BibliotecaCollege Physics SumárioPreface1Introduction: The Nature of Science and PhysicsIntroduction to Science and the Realm of Physics, Physical Quantities, and Units1.1Physics: An Introduction1.2Physical Quantities and Units1.3Accuracy, Precision, and Significant Figures1.4ApproximationGlossarySection SummaryConceptual QuestionsProblems & Exercises2KinematicsIntroduction to One-Dimensional Kinematics2.1Displacement2.2Vectors, Scalars, and Coordinate Systems2.3Time, Velocity, and Speed2.4Acceleration2.5Motion Equations for Constant Acceleration in One Dimension3Two-Dimensional KinematicsIntroduction to Two-Dimensional Kinematics3.1Kinematics in Two Dimensions: An Introduction3.2Vector Addition and Subtraction: Graphical Methods3.3Vector Addition and Subtraction: Analytical Methods3.4Projectile Motion3.5Addition of Velocities4Dynamics: Force and Newton's Laws of MotionIntroduction to Dynamics: Newton’s Laws of Motion4.1Development of Force Concept4.2Newton’s First Law of Motion: Inertia4.3Newton’s Second Law of Motion: Concept of a System4.4Newton’s Third Law of Motion: Symmetry in Forces4.5Normal, Tension, and Other Examples of Forces5Further Applications of Newton's Laws: Friction, Drag, and ElasticityIntroduction: Further Applications of Newton’s Laws5.1Friction5.2Drag Forces5.3Elasticity: Stress and StrainGlossarySection SummaryConceptual Questions6Uniform Circular Motion and GravitationIntroduction to Uniform Circular Motion and Gravitation6.1Rotation Angle and Angular Velocity6.2Centripetal Acceleration6.3Centripetal Force6.4Fictitious Forces and Non-inertial Frames: The Coriolis Force6.5Newton’s Universal Law of Gravitation7Work, Energy, and Energy ResourcesIntroduction to Work, Energy, and Energy Resources7.1Work: The Scientific Definition7.2Kinetic Energy and the Work-Energy Theorem7.3Gravitational Potential Energy7.4Conservative Forces and Potential Energy7.5Nonconservative Forces8Linear Momentum and CollisionsIntroduction to Linear Momentum and Collisions8.1Linear Momentum and Force8.2Impulse8.3Conservation of Momentum8.4Elastic Collisions in One Dimension8.5Inelastic Collisions in One Dimension9Statics and TorqueIntroduction to Statics and Torque9.1The First Condition for Equilibrium9.2The Second Condition for Equilibrium9.3Stability9.4Applications of Statics, Including Problem-Solving Strategies9.5Simple Machines10Rotational Motion and Angular MomentumIntroduction to Rotational Motion and Angular Momentum10.1Angular Acceleration10.2Kinematics of Rotational Motion10.3Dynamics of Rotational Motion: Rotational Inertia10.4Rotational Kinetic Energy: Work and Energy Revisited10.5Angular Momentum and Its Conservation11Fluid StaticsIntroduction to Fluid Statics11.1What Is a Fluid?11.2Density11.3Pressure11.4Variation of Pressure with Depth in a Fluid11.5Pascal’s Principle11.6Gauge Pressure, Absolute Pressure, and Pressure Measurement12Fluid Dynamics and Its Biological and Medical ApplicationsIntroduction to Fluid Dynamics and Its Biological and Medical Applications12.1Flow Rate and Its Relation to Velocity12.2Bernoulli’s Equation12.3The Most General Applications of Bernoulli’s Equation12.4Viscosity and Laminar Flow; Poiseuille’s Law12.5The Onset of Turbulence13Temperature, Kinetic Theory, and the Gas LawsIntroduction to Temperature, Kinetic Theory, and the Gas Laws13.1Temperature13.2Thermal Expansion of Solids and Liquids13.3The Ideal Gas Law13.4Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature13.5Phase Changes14Heat and Heat Transfer MethodsIntroduction to Heat and Heat Transfer Methods14.1Heat14.2Temperature Change and Heat Capacity14.3Phase Change and Latent Heat14.4Heat Transfer Methods14.5Conduction14.615ThermodynamicsIntroduction to Thermodynamics15.1The First Law of Thermodynamics15.2The First Law of Thermodynamics and Some Simple Processes15.3Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency15.4Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated15.5Applications of Thermodynamics: Heat Pumps and Refrigerators16Oscillatory Motion and WavesIntroduction to Oscillatory Motion and Waves16.1Hooke’s Law: Stress and Strain Revisited16.2Period and Frequency in Oscillations16.3Simple Harmonic Motion: A Special Periodic Motion16.4The Simple Pendulum16.5Energy and the Simple Harmonic Oscillator17Physics of HearingIntroduction to the Physics of Hearing17.1Sound17.2Speed of Sound, Frequency, and Wavelength17.3Sound Intensity and Sound Level17.4Doppler Effect and Sonic Booms17.5Sound Interference and Resonance: Standing Waves in Air Columns18Electric Charge and Electric FieldIntroduction to Electric Charge and Electric Field18.1Static Electricity and Charge: Conservation of Charge18.2Conductors and Insulators18.3Coulomb’s Law18.4Electric Field: Concept of a Field Revisited18.5Electric Field Lines: Multiple Charges19Electric Potential and Electric FieldIntroduction to Electric Potential and Electric Energy19.1Electric Potential Energy: Potential Difference19.2Electric Potential in a Uniform Electric Field19.3Electrical Potential Due to a Point Charge19.4Equipotential Lines19.5Capacitors and Dielectrics20Electric Current, Resistance, and Ohm's LawIntroduction to Electric Current, Resistance, and Ohm's Law20.1Current20.2Ohm’s Law: Resistance and Simple Circuits20.3Resistance and Resistivity20.4Electric Power and Energy20.5Alternating Current versus Direct Current21Circuits and DC InstrumentsIntroduction to Circuits and DC Instruments21.1Resistors in Series and Parallel21.2Electromotive Force: Terminal Voltage21.3Kirchhoff’s Rules21.4DC Voltmeters and Ammeters21.5Null Measurements22MagnetismIntroduction to Magnetism22.1Magnets22.2Ferromagnets and Electromagnets22.3Magnetic Fields and Magnetic Field Lines22.4Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field22.5Force on a Moving Charge in a Magnetic Field: Examples and Applications23Electromagnetic Induction, AC Circuits, and Electrical TechnologiesIntroduction to Electromagnetic Induction, AC Circuits and Electrical Technologies23.1Induced Emf and Magnetic Flux23.2Faraday’s Law of Induction: Lenz’s Law23.3Motional Emf23.4Eddy Currents and Magnetic Damping23.5Electric Generators24Electromagnetic WavesIntroduction to Electromagnetic Waves24.1Maxwell’s Equations: Electromagnetic Waves Predicted and Observed24.2Production of Electromagnetic Waves24.3The Electromagnetic Spectrum24.4Energy in Electromagnetic WavesGlossary25Geometric OpticsIntroduction to Geometric Optics25.1The Ray Aspect of Light25.2The Law of Reflection25.3The Law of Refraction25.4Total Internal Reflection25.5Dispersion: The Rainbow and Prisms25.626Vision and Optical InstrumentsIntroduction to Vision and Optical Instruments26.1Physics of the Eye26.2Vision Correction26.3Color and Color Vision26.4Microscopes26.5Telescopes26.6Aberrations27Wave OpticsIntroduction to Wave Optics27.1The Wave Aspect of Light: Interference27.2Huygens's Principle: Diffraction27.3Young’s Double Slit Experiment27.4Multiple Slit Diffraction27.5Single Slit Diffraction28Special RelativityIntroduction to Special Relativity28.1Einstein’s Postulates28.2Simultaneity And Time Dilation28.3Length Contraction28.4Relativistic Addition of Velocities28.5Relativistic Momentum28.629Quantum PhysicsIntroduction to Quantum Physics29.1Quantization of Energy29.2The Photoelectric Effect29.3Photon Energies and the Electromagnetic Spectrum29.4Photon Momentum29.5The Particle-Wave Duality30Atomic PhysicsIntroduction to Atomic Physics30.1Discovery of the Atom30.2Discovery of the Parts of the Atom: Electrons and Nuclei30.3Bohr’s Theory of the Hydrogen Atom30.4X Rays: Atomic Origins and Applications30.5Applications of Atomic Excitations and De-Excitations31Radioactivity and Nuclear PhysicsIntroduction to Radioactivity and Nuclear Physics31.1Nuclear Radioactivity31.2Radiation Detection and Detectors31.3Substructure of the Nucleus31.4Nuclear Decay and Conservation Laws31.5Half-Life and Activity32Medical Applications of Nuclear PhysicsIntroduction to Applications of Nuclear Physics32.1Medical Imaging and Diagnostics32.2Biological Effects of Ionizing Radiation32.3Therapeutic Uses of Ionizing Radiation32.4Food Irradiation32.5Fusion33Particle PhysicsIntroduction to Particle Physics33.1The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited33.2The Four Basic Forces33.3Accelerators Create Matter from Energy33.4Particles, Patterns, and Conservation Laws33.5Quarks: Is That All There Is?34Frontiers of PhysicsIntroduction to Frontiers of Physics34.1Cosmology and Particle Physics34.2General Relativity and Quantum Gravity34.3Superstrings34.4Dark Matter and Closure34.5Complexity and ChaosAAtomic MassesBSelected Radioactive IsotopesCUseful InformationDGlossary of Key Symbols and NotationIndexCUseful Information Appendix C Useful Information This appendix is broken into several tables. Table C1, Important Constants Table C2, Submicroscopic Masses Table C3, Solar System Data Table C4, Metric Prefixes for Powers of Ten and Their Symbols Table C5, The Greek Alphabet Table C6, SI units Table C7, Selected British Units Table C8, Other Units Table C9, Useful Formulae Symbol Meaning Best Value Approximate Value c c size 12{c} {} Speed of light in vacuum 2 . 99792458 × 10 8 m / s 2 . 99792458 × 10 8 m / s size 12{2 "." "99792458" times "10" rSup { size 8{8} } ` {m} slash {s} } {} 3 . 00 × 10 8 m / s 3 . 00 × 10 8 m / s size 12{3 "." "00" times "10" rSup { size 8{8} } ` {m} slash {s} } {} G G size 12{G} {} Gravitational constant 6 . 67408 ( 31 ) × 10 − 11 N ⋅ m 2 / kg 2 6 . 67408 ( 31 ) × 10 − 11 N ⋅ m 2 / kg 2 size 12{6 "." "67384" \( "80" \) times "10" rSup { size 8{ - "11"} } ` {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {} 6 . 67 × 10 − 11 N ⋅ m 2 / kg 2 6 . 67 × 10 − 11 N ⋅ m 2 / kg 2 size 12{6 "." "67" times "10" rSup { size 8{ - "11"} } ` {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {} N A N A size 12{N rSub { size 8{A} } } {} Avogadro’s number 6.02214076 × 10 23 6.02214076 × 10 23 size 12{6 "." "02214129" \( "27" \) times "10" rSup { size 8{"23"} } } {} 6 . 02 × 10 23 6 . 02 × 10 23 size 12{6 "." "02" times "10" rSup { size 8{"23"} } } {} k k size 12{k} {} Boltzmann’s constant 1.380649 × 10 − 23 J / K 1.380649 × 10 − 23 J / K size 12{1 "." "3806488" \( "13" \) times "10" rSup { size 8{ - "23"} } ` {J} slash {K} } {} 1 . 38 × 10 − 23 J / K 1 . 38 × 10 − 23 J / K size 12{1 "." "38" times "10" rSup { size 8{ - "23"} } ` {J} slash {K} } {} R R size 12{R} {} Gas constant 8.3144621 ( 75 ) J / mol ⋅ K 8.3144621 ( 75 ) J / mol ⋅ K size 12{8 "." "3144621" \( "75" \) ` {J} slash {"mol" cdot K} } {} 8.31 J/mol ⋅ K = 1.99 cal/mol ⋅ K = 0.0821 atm ⋅ L/mol ⋅ K 8.31 J/mol ⋅ K = 1.99 cal/mol ⋅ K = 0.0821 atm ⋅ L/mol ⋅ K size 12{8 "." "31"` {J} slash {"mol" cdot K=1 "." "99"` {"cal"} slash {"mol" cdot K=0 "." "0821"` {"atm" cdot L} slash {"mol" cdot K} } } } {} σ σ size 12{σ} {} Stefan-Boltzmann constant 5 . 670373 ( 21 ) × 10 − 8 W / m 2 ⋅ K 5 . 670373 ( 21 ) × 10 − 8 W / m 2 ⋅ K size 12{5 "." "670373" \( "21" \) times "10" rSup { size 8{ - 8} } ` {W} slash {m rSup { size 8{2} } cdot K} } {} 5 . 67 × 10 − 8 W / m 2 ⋅ K 5 . 67 × 10 − 8 W / m 2 ⋅ K size 12{5 "." "67" times "10" rSup { size 8{ - 8} } ` {W} slash {m rSup { size 8{2} } cdot K} } {} k k size 12{k} {} Coulomb force constant 8 . 987551788 . . . × 10 9 N ⋅ m 2 / C 2 8 . 987551788 . . . × 10 9 N ⋅ m 2 / C 2 size 12{8 "." "987551788" "." "." "." `` times "10" rSup { size 8{9} } ` {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {} 8.99 × 10 9 N ⋅ m 2 / C 2 8.99 × 10 9 N ⋅ m 2 / C 2 size 12{9 times "10" rSup { size 8{9} } ` {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {} q e q e size 12{q rSub { size 8{e} } } {} Charge on electron − 1.602176634 × 10 − 19 C − 1.602176634 × 10 − 19 C size 12{ - 1 "." "602176565" \( "35" \) times "10" rSup { size 8{ - "19"} } `C} {} − 1 . 60 × 10 − 19 C − 1 . 60 × 10 − 19 C size 12{ - 1 "." "60" times "10" rSup { size 8{ - "19"} } `C} {} ε 0 ε 0 size 12{ε rSub { size 8{0} } } {} Permittivity of free space 8 . 854187817 . . . × 10 − 12 C 2 / N ⋅ m 2 8 . 854187817 . . . × 10 − 12 C 2 / N ⋅ m 2 size 12{8 "." "854187817" "." "." "." `` times "10" rSup { size 8{ - "12"} } ` {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {} 8 . 85 × 10 − 12 C 2 / N ⋅ m 2 8 . 85 × 10 − 12 C 2 / N ⋅ m 2 size 12{8 "." "85" times "10" rSup { size 8{ - "12"} } ` {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {} μ 0 μ 0 size 12{μ rSub { size 8{0} } } {} Permeability of free space 4π × 10 − 7 T ⋅ m / A 4π × 10 − 7 T ⋅ m / A size 12{4π times "10" rSup { size 8{ - 7} } ` {T cdot m} slash {A} } {} 1 . 26 × 10 − 6 T ⋅ m / A 1 . 26 × 10 − 6 T ⋅ m / A size 12{1 "." "26" times "10" rSup { size 8{ - 6} } ` {T cdot m} slash {A} } {} h h size 12{h} {} Planck’s constant 6.62607015 × 10 − 34 J ⋅ s 6.62607015 × 10 − 34 J ⋅ s size 12{6 "." "62606957" \( "29" \) times "10" rSup { size 8{ - "34"} } `J cdot s} {} 6 . 63 × 10 − 34 J ⋅ s 6 . 63 × 10 − 34 J ⋅ s size 12{6 "." "63" times "10" rSup { size 8{ - "34"} } `J cdot s} {} Table C1 Important Constants 1 1 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined. Symbol Meaning Best Value Approximate Value m e m e size 12{m rSub { size 8{e} } } {} Electron mass 9 . 10938291 ( 40 ) × 10 − 31 kg 9 . 10938291 ( 40 ) × 10 − 31 kg size 12{9 "." "10938291" \( "40" \) times "10" rSup { size 8{ - "31"} } `"kg"} {} 9 . 11 × 10 − 31 kg 9 . 11 × 10 − 31 kg size 12{9 "." "11" times "10" rSup { size 8{ - "31"} } `"kg"} {} m p m p size 12{m rSub { size 8{p} } } {} Proton mass 1 . 672621777 ( 74 ) × 10 − 27 kg 1 . 672621777 ( 74 ) × 10 − 27 kg size 12{1 "." "672621777" \( "74" \) times "10" rSup { size 8{ - "27"} } `"kg"} {} 1 . 6726 × 10 − 27 kg 1 . 6726 × 10 − 27 kg size 12{1 "." "6726" times "10" rSup { size 8{ - "27"} } `"kg"} {} m n m n size 12{m rSub { size 8{n} } } {} Neutron mass 1 . 674927351 ( 74 ) × 10 − 27 kg 1 . 674927351 ( 74 ) × 10 − 27 kg size 12{1 "." "674927351" \( "74" \) times "10" rSup { size 8{ - "27"} } `"kg"} {} 1 . 6749 × 10 − 27 kg 1 . 6749 × 10 − 27 kg size 12{1 "." "6749" times "10" rSup { size 8{ - "27"} } `"kg"} {} u u size 12{u} {} Atomic mass unit 1 . 660538921 ( 73 ) × 10 − 27 kg 1 . 660538921 ( 73 ) × 10 − 27 kg size 12{1 "." "660538921" \( "73" \) times "10" rSup { size 8{ - "27"} } `"kg"} {} 1 . 6605 × 10 − 27 kg 1 . 6605 × 10 − 27 kg size 12{1 "." "6605" times "10" rSup { size 8{ - "27"} } `"kg"} {} Table C2 Submicroscopic Masses 2 2 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined. Sun mass 1 . 99 × 10 30 kg 1 . 99 × 10 30 kg size 12{1 "." "99" times "10" rSup { size 8{"30"} } `"kg"} {} average radius 6 . 96 × 10 8 m 6 . 96 × 10 8 m size 12{6 "." "96" times "10" rSup { size 8{8} } `m} {} Earth-sun distance (average) 1 . 496 × 10 11 m 1 . 496 × 10 11 m size 12{1 "." "496" times "10" rSup { size 8{"11"} } " m"} {} Earth mass 5 . 9736 × 10 24 kg 5 . 9736 × 10 24 kg size 12{5 "." "9736" times "10" rSup { size 8{"24"} } `"kg"} {} average radius 6 . 376 × 10 6 m 6 . 376 × 10 6 m size 12{6 "." "376" times "10" rSup { size 8{6} } `m} {} {} orbital period 3 . 16 × 10 7 s 3 . 16 × 10 7 s size 12{3 "." "16" times "10" rSup { size 8{7} } " s "} {} Moon mass 7 . 35 × 10 22 kg 7 . 35 × 10 22 kg size 12{7 "." "35" times "10" rSup { size 8{"22"} } `"kg"} {} average radius 1 . 74 × 10 6 m 1 . 74 × 10 6 m size 12{1 "." "74" times "10" rSup { size 8{6} } `m} {} orbital period (average) 2 . 36 × 10 6 s 2 . 36 × 10 6 s size 12{2 "." "36" times "10" rSup { size 8{6} } " s"} {} Earth-moon distance (average) 3 . 84 × 10 8 m 3 . 84 × 10 8 m size 12{3 "." "84" times "10" rSup { size 8{8} } " m"} {} Table C3 Solar System Data Prefix Symbol Value Prefix Symbol Value tera T 10 12 10 12 size 12{"10" rSup { size 8{"12"} } } {} deci d 10 − 1 10 − 1 size 12{"10" rSup { size 8{ - 1} } } {} giga G 10 9 10 9 size 12{"10" rSup { size 8{9} } } {} centi c 10 − 2 10 − 2 size 12{"10" rSup { size 8{ - 2} } } {} mega M 10 6 10 6 size 12{"10" rSup { size 8{6} } } {} milli m 10 − 3 10 − 3 size 12{"10" rSup { size 8{ - 3} } } {} kilo k 10 3 10 3 size 12{"10" rSup { size 8{3} } } {} micro μ μ size 12{μ} {} 10 − 6 10 − 6 size 12{"10" rSup { size 8{ - 6} } } {} hecto h 10 2 10 2 size 12{"10" rSup { size 8{2} } } {} nano n 10 − 9 10 − 9 size 12{"10" rSup { size 8{ - 9} } } {} deka da 10 1 10 1 size 12{"10" rSup { size 8{1} } } {} pico p 10 − 12 10 − 12 size 12{"10" rSup { size 8{ - "12"} } } {} — — 10 0 ( = 1 ) 10 0 ( = 1 ) size 12{"10" rSup { size 8{0} } \( `=1` \) } {} femto f 10 − 15 10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {} Table C4 Metric Prefixes for Powers of Ten and Their Symbols Alpha Α Α size 12{Α} {} α α size 12{α} {} Eta Η Η size 12{Η} {} η η size 12{η} {} Nu Ν Ν size 12{Ν} {} ν ν size 12{ν} {} Tau Τ Τ size 12{Τ} {} τ τ size 12{τ} {} Beta Β Β size 12{Β} {} β β size 12{β} {} Theta Θ Θ size 12{Θ} {} θ θ size 12{θ} {} Xi Ξ Ξ size 12{Ξ} {} ξ ξ size 12{ξ} {} Upsilon Υ Υ size 12{Υ} {} υ υ size 12{υ} {} Gamma Γ Γ size 12{Γ} {} γ γ size 12{γ} {} Iota Ι Ι size 12{Ι} {} ι ι size 12{ι} {} Omicron Ο Ο size 12{Ο} {} ο ο size 12{ο} {} Phi Φ Φ size 12{Φ} {} ϕ ϕ size 12{ϕ} {} Delta Δ Δ size 12{Δ} {} δ δ size 12{δ} {} Kappa Κ Κ size 12{Κ} {} κ κ size 12{κ} {} Pi Π Π size 12{Π} {} π π size 12{π} {} Chi Χ Χ size 12{Χ} {} χ χ size 12{χ} {} Epsilon Ε Ε size 12{Ε} {} ε ε size 12{ε} {} Lambda Λ Λ size 12{Λ} {} λ λ size 12{λ} {} Rho Ρ Ρ size 12{Ρ} {} ρ ρ size 12{ρ} {} Psi Ψ Ψ size 12{Ψ} {} ψ ψ size 12{ψ} {} Zeta Ζ Ζ size 12{Ζ} {} ζ ζ size 12{ζ} {} Mu Μ Μ size 12{Μ} {} μ μ size 12{μ} {} Sigma Σ Σ size 12{Σ} {} σ σ size 12{σ} {} Omega Ω Ω size 12{ %OMEGA } {} ω ω size 12{ω} {} Table C5 The Greek Alphabet Entity Abbreviation Name Fundamental units Length m meter Mass kg kilogram Time s second Current A ampere Supplementary unit Angle rad radian Derived units Force N = kg ⋅ m / s 2 N = kg ⋅ m / s 2 size 12{N="kg" cdot {m} slash {s rSup { size 8{2} } } } {} newton Energy J = kg ⋅ m 2 / s 2 J = kg ⋅ m 2 / s 2 size 12{J="kg" cdot {m rSup { size 8{2} } } slash {s rSup { size 8{2} } } } {} joule Power W = J / s W = J / s size 12{W= {J} slash {s} } {} watt Pressure Pa = N / m 2 Pa = N / m 2 size 12{"Pa"= {N} slash {m rSup { size 8{2} } } } {} pascal Frequency Hz = 1 / s Hz = 1 / s size 12{"Hz"= {1} slash {s} } {} hertz Electronic potential V = J / C V = J / C size 12{V= {J} slash {C} } {} volt Capacitance F = C / V F = C / V size 12{F= {C} slash {V} } {} farad Charge C = s ⋅ A C = s ⋅ A size 12{C=s cdot A} {} coulomb Resistance Ω = V / A Ω = V / A size 12{ %OMEGA = {V} slash {A} } {} ohm Magnetic field T = N / A ⋅ m T = N / A ⋅ m size 12{T= {N} slash { left (A cdot m right )} } {} tesla Nuclear decay rate Bq = 1 / s Bq = 1 / s size 12{"Bq"= {1} slash {s} } {} becquerel Table C6 SI Units Length 1 inch ( in . ) = 2 . 54 cm ( exactly ) 1 inch ( in . ) = 2 . 54 cm ( exactly ) size 12{1" inch " \( "in" "." \) =2 "." "54"" cm " \( "exactly" \) } {} 1 foot ( ft ) = 0 . 3048 m 1 foot ( ft ) = 0 . 3048 m size 12{1" foot " \( "ft" \) =0 "." "3048"" m"} {} 1 mile ( mi ) = 1 . 609 km 1 mile ( mi ) = 1 . 609 km size 12{1" mile " \( "mi" \) =1 "." "609"" km"} {} Force 1 pound ( lb ) = 4 . 448 N 1 pound ( lb ) = 4 . 448 N size 12{1" pound " \( "lb" \) =4 "." "448"" N"} {} Energy 1 British thermal unit ( Btu ) = 1 . 055 × 10 3 J 1 British thermal unit ( Btu ) = 1 . 055 × 10 3 J size 12{1" British thermal unit " \( "Btu" \) =1 "." "055" times "10" rSup { size 8{3} } " J"} {} Power 1 horsepower ( hp ) = 746 W 1 horsepower ( hp ) = 746 W size 12{1" horsepower " \( "hp" \) ="746"" W"} {} Pressure 1 lb / in 2 = 6 . 895 × 10 3 Pa 1 lb / in 2 = 6 . 895 × 10 3 Pa size 12{1 {"lb"} slash {"in" rSup { size 8{2} } } =6 "." "895" times "10" rSup { size 8{3} } " Pa"} {} Table C7 Selected British Units Length 1 light year ( ly ) = 9 . 46 × 10 15 m 1 light year ( ly ) = 9 . 46 × 10 15 m size 12{1`" light"`" year"` \( "ly" \) ` =9 "." "46" times "10" rSup { size 8{"15"} } " m"} {} 1 astronomical unit ( au ) = 1 . 50 × 10 11 m 1 astronomical unit ( au ) = 1 . 50 × 10 11 m size 12{1`" astronomical"`" unit"` \( "au" \) ` =1 "." "50" times "10" rSup { size 8{"11"} } " m"} {} 1 nautical mile = 1 . 852 km 1 nautical mile = 1 . 852 km size 12{1`" nautical"`" mile"` =1 "." "852"`" km"} {} 1 angstrom ( Å ) = 10 − 10 m 1 angstrom ( Å ) = 10 − 10 m size 12{1`" angstrom"` \( Å \) ` ="10" rSup { size 8{ - "10"} } " m"} {} Area 1 acre ( ac ) = 4 . 05 × 10 3 m 2 1 acre ( ac ) = 4 . 05 × 10 3 m 2 size 12{1`" acre"` \( "ac" \) ` =4 "." "05" times "10" rSup { size 8{3} } " m" rSup { size 8{2} } } {} 1 square foot ( ft 2 ) = 9 . 29 × 10 − 2 m 2 1 square foot ( ft 2 ) = 9 . 29 × 10 − 2 m 2 size 12{1`"square"`"foot"` \( "ft" rSup { size 8{2} } \) ` =9 "." "29" times "10" rSup { size 8{ - 2} } " m" rSup { size 8{2} } } {} 1 barn ( b ) = 10 − 28 m 2 1 barn ( b ) = 10 − 28 m 2 size 12{1`" barn"` \( b \) ` ="10" rSup { size 8{ - "28"} } " m" rSup { size 8{2} } } {} Volume 1 liter ( L ) = 10 − 3 m 3 1 liter ( L ) = 10 − 3 m 3 size 12{1`" liter"` \( L \) ` ="10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {} 1 U.S. gallon ( gal ) = 3 . 785 × 10 − 3 m 3 1 U.S. gallon ( gal ) = 3 . 785 × 10 − 3 m 3 size 12{1`" U" "." S "." `" gallon"` \( "gal" \) ` =3 "." "785" times "10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {} Mass 1 solar mass = 1 . 99 × 10 30 kg 1 solar mass = 1 . 99 × 10 30 kg size 12{1`" solar"`" mass"` =1 "." "99" times "10" rSup { size 8{"30"} } " kg"} {} 1 metric ton = 10 3 kg 1 metric ton = 10 3 kg size 12{1`" metric"`" ton"` ="10" rSup { size 8{3} } " kg"} {} 1 atomic mass unit ( u ) = 1 . 6605 × 10 − 27 kg 1 atomic mass unit ( u ) = 1 . 6605 × 10 − 27 kg size 12{1`" atomic"`" mass"`" unit"`` \( u \) ` =1 "." "6605" times "10" rSup { size 8{ - "27"} } " kg"} {} Time 1 year ( y ) = 3 . 16 × 10 7 s 1 year ( y ) = 3 . 16 × 10 7 s size 12{1`" year"` \( y \) ` =3 "." "16" times "10" rSup { size 8{7} } " s"} {} 1 day ( d ) = 86 , 400 s 1 day ( d ) = 86 , 400 s size 12{1`" day"` \( d \) ` ="86","400"`" s"} {} Speed 1 mile per hour ( mph ) = 1 . 609 km / h 1 mile per hour ( mph ) = 1 . 609 km / h size 12{1`" mile"`"per"`"hour"` \( "mph" \) `=1 "." "609"` {"km"} slash {h} } {} 1 nautical mile per hour ( naut ) = 1 . 852 km / h 1 nautical mile per hour ( naut ) = 1 . 852 km / h size 12{1`" nautical"`"mile"`"per"`"hour"` \( "naut" \) `=1 "." "852"` {"km"} slash {h} } {} Angle 1 degree ( ° ) = 1 . 745 × 10 − 2 rad 1 degree ( ° ) = 1 . 745 × 10 − 2 rad size 12{1`" degree"` \( ° \) ` =1 "." "745" times "10" rSup { size 8{ - 2} } " rad"} {} 1 minute of arc ( ' ) = 1 / 60 degree 1 minute of arc ( ' ) = 1 / 60 degree size 12{1`" minute"`"of"`"arc"` { { \( }} sup { ' } \) `= {1} slash {"60"} `" degree"} {} 1 second of arc ( '' ) = 1 / 60 minute of arc 1 second of arc ( '' ) = 1 / 60 minute of arc size 12{1`" second"`"of"`"arc"` { { \( }} sup { '' } \) `= {1} slash {"60"`} " minute of arc"} {} 1 grad = 1 . 571 × 10 − 2 rad 1 grad = 1 . 571 × 10 − 2 rad size 12{1`" grad"` =1 "." "571" times "10" rSup { size 8{ - 2} } " rad"} {} Energy 1 kiloton TNT ( kT ) = 4 . 2 × 10 12 J 1 kiloton TNT ( kT ) = 4 . 2 × 10 12 J size 12{1`" kiloton"`" TNT"` \( "kT" \) ` =4 "." 2 times "10" rSup { size 8{"12"} } " J"} {} 1 kilowatt hour ( kW ⋅ h ) = 3 . 60 × 10 6 J 1 kilowatt hour ( kW ⋅ h ) = 3 . 60 × 10 6 J size 12{1`" kilowatt"`" hour"` \( "kW" cdot h \) ` =3 "." "60" times "10" rSup { size 8{6} } " J"} {} 1 food calorie ( kcal ) = 4186 J 1 food calorie ( kcal ) = 4186 J size 12{1`" food"`"calorie"` \( "kcal" \) `="4186"`" J"} {} 1 calorie ( cal ) = 4 . 186 J 1 calorie ( cal ) = 4 . 186 J size 12{1`" calorie"` \( "cal" \) `=4 "." "186"`" J"} {} 1 electron volt ( eV ) = 1 . 60 × 10 − 19 J 1 electron volt ( eV ) = 1 . 60 × 10 − 19 J size 12{1`" electron"`" volt"` \( "eV" \) ` =1 "." "60" times "10" rSup { size 8{ - "19"} } " J"} {} Pressure 1 atmosphere ( atm ) = 1 . 013 × 10 5 Pa 1 atmosphere ( atm ) = 1 . 013 × 10 5 Pa size 12{1`" atmosphere"` \( "atm" \) ` =1 "." "013" times "10" rSup { size 8{5} } " Pa"} {} 1 millimeter of mercury ( mm Hg ) = 133 . 3 Pa 1 millimeter of mercury ( mm Hg ) = 133 . 3 Pa size 12{1`" millimeter"`"of"`"mercury"` \( "mm"`"Hg" \) `="133" "." 3`" Pa"} {} 1 torricelli ( torr ) = 1 mm Hg = 133 . 3 Pa 1 torricelli ( torr ) = 1 mm Hg = 133 . 3 Pa size 12{1`" torricelli"` \( "torr" \) `=1`" mm"``"Hg "="133" "." 3`" Pa"} {} Nuclear decay rate 1 curie ( Ci ) = 3 . 70 × 10 10 Bq 1 curie ( Ci ) = 3 . 70 × 10 10 Bq size 12{1`" curie"` \( "Ci" \) ` =3 "." "70" times "10" rSup { size 8{"10"} } " Bq"} {} Table C8 Other Units Circumference of a circle with radius rr size 12{r} {} or diameter dd size 12{d} {} C = 2 πr = πd C = 2 πr = πd size 12{C=2πr=πd} {} Area of a circle with radius rr size 12{r} {} or diameter dd size 12{d} {} A = πr 2 = πd 2 / 4 A = πr 2 = πd 2 / 4 size 12{A=πr rSup { size 8{2} } = {πd rSup { size 8{2} } } slash {4} } {} Area of a sphere with radius rr size 12{r} {} A = 4 πr 2 A = 4 πr 2 size 12{A=4πr rSup { size 8{2} } } {} Volume of a sphere with radius rr size 12{r} {} V = 4 / 3 πr 3 V = 4 / 3 πr 3 size 12{V= left ( {4} slash {3} right ) left (πr rSup { size 8{3} } right )} {} Table C9 Useful Formulae