles 327 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 328 11. COLLISIONS 338 11.1 Impulsive Forces 339 11.2 Elastic Collisions in One Dimension 344 11.3 Inelastic Collisions in One Dimension 348 11.4* Collisions in Two and Three Dimensions 351 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 354 12. ROTATION OF A RIGID BODY 365 12.1 Motion of a Rigid Body 366 12.2 Rotation about a Fixed Axis 367 12.3 Motion with Constant Angular Acceleration 374 12.4* Motion with Time-Dependent Angular Acceleration 376 12.5 Kinetic Energy of Rotation; Moment of Inertia 378 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 384 13. DYNAMICS OF A RIGID BODY 394 13.1 Work, Energy, and Power in Rotational Motion; Torque 395 13.2 The Equation of Rotational Motion 399 13.3 Angular Momentum and its Conservation 406 13.4* Torque and Angular Momentum as Vectors 410 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 417 14. STATICS AND ELASTICITY 429 14.1 Statics of Rigid Bodies 430 14.2 Examples of Static Equilibrium 433 14.3 Levers and Pulleys 441 14.4 Elasticity of Materials 445 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 450 PART II OSCILLATIONS, WAVES, AND FLUIDS 466 15. OSCILLATIONS 468 15.1 Simple Harmonic Motion 469 15.2 The Simple Harmonic Oscillator 476 15.3 Kinetic Energy and Potential Energy 480 15.4 The Simple Pendulum 484 15.5* Damped Oscillations and Forced Oscillations 488 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 494 16. WAVES 507 16.1 Transverse and Longitudinal Wave Motion 508 16.2 Periodic Waves 509 viii CONTENTS Physics_FM.qxd 7/10/06 12:29 PM Page viii PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] 16.3 The Superposition of Waves 516 16.4 Standing Waves 520 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 524 17. SOUND 536 17.1 Sound Waves in Air 538 17.2 Intensity of Sound 540 17.3 The Speed of Sound; Standing Waves 543 17.4 The Doppler Effect 574 17.5* Diffraction 553 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 555 18. FLUID MECHANICS 565 18.1 Density and Flow Velocity 567 18.2 Incompressible Steady Flow; Streamlines 569 18.3 Pressure 573 18.4 Pressure in a Static Fluid 575 18.5 Archimedes’ Principle 580 18.6 Fluid Dynamics; Bernoulli’s Equation 582 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 587 PART III TEMPERATURE, HEAT, AND THERMODYNAMICS 600 19. THE IDEAL GAS 602 19.1 The Ideal-Gas Law 603 19.2 The Temperature Scale 609 19.3 Kinetic Pressure 613 19.4 The Internal Energy of an Ideal Gas 616 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 619 20. HEAT 628 20.1 Heat as a Form of Energy Transfer 629 20.2 Thermal Expansion of Solids and Liquids 633 20.3 Thermal Conduction 638 20.4 Changes of State 642 20.5 The Specific Heat of a Gas 644 20.6* Adiabatic Expansion of a Gas 647 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 650 21. THERMODYNAMICS 661 21.1 The First Law of Thermodynamics 663 21.2 Heat Engines; The Carnot Engine 665 21.3 The Second Law of Thermodynamics 675 21.4 Entropy 677 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 681 PART IV ELECTRICITY AND MAGNETISM 22. ELECTRIC FORCE AND ELECTRIC CHARGE 22.1 The Electrostatic Force 22.2 Coulomb’s Law 22.3 The Superposition of Electrical Forces 22.4 Charge Quantization and Charge Conservation 22.5 Conductors and Insulators; Charging by Friction or by Induction SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 23. THE ELECTRIC FIELD 23.1 The Electric Field of Point Charges 23.2 The Electric Field of Continuous Charge Distributions 23.3 Lines of Electric Field 23.4 Motion in a Uniform Electric Field 23.5 Electric Dipole in an Electric Field SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 24. GAUSS’ LAW 24.1 Electric Flux 24.2 Gauss’ Law 24.3 Applications of Gauss’ Law 24.4 Superposition of Electric Fields 24.5 Conductors and Electric Fields SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 25. ELECTROSTATIC POTENTIAL AND ENERGY 25.1 The Electrostatic Potential 25.2 Calculation of the Potential from the Field CONTENTS ix Physics_FM.qxd 7/10/06 12:29 PM Page ix PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] 30. CHARGES AND CURRENTS IN MAGNETIC FIELDS 30.1 Circular Motion in a Uniform Magnetic Field 30.2 Force on a Wire 30.3 Torque on a Loop 30.4 Magnetism in Materials 30.5* The Hall Effect SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 31. ELECTROMAGNETIC INDUCTION 31.1 Motional EMF 31.2 Faraday’s Law 31.3 Some Examples; Lenz’ Law 31.4 Inductance 31.5 Magnetic Energy 31.6* The RL Circuit SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 32. ALTERNATING CURRENT CIRCUITS* 32.1 Resistor Circuit 32.2 Capacitor Circuit 32.3 Inductor Circuit 32.4* Freely Oscillating LC and RLC Circuits 32.5* Series Circuits with Alternating EMF 32.6 Transformers SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS PART V WAVES AND OPTICS 33. ELECTROMAGNETIC WAVES 33.1 Induction of Magnetic Fields; Maxwell’s Equations 33.2* The Electromagnetic Wave Pulse 33.3 Plane Waves; Polarization 33.4 The Generation of Electromagnetic Waves 33.5 Energy of a Wave 33.6* The Wave Equation SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS x CONTENTS 25.3 Potential in Conductors 25.4 Calculation of the Field from the Potential 25.5 Energy of Systems of Charges SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 26. CAPACITORS AND DIELECTRICS 26.1 Capacitance 26.2 Capacitors in Combination 26.3 Dielectrics 26.4 Energy in Capacitors SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 27. CURRENTS AND OHM’S LAW 27.1 Electric Current 27.2 Resistance and Ohm’s Law 27.3 The Resistivity of Materials 27.4 Resistances in Combination SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 28. DIRECT CURRENTS CIRCUITS 28.1 Electromotive Force 28.2 Sources of Electromotive Force 28.3 Single-Loop Circuits 28.4 Multi-Loop Circuits 28.5 Energy in Circuits; Joule Heat 28.6* Electrical Measurements 28.7* The RC Circuit 28.8* The Hazards of Electric Currents SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 29. MAGNETIC FORCE AND FIELD 29.1 The Magnetic Force 29.2 The Magnetic Field 29.3 Ampére’s Law 29.4 Solenoids and Magnets 29.5 The Biot-Savart Law SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS Physics_FM.qxd 7/10/06 12:29 PM Page x PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] 34. REFLECTION, REFRACTION, AND OPTICS 34.1 Huygens’ Construction 34.2 Reflection 34.3 Refraction 34.4 Spherical Mirrors 34.5 Thin Lenses 34.6* Optical Instruments SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 35. INTERFERENCE AND DIFFRACTION 35.1 Thin Films 35.2* The Michelson Interferometer 35.3 Interference from Two Slits 35.4 Interference from Multiple Slits 35.5 Diffraction by a Single Slit 35.6 Diffraction by a Circular Aperture; Rayleigh’s Criterion SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS PART VI RELATIVITY, QUANTA, AND PARTICLES 36. THE THEORY OF SPECIAL RELATIVITY 36.1 The Speed of Light; the Ether 36.2 Einstein’s Principle of Relativity 36.3 Time Dilation 36.4 Length Contraction 36.5 The Lorentz Transformations and the Combination of Velocities 36.6 Relativistic Momentum and Energy 36.7* Mass and Energy SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 37. QUANTA OF LIGHT 37.1 Blackbody Radiation 37.2 Energy Quanta 37.3 Photons and the Photoelectric Effect 37.4 The Compton Effect 37.5 X Rays 37.6 Wave vs. Particle SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS CONTENTS xi 38. SPECTRAL LINES, BOHR’S THEORY, AND QUANTUM MECHANICS 38.1 Spectral Lines 38.2 Spectral Series of Hydrogen 38.3 The Nuclear Atom 38.4 Bohr’s Theory 38.5 Quantum Mechanics; The Schrödinger Equation SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 39. QUANTUM STRUCTURE OF ATOMS, MOLECULES, AND SOLIDS 39.1 Principal, Orbital, and Magnetic Quantum Numbers; Spin 39.2 The Exclusion Principle and the Structure of Atoms 39.3* Energy Levels in Molecules 39.4 Energy Bands in Solids 39.5 Semiconductor Devices SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 40. NUCLEI 40.1 Isotopes 40.2 The Strong Force and the Nuclear Binding Energy 40.3 Radioactivity 40.4 The Law of Radioactive Decay 40.5 Fission 40.6* Nuclear Bombs and Nuclear Reactors 40.7 Fusion SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 41. ELEMENTARY PARTICLES AND COSMOLOGY 41.1 The Tools of High-Energy Physics 41.2 The Multitude of Particles 41.3 Interactions and Conservation Laws 41.4 Fields and Quanta 41.5 Quarks 41.6 Cosmology SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS Physics_FM.qxd 7/10/06 12:29 PM Page xi PMAC-291 PMAC-291:Desktop Folder:GK023: TechBooks [PPG -QUARK] APPENDIX 6: THE INTERNATIONAL SYSTEM OF UNITS (SI) A-21 A6.1 Base Units A-21 A6.2 Derived Units A-23 A6.3 Prefixes A-23 APPENDIX 7: BEST VALUES OF FUNDAMENTAL CONSTANTS A-23 APPENDIX 8: CONVERSION FACTORS A-26 APPENDIX 9: THE PERIODIC TABLE AND CHEMICAL ELEMENTS A-31 APPENDIX 10: FORMULA SHEETS A-33 Chapters 1–21 A-33 Chapters 22–41 A-34 APPENDIX 11: ANSWERS TO ODD-NUMBERED PROBLEMS AND REVIEW PROBLEMS A-35 PHOTO CREDITS A-51 INDEX A-55 xii CONTENTS APPENDICES APPENDIX 1: GREEK ALPHABET A-1 APPENDIX 2: MATHEMATICS REVIEW A-1 A2.1 Symbols A-1 A2.2 Powers and Roots A-1 A2.3 Arithmetic in Scientific Notation A-2 A2.4 Algebra A-3 A2.5 Equations with Two Unknowns A-5 A2.6 The Quadratic Formula A-5 A2.7 Logarithms and the Exponential Function A-5 APPENDIX 3: GEOMETRY AND TRIGONOMETRY REVIEW A-7 A3.1 Perimeters, Areas, and Volumes A-7 A3.2 Angles A-7 A3.3 The Trigonometric Functions A-8 A3.4 The Trigonometric Identities A-9 A3.5 The Laws of Cosines and Sines A-10 APPENDIX 4: CALCULUS REVIEW A-10 A4.1 Derivatives A-10 A4.2 Important Rules for Differentiation A-11 A4.3 Integrals A-12 A4.4 Important Rules for Integration A-15 A4.5 The Taylor Series A-18 A4.6 Some Approximations A-18 APPENDIX 5: PROPAGATING UNCERTAINTIES A-19 Physics_FM.qxd 7/10/06 4:40 PM Page xii PMAC-291 PMAC-291:Books:GK-Jobs: TechBooks [PPG -QUARK]