www.EngineeringEBooksPdf.com Physics for Scientists and Engineers (with PhysicsNOW and InfoTrac) Raymond A Serway - Emeritus, James Madison University John W Jewett - California State Polytechnic University, Pomona ISBN 0534408427 1296 pages Case Bound 1/2 x 10 7/8 Thomson Brooks/Cole © 2004; 6th Edition This best-selling, calculus-based text is recognized for its carefully crafted, logical presentation of the basic concepts and principles of physics PHYSICS FOR SCIENTISTS AND ENGINEERS, Sixth Edition, maintains the Serway traditions of concise writing for the students, carefully thought-out problem sets and worked examples, and evolving educational pedagogy This edition introduces a new co-author, Dr John Jewett, at Cal Poly – Pomona, known best for his teaching awards and his role in the recently published PRINCIPLES OF PHYSICS, Third Edition, also written with Ray Serway Providing students with the tools they need to succeed in introductory physics, the Sixth Edition of this authoritative text features unparalleled media integration and a newly enhanced supplemental package for instructors and students! Features A GENERAL PROBLEM-SOLVING STRATEGY is outlined early in the text This strategy provides a series of steps similar to those taken by professional physicists in solving problems This problem solving strategy is integrated into the Coached Problems (within PhysicsNow) to reinforce this key skill A large number of authoritative and highly realistic WORKED EXAMPLES promote interactivity and reinforce student understanding of problem-solving techniques In many cases, these examples serve as models for solving end-of-chapter problems The examples are set off from the text for ease of location and are given titles to describe their content Many examples include specific references to the GENERAL PROBLEM-SOLVING STRATEGY to illustrate the underlying concepts and methodology used in arriving at a correct solution This will help students understand the logic behind the solution and the advantage of using a particular approach to solve the problem About one-third of the WORKED EXAMPLES include new WHAT IF? extensions CONCEPTUAL EXAMPLES include detailed reasoning statements to help students learn how to think through physical situations A concerted effort was made to place more emphasis on critical thinking and teaching physical concepts in this new edition Both PROBLEM-SOLVING STRATEGIES and HINTS help students approach homework assignments with greater confidence General strategies and suggestions are included for solving the types of problems featured in the worked examples, end-of-chapter problems, and PhysicsNow This feature helps students identify the essential steps in solving problems and increases their skills as problem solvers END-OF-CHAPTER PROBLEMS – An extensive set of problems is included at the end of each chapter Answers to odd-numbered problems are given at the end of the book For the convenience of both the student and instructor, about two thirds of the problems are keyed to specific sections of the chapter All problems have been carefully worded and have been checked for clarity and accuracy Solutions to approximately 20 percent of the end-of-chapter problems are included in the Student Solutions Manual and Study Guide These problems are identified with a box around the problem number Serway and Jewett have a clear, relaxed writing style in which they carefully define new terms and avoid jargon whenever possible The presentation is accurate and precise The International System of units (SI) is used throughout the book The U.S customary system of units is used only to a limited extent in the problem sets of the early chapters on mechanics www.EngineeringEBooksPdf.com Table of Contents Part I: MECHANICS Physics and Measurement Standards of Length, Mass, and Time Matter and Model Building Density and Atomic Mass Dimensional Analysis Conversion of Units Estimates and Order-of-Magnitude Calculations Significant Figures 2 Motion in One Dimension Position, Velocity, and Speed Instantaneous Velocity and Speed Acceleration Motion Diagrams One-Dimensional Motion with Constant Acceleration Freely Falling Objects Kinematic Equations Derived from Calculus General Problem-Solving Strategy 23 Vectors Coordinate Systems Vector and Scalar Quantities Some Properties of Vectors Components of a Vector and Unit Vectors 58 Motion in Two Dimensions The Position, Velocity, and Acceleration Vectors Two-Dimensional Motion with Constant Acceleration Projectile Motion Uniform Circular Motion Tangential and Radial Acceleration Relative Velocity and Relative Acceleration 77 The Laws of Motion The Concept of Force Newton's First Law and Inertial Frames Mass Newton's Second Law The Gravitational Force and Weight Newton's Third Law Some Applications of Newton's Laws Forces of Friction 111 Circular Motion and Other Applications of Newton's Laws Newton's Second Law Applied to Uniform Circular Motion Nonuniform Circular Motion Motion in Accelerated Frames Motion in the Presence of Resistive Forces Numerical Modeling in Particle Dynamics 150 www.EngineeringEBooksPdf.com Energy and Energy Transfer Systems and Environments Work Done by a Constant Force The Scalar Product of Two Vectors Work Done by a Varying Force Kinetic Energy and the Work Kinetic Energy Theorem The Non-Isolated System Conservation of Energy Situations Involving Kinetic Friction Power Energy and the Automobile 181 Potential Energy Potential Energy of a System The Isolated System Conservation of Mechanical Energy Conservative and Nonconservative Forces Changes in Mechanical Energy for Nonconservative Forces Relationship Between Conservative Forces and Potential Energy Energy Diagrams and Equilibrium of a System 217 Linear Momentum and Collisions Linear Momentum and Its Conservation Impulse and Momentum Collisions in One Dimension Two-Dimensional Collisions The Center of Mass Motion of a System of Particles Rocket Propulsion 251 10 Rotation of a Rigid Object about a Fixed Axis Angular Position, Velocity, and Acceleration Rotational Kinematics: Rotational Motion with Constant Angular Acceleration Angular and Linear Quantities Rotational Kinetic Energy Calculation of Moments of Inertia Torque Relationship Between Torque and Angular Acceleration Work, Power, and Energy in Rotational Motion Rolling Motion of a Rigid Object 292 11 Angular Momentum The Vector Product and Torque Angular Momentum Angular Momentum of a Rotating Rigid Object Conservation of Angular Momentum The Motion of Gyroscopes and Tops Angular Momentum as a Fundamental Quantity 336 12 Static Equilibrium and Elasticity The Conditions for Equilibrium More on the Center of Gravity Examples of Rigid Objects in Static Equilibrium Elastic Properties of Solids 362 www.EngineeringEBooksPdf.com 13 Universal Gravitation Newton's Law of Universal Gravitation Measuring the Gravitational Constant Free-Fall Acceleration and the Gravitational Force Kepler's Laws and the Motion of Planets The Gravitational Field Gravitational Potential Energy Energy Considerations in Planetary and Satellite Motion 389 14 Fluid Mechanics Pressure Variation of Pressure with Depth Pressure Measurements Buoyant Forces and Archimedes's Principle Fluid Dynamics Bernoulli's Equation Other Applications of Fluid Dynamics 420 Part II: OSCILLATIONS AND MECHANICAL WAVES 451 15 Oscillatory Motion Motion of an Object Attached to a Spring Mathematical Representation of Simple Harmonic Motion Energy of the Simple Harmonic Oscillator Comparing Simple Harmonic Motion with Uniform Circular Motion The Pendulum Damped Oscillations/ Forced Oscillations 452 16 Wave Motion Propagation of a Disturbance Sinusoidal Waves The Speed of Waves on Strings Reflection and Transmission Rate of Energy Transfer by Sinusoidal Waves on Strings The Linear Wave Equation 486 17 Sound Waves Speed of Sound Waves Periodic Sound Waves Intensity of Periodic Sound Waves The Doppler Effect Digital Sound Recording Motion Picture Sound 512 18 Superposition and Standing Waves Superposition and Interference Standing Waves Standing Waves in a String Fixed at Both Ends Resonance Standing Waves in Air Columns Standing Waves in Rods and Membranes Beats: Interference in Time Nonsinusoidal Wave Patterns 543 www.EngineeringEBooksPdf.com Part III: THERMODYNAMICS 579 19 Temperature Temperature and the Zeroth Law of Thermodynamics Thermometers and the Celsius Temperature Scale The Constant-Volume Gas Thermometer and the Absolute Temperature Scale Thermal Expansion of Solids and Liquids Macroscopic Description of an Ideal Gas 580 20 Heat and the First Law of Thermodynamics Heat and Internal Energy Specific Heat and Calorimetry Latent Heat Work and Heat in Thermodynamic Processes The First Law of Thermodynamics Some Applications of the First Law of Thermodynamics Energy Transfer Mechanisms 604 21 The Kinetic Theory of Gases Molecular Model of an Ideal Gas Molar Specific Heat of an Ideal Gas Adiabatic Processes for an Ideal Gas The Equipartition of Energy The Boltzmann Distribution Law Distribution of Molecular Speeds/ Mean Free Path 640 22 Heat Engines, Entropy, and the Second Law of Thermodynamics Heat Engines and the Second Law of Thermodynamics Heat Pumps and Refrigerators Reversible and Irreversible Processes The Carnot Engine Gasoline and Diesel Engines Entropy Entropy Changes in Irreversible Processes Entropy on a Microscopic Scale 667 Part IV: ELECTRICITY AND MAGNETISM 705 23 Electric Fields Properties of Electric Charges Charging Objects by Induction Coulomb's Law The Electric Field Electric Field of a Continuous Charge Distribution Electric Field Lines Motion of Charged Particles in a Uniform Electric Field 706 24 Gauss's Law Electric Flux Gauss's Law Application of Gauss's Law to Various Charge Distributions Conductors in Electrostatic Equilibrium Formal Derivation of Gauss's Law 739 www.EngineeringEBooksPdf.com 25 Electric Potential Potential Difference and Electric Potential Potential Differences in a Uniform Electric Field Electric Potential and Potential Energy Due to Point Charges Obtaining the Value of the Electric Field from the Electric Potential Electric Potential Due to Continuous Charge Distributions Electric Potential Due to a Charged Conductor The Millikan Oil-Drop Experiment Applications of Electrostatics 762 26 Capacitance and Dielectrics Definition of Capacitance Calculating Capacitance Combinations of Capacitors Energy Stored in a Charged Capacitor Capacitors with Dielectrics Electric Dipole in an Electric Field An Atomic Description of Dielectrics 795 27 Current and Resistance Electric Current Resistance A Model for Electrical Conduction Resistance and Temperature Superconductors Electrical Power 831 28 Direct Current Circuits Electromotive Force Resistors in Series and Parallel Kirchhoff's Rules RC Circuits Electrical Meters Household Wiring and Electrical Safety 858 29 Magnetic Fields Magnetic Field and Forces Magnetic Force Acting on a Current-Carrying Conductor Torque on a Current Loop in a Uniform Magnetic Field Motion of a Charged Particle in a Uniform Magnetic Field Applications Involving Charged Particles Moving in a Magnetic Field The Hall Effect 894 30 Sources of Magnetic Field The Biot-Savart Law The Magnetic Force Between Two Parallel Conductors Ampere's Law The Magnetic Field of a Solenoid Magnetic Flux Gauss's Law in Magnetism Displacement Current and the General Form of Ampere's Law Magnetism in Matter The Magnetic Field of the Earth 926 www.EngineeringEBooksPdf.com 31 Faraday's Law Faraday's Law of Induction Motional emf Lenz's Law Induced emf and Electric Fields Generators and Motors/ Eddy Currents Maxwell's Equations 967 32 Inductance Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Oscillations in an LC Circuit The RLC Circuit 1003 33 Alternating Current Circuits AC Sources Resistors in an AC Circuit Inductors in an AC Circuit Capacitors in an AC Circuit The RLC Series Circuit Power in an AC Circuit Resonance in a Series RLC Circuit The Transformer and Power Transmission Rectifiers and Filters 1033 34 Electromagnetic Waves Maxwell's Equations and Hertz's Discoveries Plane Electromagnetic Waves Energy Carried by Electromagnetic Waves Momentum and Radiation Pressure Production of Electromagnetic Waves by an Antenna 1066 Part V: LIGHT AND OPTICS 35 The Nature of Light and the Laws of Geometric Optics The Nature of Light Measurements of the Speed of Light The Ray Approximation in Geometric Optics Reflection Refraction Huygens's Principle Dispersion and Prisms Total Internal Reflection Fermat's Principle www.EngineeringEBooksPdf.com 1093 1094 36 Image Formation Images Formed by Flat Mirrors Images Formed by Spherical Mirrors Images Formed by Refraction Thin Lenses Lens Aberrations The Camera The Eye The Simple Magnifier The Compound Microscope The Telescope 1126 37 Interference of Light Waves Conditions for Interference Young's Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern Phasor Addition of Waves Change of Phase Due to Reflection Interference in Thin Films The Michelson Interferometer 1176 38 Diffraction Patterns and Polarization Introduction to Diffraction Patterns Diffraction Patterns from Narrow Slits Resolution of Single-Slit and Circular Apertures The Diffraction Grating Diffraction of X-rays by Crystals Polarization of Light Waves 1205 Part VI: MODERN PHYSICS 1243 39 Relativity The Principle of Galilean Relativity The Michelson-Morley Experiment Einstein's Principle of Relativity Consequences of the Special Theory of Relativity The Lorentz Transformation Equations The Lorentz Velocity Transformation Equations Relativistic Linear Momentum and the Relativistic Form of Newton's Laws Relativistic Energy Mass and Energy The General Theory of Relativity 1244 APPENDIXES: A Tables Conversion Factors Symbols, Dimensions, and Units of Physical Quantities Table of Atomic Masses B Mathematics Review Scientific Notation Algebra Geometry Trigonometry Series Expansions Differential Calculus Integral Calculus Propagation of Uncertainty C Periodic Table of the Elements D SI Units E Nobel Prize Winners Answers to Odd-Numbered Problems A.1 A.1 A.14 A.30 A.32 A.33 A.37 Index I.1 www.EngineeringEBooksPdf.com Mechanics PA R T hysics, the most fundamental physical science, is concerned with the basic principles of the Universe It is the foundation upon which the other sciences— astronomy, biology, chemistry, and geology—are based The beauty of physics lies in the simplicity of the fundamental physical theories and in the manner in which just a small number of fundamental concepts, equations, and assumptions can alter and expand our view of the world around us The study of physics can be divided into six main areas: P classical mechanics, which is concerned with the motion of objects that are large relative to atoms and move at speeds much slower than the speed of light; relativity, which is a theory describing objects moving at any speed, even speeds approaching the speed of light; thermodynamics, which deals with heat, work, temperature, and the statistical behavior of systems with large numbers of particles; electromagnetism, which is concerned with electricity, magnetism, and electromagnetic fields; optics, which is the study of the behavior of light and its interaction with materials; quantum mechanics, a collection of theories connecting the behavior of matter at the submicroscopic level to macroscopic observations The disciplines of mechanics and electromagnetism are basic to all other branches of classical physics (developed before 1900) and modern physics (c 1900–present) The first part of this textbook deals with classical mechanics, sometimes referred to as Newtonian mechanics or simply mechanics This is an appropriate place to begin an introductory text because many of the basic principles used to understand mechanical systems can later be used to describe such natural phenomena as waves and the transfer of energy by heat Furthermore, the laws of conservation of energy and momentum introduced in mechanics retain their importance in the fundamental theories of other areas of physics Today, classical mechanics is of vital importance to students from all disciplines It is highly successful in describing the motions of different objects, such as planets, rockets, and baseballs In the first part of the text, we shall describe the laws of classical mechanics and examine a wide range of phenomena that can be understood with these fundamental ideas ■ ᭣ Liftoff of the space shuttle Columbia The tragic accident of February 1, 2003 that took the lives of all seven astronauts aboard happened just before Volume of this book went to press The launch and operation of a space shuttle involves many fundamental principles of classical mechanics, thermodynamics, and electromagnetism We study the principles of classical mechanics in Part of this text, and apply these principles to rocket propulsion in Chapter (NASA) www.EngineeringEBooksPdf.com Index Mass (m) (Continued) units of, 4–6, 5, 116, 118t, A.1t vs weight, 116 Mass number (A), 8, A.4t–A.13t Mass spectrometers, 911–912 Materials science See also Deformable systems; Friction; Gases; Liquids; Optics; Rigid Objects; Solids and crystalline vs amorphous materials, 1229 and electrical properties of solids, 709, 835–845, 838, 1031 and magnetic properties of solids, 947–952, 1031 and mechanical properties of materials, 373–376 and optical properties of materials, 1104–1107, 1230, 1230 and thermal properties of materials, 197, 583, 586–591, 620–622, 623–627 Mathematical Principles of Natural Philosophy [Newton], 390 Mathematics, A.14–A.29 See also Addition; Algebra; Approximating; Calculus; Determinants; Division; Equations; Fourier series; Geometry; Logarithms; Measurement; Multiplication; Numerical modeling; Rounding; Series expansions; Significant figures; Subtraction; Trigonometric functions; Units; Vectors Matrix algebra, 870 Matter fundamental particles of, 912 structure of, 7–9, Matter transfer, 197 See also Convection and energy transfer, 197–198, 627–628 and waves, 487 Maxima of intensity, 1180, 1187–1188, 1206, 1219 Maximum angular position (max) [pendulums], 468 Maximum angular separation (max) [apertures], 1215 Maximum height (h) of a projectile, 86–91 Maxwell, James Clerk, 1067 and electromagnetic waves, 1067–1068, 1093, 1095 and electromagnetism, 705, 896, 942, 944 and Maxwell’s equations, 988, 1067–1068 and molecular speed distributions, 655 Maxwell–Boltzmann speed distribution function (Nv ), 655–657, 656 Maxwell’s equations, 988–989 and electromagnetic waves, 1067–1069 and special relativity, 1245, 1247 Mean free path (ᐉ), 658–659, 842 Mean free time, 658 Mean solar day, Mean value theorem, 257 Measurement, 2–22 See also Experiments; Instrumentation of density, 443 and disturbing the system, 582 of electric current, 879 of forces, 113–114 of the gravitational constant, 393–394 of magnetic fields, 914 of moments of inertia, 470 of potential difference, 879–880 of pressure, 421, 426–427 of speed of light, 1096–1097 of temperature, 582–584 uncertainty in, A.28–A.29 of wavelength of light, 1181 Measurements of electric current, 879 Mechanical devices See also Heat engines air conditioners, 671 balances, 393–394, 895, 987–988, 1077 machines, 148 photocopiers, 784 Mechanical energy (Emech), 221 changes in, for nonconservative forces, 229–234 conservation of, 220–228, 221 heat equivalent of, 606–607 and planetary motion, 406 Mechanical engineering See also Aeronautics; Airplanes; Automobiles; Bridges; Locomotives; Satellites; Spacecraft and heat engines, 667–683, 669, 700 and machines, 148 Mechanical equivalent of heat, 606–607 Mechanical waves, 197, 450–577, 487 and energy transfer, 197–198, 487, 500–503, 516–522 motion of, 486–511 sound, 512–542 speed of, 513–514 Mechanics, 1–449 See also Classical mechanics; Dynamics; Energy; Fluid mechanics; Force; Kinematics; Momentum; Motion; Quantum mechanics; Statistical mechanics history of, 1, 112 Media for wave propagation, 487 effects of changes in, 499–501, 560 and ether, 1247–1250 Medicine See also Biophysics; Health and blood flowmeters, 915–916, 924 and contact lenses, 1169 and cyclotrons, 913 and defibrillators, 810, 825 and ears, 512, 519–522, 564 and eyeglasses, 1157–1158 and eyes, 1157–1159, 1169, 1174 and fiber optics, 1114 www.EngineeringEBooksPdf.com I.13 Medicine (Continued) and MRI, 845 and spinal taps, 442 and steam burns, 613 and sunglasses, 1081, 1229 and ultrasound, 536 Meissner effect, 952, 1031 Melting See Fusion Melting points, 612t Mercury [element] in barometers, 426 superconductivity of, 844 in thermometers, 583–584 Mercury [planet], 399t See also Planetary motion escape speed from, 408t Metal detectors, 1051 Metals and bimetallic strips, 589, 601 charge carriers in, 915 thermal conduction of, 623–625, 624t Meter (m), Michelson, Albert A., 1194, 1248–1250 Michelson interferometers, 1194–1196, 1249 Michelson–Morley experiment, 1248–1250 Microscopes compound, 1160–1162 electron, 102 interference, 1202 Microstates, 683–684, 690–693 Microwave ovens, 816, 1085 Microwaves, 1080–1081 cosmic background, 1088 Migrating planets, 399 Millikan, Robert, 708, 781–782 Minima of intensity, 1206 Minor axis, 396 Mirages, 1121 Mirror equation, 1132–1133 Mirrors, 1127–1138 See also Reflection concave, 1131–1133 convex, 1134 flat, 1127–1130 Lloyd’s, 1188 parabolic, 1164 ray diagrams for, 1134–1136 spherical, 1131–1138 Models, 7–9 of atomic nucleus, 791 computer, 169–170 of electric current, 833–835 of electrical conduction, 841–843 of entropy, 690–693 of hydrogen atom, 352–353, 759 of ideal gases, 641–646 numerical, 167–170 particle, 24, 182, 270 of phase changes, 613 of solar system, 396 of solids, 463–464 I.14 Index Models (Continued) of structure of matter, 7–9 system, 182 Moderators, 266–267 Modern physics, 3, 1242–1283 See also Quantum mechanics; Relativity Modulus, elastic, 373, 374t bulk (B ), 373–375, 374t shear (S ), 373–374t Young’s (Y ), 373–374t Mohorovicic discontinuity, 540 Molar mass (M ), 592 Molar specific heats, 646–649 See also Specific heat at constant pressure (CP), 646–647t at constant volume (CV), 646–647t, 651–652 of solids, 653–654 Mole (n), 4, 591 Molecules polar vs nonpolar, 816 Moment arm (d), 306 Moment of inertia (I ), 300–302, 304t, 343 calculation of, 302–305 changes in, 346 measurement of, 470 and rotational acceleration, 308–312 Momentum (p), 252 See also Angular momentum; Linear momentum and collisions, 260–261 in electromagnetic waves, 1076–1079 and impulses, 256–260 relativistic, 1267–1268, 1270 Monochromatic light, 1177 Monopoles, magnetic, 895, 942, 989 Moon, 399t See also Planetary motion escape speed from, 408t planetary, 389, 1096, 1217–1218 and universal gravitation, 391–392 Morley, Edward W., 1248–1250 Morse, Samuel, 959 Most probable speed (vmp), 656–657 Motion See Circular motion; Kinematics; Laws of motion; Oscillatory motion; Periodic motion; Planetary motion; Precessional motion; Projectile motion; Rotational motion; Simple harmonic motion; Waves Motion diagrams, 34–35 Motion pictures See Movies Motors, 984–986 See also Generators; Heat engines homopolar, 995 Movies Apollo 13, 595 Batman Returns, 533 Dick Tracy, 532 digital, 1101 Indiana Jones and the Last Crusade, 362 inertia portrayed in, 138 Movies (Continued) It Happened One Night, 138 Jurassic Park, 533 Last Action Hero, 533 M*A*S*H, 1233 sound recording for, 532–533 stable equilibrium portrayed in, 362 Star Wars Episode II: Attack of the Clones, 1101 MRI See Magnetic resonance imaging Multiplication commutative law of, 187, 337 and differentiation, A.24 distributive law of, 187, 338 scalar (dot) product of two vectors, 186–188, 741 and significant figures, 15 and uncertainty, A.29 vector (cross) product of two vectors, 337–339 of vectors by scalars, 65 Muons gravitational red-shifts of, 1274 length contraction of, 1259 and time dilation, 1255–1256 Musgrave, F Story, 394 Music Ariadne auf Naxos, 540 Bach, Johann Sebastian, 537 and harmonic series, 555 Mass in B minor [Bach], 537 and musical scale, 572 and pitch, 566–567 Santana, Carlos, 543 Strauss, Richard, 540 Musical instruments, 555–556 electric, 971–972 and harmonic series, 555 and nonsinusoidal waves, 566–567 percussion, 561, 563–564 and resonance, 558–562 string, 543, 555–556, 561, 567 tuning of, 561, 564, 566 wind, 559–561, 566–567 Mutual inductance (M), 1013–1015 Mutual induction, 1013 Myopia, 1157–1158 Natural convection, 628 Natural frequency (0), 471 and harmonic series, 554 of LC circuits, 1018 Natural logarithms, 163, 279, 875, A.19 Near point of the eye, 1156, 1159 Nearsightedness, 1157–1158 Negative charges, 707 Negatives of vectors, 62–63 Neptune, 399t See also Planetary motion escape speed from, 408t www.EngineeringEBooksPdf.com Net force (⌺F), 112, 117 and equilibrium, 363–365 motion under, 123 on a system of particles, 275 Net torque (⌺), 363–365 Net work (⌺W), 189 and heat engines, 670 in PV diagrams, 619 Neutral equilibrium, 237 Neutral wires, 880 Neutron stars, 347, 409 Neutrons, discovery of, Newton (N), 117–118t Newton, Isaac, 114 and development of calculus, 3, 392, A.23 and gravitation, 390–392, 401, 1273 and laws of motion, 3, 112 and linear momentum, 253 and optics, 1093, 1095, 1191 and telescopes, 1164 and time, 1252 Newtonian mechanics See Classical mechanics; Mechanics Newton и meter (N и m), 185 Newton’s laws of motion See First law of motion; Laws of motion; Second law of motion; Third law of motion Newton’s rings, 1191–1192 Nitrogen atmospheric, 408, 656 liquid, 615, 629 molecular speed distribution in, 656–657 Niven, Larry, 417 Nobel prizes, A.33–A.36 Nodes, 550, 559 Noise and harmonic series, 564, 566 signal, 529 Noise pollution, 520 Nonconservative forces, 221, 228–229 and changes in mechanical energy, 229–234, 606–607 and damped oscillations, 471–472 and induced electric fields, 981 Noninertial reference frames, 115, 159–162 and general relativity, 1273–1274 and twin paradox, 1258 Nonisolated systems, 196–199 Nonlinear waves, 544 Nonmetals thermal conduction of, 623–625, 624t Nonohmic materials, 835, 838 Nonpolar molecules, 816 Nonuniform circular motion, 157–158 See also Circular motion Normal forces (n), 121 Index Normal modes, 553–555 in air columns, 560 in circular membranes, 563 in rods, 563 on strings fixed at both ends, 553 Nuclear forces, 113 Nuclear physics See Subatomic physics Nuclear reactors, 1272 Nucleus, discovery of, magnetic dipole moment of, 946 Number density (nV (E)), 654–655 Numerical modeling, 167–170 Object, optical (O), 1127 virtual, 1149 Object distance (p), 1127 Objective lenses, 1160–1163 Objects, physical See also Deformable systems; Rigid objects extended, 271–272 floating, 428–430 submerged, 428–430 Oersted, Hans Christian, 705, 895, 927, 933 Ohm, Georg Simon, 835 Ohm (⍀), 836 Ohmic materials, 835, 838 Ohm’s law, 835, 838 Oil-drop experiment, 781–782 One-time isothermal processes, 671 O’Neill, G K., 418 Open-circuit voltage (), 860 Optic axis, 1229 Optical activity, 1232 Optical devices See also Cameras; Lenses; Microscopes; Mirrors; Telescopes optical fibers, 1114 Optical fibers, 1114 Optical illusions, 1130, 1174 Optical resolution, 1214–1217 Optical stress analysis, 1230 Optics, 1, 1092–1241 See also Diffraction; Dispersion; Electromagnetic waves; Image formation; Interference; Light; Polarization; Reflection; Refraction; Speed of light geometric, 1094–1175 history of, 1093 wave, 1176–1241 Orbits See Planetary motion Order number (m), 1180 Order-of-magnitude (~) calculations, 13–14 See also Approximating Ordinary (O) rays, 1229–1230 Oscillatory motion, 451–485 See also Periodic motion; Simple harmonic motion damped, 471–472, 1020–1022 forced, 472–474 stick-and-slip, 484 Oscilloscopes, 728 Otto cycles, 679–680 Overdamped oscillators, 472–472, 1022 Oxygen atmospheric, 408, 656 liquid, 615, 629 paramagnetism of, 952 P waves, 489 Paleomagnetism, 954 Parabolas, 36, 84, A.21 and orbits, 397 and projectile motion, 77, 84–91 Parabolic mirrors, 1164 Paradoxes moving clocks, 1255 pole-in-the-barn, 1260–1261 speed of light, 1248 twin, 1257–1259 Parallax, 1167 Parallel-axis theorem, 304–305, 317, 349 Parallel combinations of capacitors, 803–804 of resistors, 862–869, 864 Paramagnetism, 947–948, 951–952 Paraxial rays, 1132 Partial derivatives, 235, 495, 503–504, 516, 773, 1069–1070 See also Differentiation Partial integration, A.26–A.27 Partial pressure (P i), 602 Particle models of motion, 24, 182, 270 Pascal, Blaise, 424 Pascal (Pa), 422 Pascal’s law, 424 Path dependence of work done by nonconservative forces, 229 of work in PV diagrams, 616–617 Path difference (␦), 1180, 1182–1183 Path independence of average velocity, 79 of entropy changes, 684 of internal energy changes, 618–619 of work done by conservative forces, 228 Path length (r), 548–549 Pendulums, 468–470 as accelerometers, 161 ballistic, 264–265 as clocks, 140, 468 conical, 153 and conservation of mechanical energy, 225 physical, 469–470 and resonance, 558 simple, 468–469 torsional, 470 Penzias, Arno, 1088 Percent uncertainty, A.29 Perfect diamagnetism, 952, 1031 www.EngineeringEBooksPdf.com I.15 Perfect differentials, A.27 Perfectly inelastic collisions, 261, 278 Perigee, 397 Perihelion, 397 Period (T ) of periodic waves, 492 of simple harmonic motion, 455–456 of uniform circular motion, 93, 908 Periodic motion, 450–577 See also Oscillatory motion; Simple harmonic motion; Waves Periscopes, 1117 Permeability, magnetic (m), 948 Permeability of free space (0), 928, 943 Permittivity of free space (⑀0), 712, 943 Pfund, A H., 1124 Phase (t ϩ ), 455 in AC circuits, 1035 and reflection, 1188–1189 and superposition and interference of sinusoidal waves, 547–549 Phase constant () and interference, 547–549, 1182–1183 of periodic waves, 493 in series RLC circuits, 1044–1045 of simple harmonic motion, 455, 1018 Phases of matter, 421, 604 See also Fluids; Gases; Liquids; Solids changes in, 607, 611–613 Phasor diagrams, 1035 for circuits, 1035–1036, 1039, 1041–1042, 1044–1046 for diffraction patterns, 1210–1211 for interference patterns, 1186–1188 Phasors, 1036, 1184–1188 Phonographs, 528–529 Photoconductors, 784 Photocopiers, 784 Photoelectric effect, 1095 Photons, 1096, 1270 Physical chemistry See also Thermodynamics and batteries, 799, 845–846, 858–861, 1014–1015, 1061 and bond energy, 605 and chemical energy, 278, 679, 799, 845–846 and scrubbers, 783 and surfactants, 816 Physical optics See Wave optics Physical pendulums, 469–470 Physics See also Astronomy and astrophysics; Biophysics; Engineering; Geophysics; History of physics; Laws of physics; Physical chemistry interdisciplinary nature of, 3–4 subdisciplines of, 1, Physics [Aristotle], 215–216 Physiology, 367–368, 384, 512 Pickup coils, 971–972 I.16 Index Pinch effect, 960 Pinhole cameras, 1239 Pions (ϩ and Ϫ), 256 Pitch, musical, 566–567 Pitot tubes, 445 Pits, CD, 299, 530–531 Planck, Max, 1093, 1095, 1243 Planck length, 418 Planck’s constant (h), 352, 945, 1096 Plane polar coordinates (r, ), 59 Plane-polarized light, 1226 Plane waves, 1069 Planetary motion, 396–401 See also Astronomy; Gravitation; Kepler’s laws and energy, 405–410 Planets, 399t See also specific planet escape speeds from, 408t Plasma, 910 balls of, 739 Plates of capacitors, 796 Platinum–iridium bars and standard meter, Plug-in problems, 47 See also Problemsolving strategies Pluto, 397, 399t See also Planetary motion escape speed from, 408t moon of, 1217–1218 Point charges, 711 electric field lines for, 724, 772 electric potential due to, 768–771, 769 equipotential surfaces for, 772 Poisson, Simeon, 1207 Polar coordinate systems, 59 Polar coordinates (r, ), 59, 293 Polar molecules, 816 Polarization, 1069, 1225–1232 by double refraction, 1229–1230 induced, 816 linear, 1069 of molecules, 816 by reflection, 1227–1229 rotation of plane of, 1232 by scattering, 1230–1231 by selective absorption, 1226–1227 Polarization angle (p), 1228 Polarizers, 1226 Polarizing angle, 1119 Polaroid materials, 1226 Pole-in-the-barn paradox, 1260–1261 Position (x), 24–28 angular (), 293–296, 294 average (x CM), 270–271 equilibrium, 453 Position–time graphs, 25, 33, 458–459 Position vectors (r), 78–80 average (rCM), 271 Positive charges, 707 Potential difference (⌬V ), 764 due to point charges, 768–771 in uniform electric fields, 765–768 Potential energy (U ), 197, 217–250, 219, 234 See also Conservation of energy; Electric potential; Energy; Kinetic energy; Lennard–Jones law in capacitors, 807–810, 876, 878 chemical, 278, 679, 799, 845–846 and conservative forces, 234–236, 403 elastic (Us), 197, 222–228, 462 electric (V ), 763–766, 764, 1015–1017 of electric dipoles in electric fields, 815 and equipartition of energy, 650–654 gravitational (Ug), 219, 403–405 of magnetic dipoles in magnetic fields, 906 and planetary motion, 405–408 of a system, 218–220 Pound (lb), 118t Power (ᏼ), 203–205 in AC circuits, 1037, 1047–1051 average (ᏼ), 203, 1048 delivered by automobile engines, 206, 681–683 and efficiency of heat engines, 677 electrical, 845–849, 860 and forced oscillators, 473 instantaneous (ᏼ), 203–204 and rotational motion, 312–316 Power factor (cos ), 1048, 1051 Power of a lens (P), 1158 Power strokes, 679–680 Power transfer by electricity, 198, 831, 846–847 by mechanical waves, 501–503, 516–522 by thermal conduction, 623–626 Powers See Exponents Poynting vectors (S), 1074–1079 Pre-emphasis, 529 Precessional frequency (p), 351 Precessional motion, 350–351 Prefixes for powers of ten, 7t Presbyopia, 1158 Pressure (P), 375, 421–423 absolute (P), 426 atmospheric (P0), 426 gauge, 426 and kinetic theory of gases, 641–644 measurement of, 421, 426–427 and musical instruments, 559–561 partial (Pi ), 602 radiation, 1076–1079 units of, 422, A.2t variation of, with depth, 423–426 waves of, 515–516 Pressure amplitude (⌬Pmax), 515 Primary coils of AC transformers, 1051 and Faraday’s law of induction, 968–969 of Rowland rings, 949 www.EngineeringEBooksPdf.com Primary maxima, 1187–1188 Principal axes and moment of inertia, 344 of spherical mirrors, 1131 Principle of equivalence, 1274 Prisms, 1109–1111 Probability and distribution functions, 654–657 and entropy, 684 and Gauss’s probability integral, A.28t Problem-solving strategies, 46–47 for calorimetry, 614 for capacitors, 806 for conservation of mechanical energy, 224 for electric fields, 720–721 for electric potential, 775 for isolated systems, 224, 230 for Kirchhoff’s rules, 871 for laws of motion, 124 for nonconservative forces, 230 for static equilibrium, 366 for thin-film interference, 1192 for two-dimensional collisions, 268 Processes adiabatic, 619, 649–650, 675–676 cyclic, 619, 670, 671 irreversible, 668, 673–675, 674, 687–690 isobaric, 620 isothermal, 620, 671, 675–676 isovolumetric, 620 quasi-static, 616, 686 random-walk, 658 reversible, 673–675, 686–687 thermodynamic, heat and work in, 615–617 Products See Multiplication Projectile motion, 83–91, 277 Propagation of uncertainty, A.28–A.29 Proper length (Lp), 1258–1259 Proper time intervals (⌬tp), 1253–1256, 1254, 1259 Proportionalities (ϰ) and dimensional analysis, 11 Propulsion, rocket, 277–280 Protons, collisions between, 269 discovery of, Ptolemy, Claudius, 396 Pulses, 488, 490 inverted, 499 Pupils, eye, 1155 Pure numbers, 455 Pure rolling motion, 316–319 PV diagrams, 616–617 and adiabatic processes, 650 and Carnot cycles, 676 for diesel engines, 681 and heat engines, 670 Index PV diagrams (Continued) and net work, 619 and Otto cycles, 680 Pythagorean theorem, 60, 643, 1254, A.21 Quadratic equations, 89, A.17 Quality factor (Q), 1051 Quantities basic vs derived, vector vs scalar, 26 Quantization, 553 of angular momentum, 352–353, 945 of electric charge, 708 of energy, 652–653 of standing-wave frequencies, 544, 553–555 Quantum mechanics, See also Mechanics and ferromagnetism, 949 history of, and magnetic dipole moments of atoms, 945–946 Quarks, 8, 9, 712 Quarter-wave plates, 1240 Quasi-static processes, 616 for an ideal gas, 686 Queckensted tests, 442 Quenching, 631 R values, 626–627t Radar, police, 525, 1278–1279 Radial acceleration component (ar), 94–96, 151–158, 298 Radial forces (Fr), 151–158, 312 Radian (rad), 293–294, A.20 Radiation, 628–629 See also Electromagnetic radiation Cerenkov, 539 cosmic background, 1088 and energy transfer, 197–198 thermal, 845–846 Radiation pressure (P ), 1076–1079 Radiators, 628 Radio, 813, 1051, 1061 waves, discovery of, 1068–1069 waves, in electromagntic spectrum, 1080–1081 Rail guns, 926, 964 Rainbow holograms, 1224 Rainbows, 1094, 1109–1111 Random-walk processes, 658 Range (R), horizontal, of a projectile, 86–91 Rarefaction, 515 Ray approximation, 1097–1098 Ray diagrams for mirrors, 1134–1136 for thin lenses, 1145–1149 Rayleigh, John William Strutt, Lord, 1233 Rayleigh’s criterion, 1214 Rays, 1069 gravitational deflection of light, 1273–1275 ordinary vs extraordinary, 1229–1230 paraxial, 1132 RC circuits, 873–878 as filters, 1055–1056 as rectifiers, 1054–1055 Reactance capacitive (XC ), 1042, 1056 inductive (XL ), 1040 Reaction forces, 120, 342 Reasonable values, Reber, Grote, 1235 Recoil, 255–256 Rectangular coordinate systems, 59 Rectangular coordinates See Cartesian coordinates Rectification, 1054 Rectifiers, 1054–1056 Red shifts, 525, 1262, 1274, 1279 Reference circles, 466 Reference frames inertial, 114–115, 1246 moving, 96–99, 496 noninertial or accelerating, 115, 159–162, 1258, 1273–1274 Reference intensity (I 0), 519 Reference lines, 293–294 Reflecting telescopes, 1162, 1164 Reflection, 499–501, 1069, 1098–1102 See also Mirrors and Huygens’s principle, 1108–1109 images formed by, 1127–1138 law of, 1099, 1108–1109, 1115 phase changes upon, 1188–1189 polarization by, 1227–1229 total internal, 1111–1114 Reflection gratings, 1217–1218 Reflections on the Motive Power of Heat [Carnot], 675 Refracting telescopes, 1162–1163 Refraction, 1069, 1102–1107 See also Lenses and Huygens’s principle, 1108–1109, 1178 images formed by, 1138–1141 index of, 1104t, 1124–1125 polarization by double, 1229–1230 Snell’s law of, 1105, 1108–1109, 1115 Refrigerators, 671–673, 672 Relative acceleration (aЈ), 96–99 Relative speed (vЈ), 522–523 Relative velocity (vЈ), 96–99 Relativity, Galilean, 98–99, 1246–1248 Relativity, general, 402, 1273–1275 See also Gravitation history of, 3, 1273 www.EngineeringEBooksPdf.com I.17 Relativity, special, 1, 1244–1283 consequences of, 1251–1262 history of, 3, 1243, 1245, 1250–1251 and Maxwell’s equations, 988 and spin, 945 and standard second, Resistance (R), 831–857 defined, 835–840, 836 equivalent (R eq), 863–868 internal (r ), 860 load (R), 860 temperature dependence of, 841, 843–844 Resistive forces (R), 162–167 See also Friction and automobiles, 205–206t Resistivity (), 836–837t, 842 temperature dependence of, 843–844 Resistors, 837–838 in AC circuits, 1034–1038 composition, 838 shunt (R p), 879 wire-wound, 838 Resolution, optical, 1214–1217, 1221–1222 Resolving power (R), 1221–1222 Resonance, 473, 558–559 in forced oscillators, 472–474 in LC circuits, 1016 in musical instruments, 558–562 in planetary motion, 399 in series RLC circuits, 1049–1051 Resonance frequency (0), 473, 558, 1049 Rest energy (ER ), 1270 Restoring forces, 191, 453 and pendulums, 468 and springs, 191–192, 453 Resultant force See Net force Resultant vectors (R), 61 Retardation plates, 1240 Retinas, 1155–1156 Retroreflection, 1100–1101 Revere, Paul, 1235 Reversible processes, 673–675 and entropy changes, 686–687 Richer, Jean, 140 Richter scale, 240–241 Right-hand rule, 295 and angular momentum, 340 and magnetic forces, 898, 905, 930 and vector (cross) products, 337–338 Rigid objects, 293 See also Deformable systems angular momentum of, 343–345 moment of inertia of, 300–305, 308–312 rolling of, 316–319 rotational dynamics of, 302–319 rotational kinematics of, 296–297 in static equilibrium, 366–373 I.18 Index Rings astronomical, 417 Newton’s, 1191–1192 Rowland, 949 Ripple, 1055 RL circuits, 1006–1011, 1007 rms See Root-mean-square Rocketry See Spacecraft Rods, eye, 1156 Roemer, Ole, 1096, 1118 Roentgen, Wilhelm, 1224 Rogowski coils, 993–994 Roller coasters, 157 Rolling motion, 316–319 Romognosi, Gian Dominico, 895 Root-mean-square electric current (I rms ), 1037 Root-mean-square speed (vrms), 645t, 656–657 Root-mean-square voltage (⌬Vrms), 1038 Rotational equilibrium, 363–364 Rotational motion, 292–335 dynamics of, 302–319 kinematics of, 296–297 kinetic energy (K R ) of, 300–302 reference frames for, 159–160 Rounding and significant figures, 15 Rowland rings, 949 Rutherford, Ernest, 790 S waves, 489 Saddle coils, 963 Sampling, digital, 530 Satellites See also Spacecraft attitude control of, 907 geosynchronous, 400–401, 407 Hubble Space Telescope, 394, 410 Solar and Heliospheric Observatory (SOHO), 416–417 Saturation, magnetic, 950 Saturn, 399t See also Planetary motion escape speed from, 408t rings of, 417 Savart, Félix, 927 Scalar product, 186–188, 741 Scalar quantities, 26, 60–61 Scattering, 1230 polarization by, 1230–1231 Schwarzschild radius (R S), 409 Science role of physics in, 3–4 Science fiction Heinlein, Robert, 416 Niven, Larry, 417 Turtledove, Harry, 596 Verne, Jules, 51, 1167 Scientific notation, A.14–A.15 and significant figures, 15 Scott, David, 40 Scrubbers, 783 SDDS See Sony Dynamic Digital Sound Search coils, 999 Second (s), 4–6, Second law of motion, 116–118, 117 and charged particles, 725 and linear wave equations, 503–504 relativistic, 1268 and rotational motion, 307–312, 340–342 and simple harmonic motion, 453–454 Second law of thermodynamics, 668–672 Clausius statement of, 671–672 Kelvin–Planck form of, 670 Secondary coils of AC transformers, 1051 and Faraday’s law of induction, 968–969 of Rowland rings, 949 Secondary maxima, 1187–1188 Seesaws, 344–345, 367 Seiches, 573 Self-inductance, 1004–1006 Semiconductors, 709, 844 charge carriers in, 915 Semimajor axis, 396 Semiminor axis, 396 Series combinations of capacitors, 804–806 of heat engines, 697 of resistors, 862–869 of springs, 211 Series expansions, mathematical, 1250, 1269, A.23 Seurat, Georges, 1235 Shadows, 1097 Shear modulus (S), 373–374t Shear strain, 374 Shear stress, 374 in fluids, 421 Shock waves, 527–528 Short circuits, 881–882 Shunt resistors (Rp), 879 SI system of units, 4–7, 118t, A.1t–A.3t, A.32t Side maxima, 1206 Sight See Eyes Significant figures, 15–16 Simple harmonic motion, 451–485, 454 See also Oscillatory motion; Periodic motion and energy, 462–465, 1017 mathematical representation of, 454–461 and restoring forces in springs, 191–192, 453 and sinusoidal waves, 491 and standing waves, 550, 553 vs uniform circular motion, 465–467 www.EngineeringEBooksPdf.com Simple pendulums, 468–469 Simultaneity, 1252–1253 Sine function, A.21 See also Trigonometric functions and components of vectors, 65, 83 and law of sines, 64, A.22 Sinusoidal waves, 491–496 rate of energy transfer by, 501–503 superposition of, 547–548 Skin effect, 999 Sky color, 1092, 1231 Slingshots, gravitational, 282 Slits diffraction of light waves from, 1207–1214 interference of light waves from, 1177–1184, 1186–1188, 1212–1213 Slopes of graphs, 28–29, 36, A.17 Slugs, 7, 118t Smokestacks, falling, 310, 329 Snell, Willebrord, 1105 Snell’s law of refraction, 1105 and Brewster’s law, 1228 from Fermat’s principle, 1115 from Huygens’s principle, 1108–1109 Soap, 816 Soap bubbles, 1191, 1194 Solar and Heliospheric Observatory (SOHO) [satellite], 416–417 Solar cells, 1193 Solar energy, 628, 1078–1079 Solar sailing, 1077, 1086 Solenoids, 938–940, 982, 1006 Solid angles (⌬⍀), 752 Solidification latent heat of, 611-612t Solids See also Materials science and bulk modulus, 375 crystalline vs amorphous, 1229 elastic properties of, 373–376 models for, 463–464 molar specific heat of, 653–654 speed of sound in, 514t thermal expansion of, 586–591 Sonic booms, 528 Sony Dynamic Digital Sound (SDDS), 533 Sound, 512–542 Doppler effect for, 522–528, 541 and energy transfer, 197, 516–522 intensity of, 516–522, 565 interference of, 548–549 and linear wave equations, 504 as longitudinal pressure waves, 488, 515–516 medium for, 487 recording of, 528–533 speed of, 513–514t, 665 Sound level (), 519–521, 520t Index Sound recording, 528–533 See also Audiovisual devices digital, 530–532 for movies, 532–533 and pickup coils, 971–972 synthesized, 568 Soundtracks, 532–533 Source charges, 715–716 Source particles, 402 Space shuttles See also Spacecraft Columbia, 0, 278 Endeavor, 394 shock waves from, 528 Space–time, curvature of, 1274–1275 Space–time coordinates (x, y, z, t),1263 Space–time graphs, 1259–1262 Spacecraft See also Satellites; Space shuttles Apollo 11, 1100, 1118–1119 Apollo 13, 412 Galileo, 389 and gyroscopes, 351 Mariner 10, 1077 and propulsion, 277–280 Voyager, 412 Voyager 2, 351 Spatial interference, 564 Special relativity See Relativity, special Specific heat (c), 607–611, 608t See also Heat capacity molar, at constant pressure (CP ), 646–649, 647t molar, at constant volume (CV ), 646–649, 647t, 651–652 Spectra atomic, 1222 electromagnetic, 1080–1082 visible, 1109 Spectrometers diffraction grating, 1219 mass, 911–912 Spectroscopy, 1195 atomic, 1220 Specular reflection, 1098–1099 Speed (v), 24–28, 79 average (vϪ), 27, 656–657 Ϫ), 293–296, 294 average angular ( and dimensional analysis, 11t distribution of molecular, 655–657 drift (vd ), 834, 841–842 escape (vesc ), 407–408t exhaust (ve ), 278 instantaneous (v), 28–30, 29 instantaneous angular (), 293–296, 294 most probable (vmp), 656–657 relative (vЈ), 522–523 root-mean-square (v rms ), 645t, 656–657 of sound waves, 513–514t, 665 terminal (vT ), 163, 165t transverse (vy ), 495 Speed (v)(Continued) units of, A.1t vs velocity, 27 of waves (v), 492–493 Speed of light (c), and electromagnetic waves, 988, 1069–1070 and ether, 1248–1250 and Lorentz transformation equations, 1265, 1268 in materials, 1103–1105 measurement of, 1096–1097 and Schwarzschild radius, 409 and special relativity, 1245, 1247–1248 Spherical aberration, 1132, 1152–1154, 1164 Spherical mirrors, 1131–1138 See also Mirrors Spherical waves, 518, 1069, 1098 and Doppler effect, 522–523 Spin, 945–946 Spin angular momentum (S), 946 Spinal taps, 442 Spirit-in-glass thermometers, 448 Spontaneity See also Entropy; Second law of thermodynamics of energy transfers by heat, 672 Sports acrobatics, 346 air hockey, 114 baseball, 79, 106, 437 basketball, 26, 103–104, 107 billiards, 267, 269–270 Bonds, Barry, 106 bowling, 251 bungee jumping, 242, 478 cycling, 72 discus, 103–104 diving, 336, 346 drag racing, 23, 144 Eldridge, Todd, 346 football, 113 Fosbury, Dick, 286 gasing, 292 golf, 436–437 high jumping, 241, 286 hockey, ice, 118 Johnson, Dave, 241 Lackey, John, 665 long jumping, 88 Matsushima, Akira, 72 merry-go-rounds, 159–160, 347–348 Muldowney, Shirley, 144 pole vaulting, 217 Powell, Mike, 88 rock climbing, 122 Ruiz, Mark, 336 skateboarding, 248, 358–359 skating, 346 ski jumping, 90–91, 108–109, 438 skiing, 232–233 www.EngineeringEBooksPdf.com I.19 Sports (Continued) sky diving, 165 sledding, 133 “the wave,” 509 Spring constant (k), 190 Springs potential energy in, 222–228 and simple harmonic motion, 453–454 torsional, 907 work done by, 190–193 Square waves, 568, 1058 Stable equilibrium, 236 Standards, of amount of substance, of electric current, of length, 4–5t of luminous intensity, of mass, 4–5t of temperature, of time, 4–6t Standing waves, 543–577, 550 in air columns, 559–562 electromagnetic, 1069 properties of, 549–552 and resonance, 558–559 in rods and membranes, 563–564 in strings fixed at both ends, 552–557 vs interference patterns, 1178 Stars See also Astronomy; Sun binary, 409 neutron, 347, 409 red shifts of, 525, 1262, 1274, 1279 white dwarf, 409, 415 State variables, 615, 618, 684–686 States of matter, 421, 604 See also Fluids; Gases; Liquids; Solids Static equilibrium, 364, 366–373 Statistical mechanics, 651, 654–657, 683 See also Entropy; Kinetic theory of gases Steady flow See Laminar flow Steady-state conditions of forced oscillators, 473 Steam burns, 613 Steam point of water, 583 Stefan’s law, 628–629 Steradian, 752–753 Stick-and-slip motion, 484 Stiffness of springs, 190 Stirling, Robert, 700 Stirling engines, 700 Strain, 373 shear, 374 tensile, 373 volume, 374–375 Stapp, Col John P., 52 Streamlines, 431 and airplane wings, 436 Stress, 373 optical analysis of, 1230 shear, 374, 421 I.20 Index Stress (Continued) tensile, 373, 421 volume, 374–375, 421 Strings and musical instruments, 543, 555–556, 561 rate of energy transfer by waves on, 501–503 reflection and transmission of waves on, 499–501 sinusoidal waves on, 494–496 speed of waves on, 496–499 standing waves on, 552–557 tension in, 488, 496–499 Stroboscopic photographs, 34–35 of motion of center of mass, 276 of standing waves, 550 Struts, 142 Strutt, John William, Lord Rayleigh, 1233 Stud-finders, 813 Subatomic physics, 1270, 1272, 1282–1283 Submerged objects, 428–430 Subtraction and significant figures, 15–16 and uncertainty, A.29 of vectors, 63–64 Sun, 399t See also Astronomy; Stars chromosphere of, 1200 escape speed from, 408t mass of, 399t, 400 radiation from, 628, 1078 Sunday Afternoon on the Island of La Grande Jatte [Seurat], 1235 Sunglasses, 1081, 1229 Sunsets, 1231 Sunspots, 639 Superconductors, 844–845 and Meissner effect, 952, 1031 resistance of, 1030–1031 Supernovae, 347, 409 Superposition, 544–549 of electric potentials, 769 of fields, 718–719, 744 of harmonics, 566–568 of sinusoidal waves, 547–548 Superposition principle, 544 for electric fields, 718–719, 744 for electromagnetic waves, 1071–1072 for gravitational forces, 404 Surface charge density (), 720, 779, 818 Surfactants, 816 Susceptibility, magnetic ( ), 947–948t Symbols for quantities, 11, A.2t–A.3t in circuits, 710 Synchrotrons, 913 Synthesizers, 568 System boundaries, 183 System models, 182 Système International (SI), Systems, 182–183 deformable, 346, 605 and entropy changes, 687 in equilibrium, 236–238 isolated, 196, 220–228, 221, 254 mechanical vs electrical, 1021t nonisolated, 196–199 of particles, angular momentum of, 341–343 of particles, motion of, 274–277 Tangent function, A.21 See also Trigonometric functions Tangential acceleration component (at ), 94–96, 298 Tangential forces (Ft ), 157–158, 312–313 Tangential velocity (v), 298 Tangents to curves, 28–29, 79 See also Derivatives Target of a projectile, 88 Technology See also Engineering role of physics in, 3–4 Telecommunications, 1114 See also Movies; Radio; Television and antennas, 1079–1080, 1133 Telescopes, 1162–1165 See also Hubble Space Telescope reflecting, 1162, 1164 refracting, 1162–1163 resolution of, 1217 Very Large Array, 1238 Television, 728, 765, 900, 1156–1157 Temperature (T ), 4, 580–603, 582 See also Heat; Internal energy critical (Tc), 844–845t Curie (TCurie), 951t and electric current, 834 and internal energy, 197 measurement of, 582–584 molecular interpretation of, 644–646 and resistance, 841, 843–844 as scalar quantity, 60 and speed of sound waves, 514 Temperature coefficient of resistivity (␣), 837t, 843, 855 Temperature gradient, 624 of the ocean, 697 Temperature scales absolute, 584–586, 585 Celsius, 583, 585–586, 610 Fahrenheit, 585–586 Kelvin, 585–586, 610 Temporal interference, 564–566 Tensile strain, 373 Tensile stress, 373 in fluids, 421 Tension (T ), 122 and conservation of mechanical energy, 225–226 www.EngineeringEBooksPdf.com Tension (T )(Continued) and speed of wave propagation, 488, 496–499, 554 Terminal speed (vT), 163, 165t Terminal voltage, 860–861 Tesla, Nikola, 1053 Tesla (T), 899 Test charges, 715–716 Test particles, 402 Thermal conduction, 197, 623–627 and entropy changes, 687–688 Thermal conductivity (k), 624t–625 Thermal contact, 581–582 Thermal efficiency (e), 670 of Carnot cycles (e C), 676–678 Curzon–Ahlborn (e C–A), 677 of diesel engines, 701 of ideal engines, 675–679 of Otto cycles, 680 of real engines, 675, 680–681 Thermal energy, 605 See also Internal energy Thermal equilibrium, 581–582 and state variables, 615 Thermal excitation, 655 Thermal expansion, 586 of solids and liquids, 586–591 and thermometers, 583 Thermal radiation, 845–846 Thermodynamic variables, 593 Thermodynamics, 1, 578–702 See also Entropy; Heat; Kinetic theory of gases; Laws of thermodynamics; Temperature Thermometers alcohol, 583–584 constant-volume gas, 584–586 mercury, 583–584 resistance, 843 spirit-in-glass, 448 Thermos bottles, 629 Thermostats, 589, 601 Thin films interference in, 1189–1194 Thin lens equation, 1143–1144 Third law of motion, 120–122 and rotational motion, 342 and universal gravitation, 391 Thompson, Benjamin, 607 Thomson, Joseph John, 8, 759, 912 Thomson, William, Lord Kelvin, 4, 585, 669 Thomson’s apparatus, 912 Thoreau, Henry David, 1117 Thought experiments for relativity of time, 1252–1253 for time dilation, 1257–1258 Threshold of hearing, 519–521 Threshold of pain, 519, 521 Thrust, 278–279 Tidal waves See Tsunamis Index Tides lunar, 417, 452 Timbre, 566 Time (t) and general relativity, 1274 relativity of, 1247, 1252–1253 standards of, 5–6t units of, A.1t Time constant () See also Half-life of RC circuits, 875–876 of RL circuits, 1008, 1010–1011 of terminal speeds, 163 Time dilation, 1253–1257, 1254 Tokamaks, 960 Toner, 784 Tops, 292, 327, 350–351 Toroids, 936 Torque (), 306–307 and angular acceleration, 307–312 and angular momentum, 340 on electric dipoles in electric fields, 815, 817, 905 on magnetic dipoles in magnetic fields, 879, 904–907 net (⌺), 363–365 and potential energy, 815 and rotational equilibrium, 363–364 and vector (cross) products, 337–339, 815 Torquers, 907 Torricelli, Evangelista, 426, 446 Torricelli’s law, 435–436 Torsion constant (), 470 Torsional balances, 393–394, 895, 1077 Torsional pendulums, 470 Total energy (E), 1270 Total force See Net force Total internal reflection, 1111–1114 Total kinetic energy See under Kinetic energy Transfer variables, 615 Transformers, 846–847, 1033, 1051–1054 and eddy currents, 987, 1051 and hysteresis, 1051 ideal, 1051 step-up vs step-down, 1051 Transistors, 838 Transmission, 499–501, 500 Transmission axis, 1226 Transmission gratings, 1217 Transportation See Aeronautics; Airplanes; Automobiles; Locomotives; Satellites; Space shuttles; Spacecraft Transverse acceleration (ay ), 495 Transverse speed (vy ), 495 Transverse waves, 488 Trigonometric functions, A.21–A.23 arguments of, 455 on calculators, 67 Trigonometric functions (Continued) and components of vectors, 65 identities for, 547, 550, 1037, 1039, 1041, 1048, 1183, A.21–A.22t and relation between Cartesian and polar coordinates, 59–60 and second-order differential equations, 455 small-angle approximations for, 351 Triple point of water, 585 Trusses, 372–373 Tsunamis, 511 Tube of flow, 431–432 Turbines, 983 Turbulence, 431 and airplane wings, 436 and irreversible processes, 674–675 Turning points, 236–237, 463 Turtledove, Harry, 596 Twin paradox, 1257–1259 Ultrasound, 536 Ultraviolet waves, 1081 Unbalanced force See Net force Unbound systems, 397, 406 Uncertainty, A.28–A.29 Underdamped oscillators, 471–472 Uniform circular motion, 91–93 See also Circular motion and second law of motion, 151–156 vs simple harmonic motion, 465–467 ˆ ), 66–70 Unit vectors (iˆ, ˆj , k and direction cosines, 213 and scalar (dot) products, 187–188 Units See also specific quantity conversion of, 12–13, A.1t–A.2t and dimensional analysis, 10–12, 11t engineering, 626 SI, 4–7, 118t, A.1t–A.3t, A.32t U.S customary, 7, 118t, 204, A.1t–A.2t Universal gas constant (R), 592–593 Universal gravitation See Gravitation Universal gravitational constant (G), 391 measurement of, 393–394 Universe expansion of, 1262 Unknowns, A.15 Unpolarized light, 1226 Unreasonable values, Unstable equilibrium, 237 Uranus, 399t See also Planetary motion escape speed from, 408t U.S customary system of units, Van Allen belts, 910 Van de Graaff, Robert J., 782 Van de Graaff generators, 782–783 Vaporization latent heat of, 611-612t www.EngineeringEBooksPdf.com I.21 Variable-area optical soundtracks, 532 Variables See Unknowns Vector product, 337–339 Vectors, 26, 58–76, 60–61 arithmetic properties of, 61–65, 66–67 components of, 65–70 coplanar, 364 in kinematics, 78–80 scalar (dot) product of, 186–188 unit, 66–70 vector (cross) product of, 337–339 Velocity (v), 24–28, 58 Ϫ), 26–27 average (v of center of mass (vCM), 274 and dimensional analysis, 11t Galilean transformation equation for, 1247 instantaneous (v), 28–30, 29 Lorentz transformation equations for, 1264–1267 and relationship to sign of acceleration, 35 relative (vЈ), 96–99 tangential (v), 298 vs speed, 27 Velocity selectors, 911 Velocity–time graphs, 31–34, 458–459 Velocity vectors (v), 78–80 Venturi tubes, 435 Venus, 399t See also Planetary motion escape speed from, 408t magnetic field of, 954 Verne, Jules, 51, 1167 Virtual objects, 1149 Viscosity, 163, 431 Viscous forces, 431 Visible spectrum, 1109 Vision See Eyes Void fractions, 599 Volt (V), 764 Voltage, 764 See also Potential difference breakdown, 812 Hall (⌬V H), 914 instantaneous (⌬v), 1034 open-circuit (), 860 root-mean-square (⌬V rms), 1038 terminal, 860–861 Voltage amplitude (⌬V max ), 1034 Voltage drops, 862 Voltmeters, 811, 879–880 Volume (V ) and dimensional analysis, 11t displacement, 681 of geometric shapes, A.20t Volume charge density (), 720 Volume expansion, average coefficient of (), 588t Volume flux, 432 Volume strain, 374–375 Volume stress, 374–375 See also Pressure in fluids, 421 I.22 Index “Vomit Comet,” 105–106 von Laue, Max, 1224 von Neumann, John, 1027 Voyager [spacecraft], 412 Voyager [spacecraft], 351 Walden [Thoreau], 1117 Washboarded roads, 482 Water, 604 density of, 590–591 diamagnetism of, 952 ice point of, 583 as polar molecule, 816–817 specific heat of, 608t, 609 steam point of, 583 triple point of, 585 Water waves, 450, 488–489 Watt, James, 204 Watt (W), 204 Wave equations linear, 503–504, 1070 Wave fronts, 522, 1069, 1097 Wave functions (y(x, t)), 490 Wave number (k), 493 Wave optics, 1176–1241 See also Diffraction; Geometric optics; Interference; Optics; Polarization Waveforms, 490 Wavelength (), 492 Wavelets, 1107 Waves, 486–511 See also Electromagnetic waves; Mechanical waves; Sound; Standing waves gravitational, 1195 linear, 544 longitudinal, 488 nonlinear, 544 plane, 1069 and propagation of a disturbance, 487–491 Waves (Continued) reflection and transmission of, 499–501 shock, 527–528 sinusoidal, 491–496, 547–548 speed of mechanical, 513–514 spherical, 518, 522–523, 1069, 1098 square, 568, 1058 transverse, 488 water, 450, 488–489 Weak forces, 113 Weber, Wilhelm, 959 Weber (Wb), 940 Weight, 119–120 vs mass, 116, 119 Welding, induction, 991 Wheelchairs, 371 Wheeler, John, 1274 White dwarf stars, 409, 415 White light, 1109–1110 Wilson, Robert, 1088 Windmills, 181, 195 Wiring, household, 880–882 Work (W ), 183–193, 184, 197 and Bernoulli’s equation, 434 by conductors moving in magnetic fields, 974 by a conservative force, 228–229, 403, 763–764 by a constant force, 183–186 on deformable systems, 605, 615–617 in electric fields, 726, 763–764, 807, 815–817 and electric generators, 982 and energy transfer, 185, 193–201 and forced oscillators, 472 on a gas, 615–617 by gravity, 196 in magnetic fields, 934 and motors, 984–985 net (⌺W ), 189, 619, 670 path dependence of, 229, 616–617 www.EngineeringEBooksPdf.com Work (W )(Continued) and rotational motion, 312–316 by a spring, 190–193 in thermodynamic processes, 615–617 units of, 185, A.2t by a varying force, 188–193 Work–kinetic energy theorem, 193–196, 194 and charged particles in electric fields, 726 and charged particles in magnetic fields, 899 relativistic, 1268–1269 for rotational motion, 301, 312–313 World-lines, 1259–1260 X-rays, 1081 from black holes, 409–410 diffraction of by crystals, 1224–1225 Xerography, 784 y-intercepts, A.17 Yard (yd), Yerkes Observatory, 1165 Young, Thomas, 1093, 1095, 1178 Young’s double-slit experiment, 1177–1182 Young’s modulus (Y ), 373–374t and speed of sound waves, 514 Zero-gravity simulations, 105–106 Zero-point energy, 585 Zeros and significant figures, 15 Zeroth law of thermodynamics, 581–582 Zeroth-order maxima, 1180 Zonules, eye, 1156 Zoom lenses, 1172 Some Physical Constantsa Quantity Symbol Valueb Atomic mass unit u Avogadro’s number NA 1.660 538 73 (13) ϫ 10Ϫ27 kg 931.494 013 (37) MeV/c 6.022 141 99 (47) ϫ 1023 particles/mol Deuteron mass eប 2me ប2 a0 ϭ m e e ke R kB ϭ NA h C ϭ m ec ke ϭ ⑀0 md Electron mass me Electron volt Elementary charge Gas constant Gravitational constant eV e R G 2e h Bohr magneton Bohr radius Boltzmann’s constant Compton wavelength Coulomb constant Josephson frequency – voltage ratio B ϭ ⌽0 ϭ Nuclear magneton n ϭ Permeability of free space 0 Permittivity of free space Planck’s constant ⑀0 ϭ h 2e Proton mass mp Rydberg constant Speed of light in vacuum RH c 1.380 650 (24) ϫ 10Ϫ23 J/K 2.426 310 215 (18) ϫ 10Ϫ12 m 8.987 551 788 ϫ 109 N иm2/C2 (exact) 3.343 583 09 (26) ϫ 10Ϫ27 kg 2.013 553 212 71 (35) u 9.109 381 88 (72) ϫ 10Ϫ31 kg 5.485 799 110 (12) ϫ 10Ϫ4 u 0.510 998 902 (21) MeV/c 1.602 176 462 (63) ϫ 10Ϫ19 J 1.602 176 462 (63) ϫ 10Ϫ19 C 8.314 472 (15) J/K иmol 6.673 (10) ϫ 10Ϫ11 N иm2/kg2 2.067 833 636 (81) ϫ 10Ϫ15 T иm2 1.674 927 16 (13) ϫ 10Ϫ27 kg 1.008 664 915 78 (55) u 939.565 330 (38) MeV/c mn បϭ 5.291 772 083 (19) ϫ 10Ϫ11 m 4.835 978 98 (19) ϫ 1014 Hz/V Magnetic flux quantum Neutron mass h 9.274 008 99 (37) ϫ 10Ϫ24 J/T eប 2mp 5.050 783 17 (20) ϫ 10Ϫ27 J/T 4 ϫ 10Ϫ7 T иm/A (exact) 0c h 2 8.854 187 817 ϫ 10Ϫ12 C2/N иm2 (exact) 6.626 068 76 (52) ϫ 10Ϫ34 J иs 1.054 571 596 (82) ϫ 10Ϫ34 J иs 1.672 621 58 (13) ϫ 10Ϫ27 kg 1.007 276 466 88 (13) u 938.271 998 (38) MeV/c 1.097 373 156 854 (83) ϫ 107 mϪ1 2.997 924 58 ϫ 108 m/s (exact) a These constants are the values recommended in 1998 by CODATA, based on a least-squares adjustment of data from different measurements For a more complete list, see P J Mohr and B N Taylor, Rev Mod Phys 72:351, 2000 b The numbers in parentheses for the values above represent the uncertainties of the last two digits www.EngineeringEBooksPdf.com Solar System Data Body Mass (kg) Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Moon Sun 3.18 4.88 5.98 6.42 1.90 5.68 8.68 1.03 Ϸ1.4 7.36 1.991 ϫ ϫ ϫ ϫ ϫ ϫ ϫ ϫ ϫ ϫ ϫ Mean Radius (m) 1023 1024 1024 1023 1027 1026 1025 1026 1022 1022 1030 2.43 6.06 6.37 3.37 6.99 5.85 2.33 2.21 Ϸ1.5 1.74 6.96 ϫ ϫ ϫ ϫ ϫ ϫ ϫ ϫ ϫ ϫ ϫ 106 106 106 106 107 107 107 107 106 106 108 Period (s) 7.60 ϫ 1.94 ϫ 3.156 ϫ 5.94 ϫ 3.74 ϫ 9.35 ϫ 2.64 ϫ 5.22 ϫ 7.82 ϫ — — 106 107 107 107 108 108 109 109 109 Distance from the Sun (m) 5.79 ϫ 1.08 ϫ 1.496 ϫ 2.28 ϫ 7.78 ϫ 1.43 ϫ 2.87 ϫ 4.50 ϫ 5.91 ϫ — — 1010 1011 1011 1011 1011 1012 1012 1012 1012 Physical Data Often Useda 3.84 ϫ 108 m 1.496 ϫ 1011 m 6.37 ϫ 106 m 1.20 kg/m3 1.00 ϫ 103 kg/m3 9.80 m/s2 5.98 ϫ 1024 kg 7.36 ϫ 1022 kg 1.99 ϫ 1030 kg 1.013 ϫ 105 Pa Average Earth–Moon distance Average Earth–Sun distance Average radius of the Earth Density of air (20°C and atm) Density of water (20°C and atm) Free-fall acceleration Mass of the Earth Mass of the Moon Mass of the Sun Standard atmospheric pressure a These are the values of the constants as used in the text Some Prefixes for Powers of Ten Power Prefix Abbreviation Power Prefix Abbreviation 10Ϫ24 10Ϫ21 10Ϫ18 10Ϫ15 10Ϫ12 10Ϫ9 10Ϫ6 10Ϫ3 10Ϫ2 10Ϫ1 yocto zepto atto femto pico nano micro milli centi deci y z a f p n m c d 101 102 103 106 109 1012 1015 1018 1021 1024 deka hecto kilo mega giga tera peta exa zetta yotta da h k M G T P E Z Y www.EngineeringEBooksPdf.com Standard Abbreviations and Symbols for Units Symbol Unit Symbol Unit A u atm Btu C °C cal d eV °F F ft G g H h hp Hz in J ampere atomic mass unit atmosphere British thermal unit coulomb degree Celsius calorie day electron volt degree Fahrenheit farad foot gauss gram henry hour horsepower hertz inch joule K kg kmol L lb ly m mol N Pa rad rev s T V W Wb yr ⍀ kelvin kilogram kilomole liter pound lightyear meter minute mole newton pascal radian revolution second tesla volt watt weber year ohm Mathematical Symbols Used in the Text and Their Meaning Symbol Meaning ϭ ϵ is equal to is defined as is not equal to is proportional to is on the order of is greater than is less than is much greater (less) than is approximately equal to the change in x ϰ ϳ Ͼ Ͻ ϾϾ(ϽϽ) Ϸ ⌬x N ͚ xi iϭ the sum of all quantities xi from i ϭ to i ϭ N ͉x͉ ⌬x : dx dt Ѩx Ѩt the magnitude of x (always a nonnegative quantity) ⌬x approaches zero ͵ the derivative of x with respect to t the partial derivative of x with respect to t integral www.EngineeringEBooksPdf.com Conversionsa Length in ϭ 2.54 cm (exact) m ϭ 39.37 in ϭ 3.281 ft ft ϭ 0.304 m 12 in ϭ ft ft ϭ yd yd ϭ 0.914 m km ϭ 0.621 mi mi ϭ 1.609 km mi ϭ 280 ft m ϭ 10Ϫ6 m ϭ 103 nm lightyear ϭ 9.461 ϫ 1015 m Force N ϭ 0.224 lb lb ϭ 4.448 N Velocity mi/h ϭ 1.47 ft/s ϭ 0.447 m/s ϭ 1.61 km/h m/s ϭ 100 cm/s ϭ 3.281 ft/s mi/min ϭ 60 mi/h ϭ 88 ft/s Acceleration m/s2 ϭ 3.28 ft/s2 ϭ 100 cm/s2 ft/s2 ϭ 0.304 m/s2 ϭ 30.48 cm/s2 Pressure bar ϭ 105 N/m2 ϭ 14.50 lb/in.2 atm ϭ 760 mm Hg ϭ 76.0 cm Hg atm ϭ 14.7 lb/in.2 ϭ 1.013 ϫ 105 N/m2 Pa ϭ N/m2 ϭ 1.45 ϫ 10Ϫ4 lb/in.2 Area m2 ϭ 104 cm2 ϭ 10.76 ft2 ft2 ϭ 0.092 m2 ϭ 144 in.2 in.2 ϭ 6.452 cm2 Volume m3 ϭ 106 cm3 ϭ 6.102 ϫ 104 in.3 ft3 ϭ 728 in.3 ϭ 2.83 ϫ 10Ϫ2 m3 L ϭ 000 cm3 ϭ 1.057 qt ϭ 0.035 ft3 ft3 ϭ 7.481 gal ϭ 28.32 L ϭ 2.832 ϫ 10Ϫ2 m3 gal ϭ 3.786 L ϭ 231 in.3 Mass 000 kg ϭ t (metric ton) slug ϭ 14.59 kg u ϭ 1.66 ϫ 10Ϫ27 kg ϭ 931.5 MeV/c Time yr ϭ 365 days ϭ 3.16 ϫ 107 s day ϭ 24 h ϭ 1.44 ϫ 103 ϭ 8.64 ϫ 104 s Energy J ϭ 0.738 ft иlb cal ϭ 4.186 J Btu ϭ 252 cal ϭ 1.054 ϫ 103 J eV ϭ 1.6 ϫ 10Ϫ19 J kWh ϭ 3.60 ϫ 106 J Power hp ϭ 550 ft иlb/s ϭ 0.746 kW W ϭ J/s ϭ 0.738 ft иlb/s Btu/h ϭ 0.293 W Some Approximations Useful for Estimation Problems m Ϸ yd kg Ϸ lb 1 N Ϸ lb m/s Ϸ mi/h yr Ϸ ϫ 107 s 60 mi/h Ϸ 100 ft/s 1 L Ϸ gal a km Ϸ mi See Table A.1 of Appendix A for a more complete list The Greek Alphabet Alpha Beta Gamma Delta Epsilon Zeta Eta Theta 〈 〉 ⌫ ⌬ ⌭ ⌮ H ⍜ ␣  ␥ ␦ ⑀ Iota Kappa Lambda Mu Nu Xi Omicron Pi ⌱ ⌲ ⌳ ⌴ ⌵ ⌶ ⌷ ⌸ www.EngineeringEBooksPdf.com Rho Sigma Tau Upsilon Phi Chi Psi Omega ⌹ ⌺ ⌻ ⌼ ⌽ ⌾ ⌿ ⍀ Pedagogical Color Chart Part (Chapters 1–15) : Mechanics Displacement and position vectors Linear ( p) and angular (L) momentum vectors Linear (v) and angular (ω ) velocity vectors Velocity component vectors Torque vectors (τ ) Linear or rotational motion directions Force vectors (F) Force component vectors Springs Pulleys Acceleration vectors (a) Acceleration component vectors Part (Chapters 23–34) : Electricity and Magnetism Electric fields Capacitors Magnetic fields Inductors (coils) Positive charges + Voltmeters V Negative charges – Ammeters A AC Generators Resistors Batteries and other DC power supplies – + Ground symbol Switches Part (Chapters 35–38) : Light and Optics Light rays Objects Lenses and prisms Images Mirrors www.EngineeringEBooksPdf.com ... 2004; 6th Edition This best-selling, calculus-based text is recognized for its carefully crafted, logical presentation of the basic concepts and principles of physics PHYSICS FOR SCIENTISTS AND ENGINEERS, ... y, and z (for position), r (for radius), a, b, and c (for the legs of a right triangle), ᐉ (for the length of an object), d (for a distance), h (for a height), etc C H A P T E R • Physics and. .. Superposition and Standing Waves Superposition and Interference Standing Waves Standing Waves in a String Fixed at Both Ends Resonance Standing Waves in Air Columns Standing Waves in Rods and Membranes