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Engineering LibreTexts

Index

  • Page ID
    24219
  • An italic page number refers to a problem on that page. 

    A Writer’s Time xvi

    a0

     see Bohr radius

    absolute value 187, 247, 248, 302, 314

    absolute zero 182, 300

    abstractions as formula structure 133

    as naming 27

    atomic constants 179

    barrier 60

    capacitive impedance 299

    characteristic (typical) value 203

    concentration gradient 265

    diffusion constant 251

    dimensionless groups 144

    fluid 28

    for simplifying equations 130

    fostered by words 331

    fostering insight 33

    Gm 154

    higher level 313

    ideal spring 317, 353

    in easy-cases analysis 280

    in operating systems 54

    ladder 39, 43

    less-correlated quantities 273

    place value 28

    power mean 313

    Reynolds number 162, 295

    thermal conductivity 266

    transferable ideas 74

    voltage dimensions 168

    acceleration 37, 173

    relativistic 174

    accuracy 89, 201

    more than deserved 91

    proportional reasoning 118

    acoustic charge

    see charge, acoustic

    acoustic field 331

    acoustic source strength 335

    actin 205

    adding in quadrature 251

    adiabatic atmosphere 314

    adiabatic gas law 314

    adjustment factor 12, 21, 216

    advice 270

    air

    density xvii

    diffusion constant 253

    molecule

    cross-sectional area 220

    mean free path 221

    specific heat xvii, 267

    thermal conductivity xvii, 267–270

    thermal diffusivity 253

    viscosity xvii, 253

    air conditioning 268

    air travel, regulated 121

    airplane

    see Boeing 747

    Alaska 134

    algebra, reducing 285

    all-or-nothing reasoning 215, 225–228

    ampere 172

    amplitude

    acoustic charge oscillation 335

    complex 169

    energy, relation to 323

    input signal 45

    peak-to-peak 51

    piano string 323

    sound wave 320

    analogy

    acoustics–electromagnetism 335

    acoustics–electrostatics 337

    as abstraction 36–53

    bridges 37

    by defocusing 46, 140

    charge, electric–acoustic 331

    circle–sphere 53

    connected knowledge 357

    cooling tea–discharging capacitor 49

    density, areal–volume 86

    electrical–gravitational 39, 170, 172, 341

    electrical–magnetic 172

    electrical–thermal 50, 135

    energy, thermal–confinement 301

    hydrogen–neutron star 232

    mass–resistance 43

    phonons–particles 256

    phonons–photons 255

    power radiated, acoustic–electromagnetic 337

    quadrupole–dipole 340

    radiated power, multipolar 341

    solar core temperature–atmosphere height 305, 306

    spring constant–Young’s modulus 189, 190

    spring–capacitor 42

    temperature–voltage 48

    waves, sound–transverse 324

    angles 155

    dimensions of 288

    in proportional reasoning 113

    ångström 179

    angular diameter 186

    angular frequency 38, 45, 146, 324

    angular momentum 177, 188, 313

    angular resolution

    eye 181

    optical telescope 158

    radio telescope 159

    angular velocity

    Earth’s orbit 345

    falling toast 116

    animal fat, combustion energy of 31

    annuity 315

    anxiety, when estimating 11

    arcseconds 158

    area 218

    ellipse 283

    areal density 86, 163

    arithmetic mean 19, 36, 313

    geometric mean, inequality with 36

    arithmetic, mental

    see mental arithmetic

    armchair reasoning 204

    Armstrong, Lance 22, 95

    aspect ratio 240, 283

    assumptions

    checking 297

    making 204, 297

    refining 217

    asteroids 228

    astronomical unit (AU) xvii, 112

    astrophysical scalings 232

    atmosphere

    adiabatic 314

    isothermal 234, 314

    lumped model 351

    scale height 167, 299–301, 351

    sea-level pressure xvii

    standardized parameters 167

    atmospheres (pressure) 191

    atomic bomb, yield of 150–151, 211–212

    atomic diameter 179, 221

    atomic mass 273

    atomic theory 175

    atomic volume 189, 213

    attenuation 47

    Atwood machine 283–286

    Atwood, George 284

    AU (astronomical unit) xvii, 112

    audibility 337

    Avogadro’s number xvii, 29, 67, 166, 213, 222, 267, 307

     

    baby boomers 215

    baggage worth carrying 348

    baking 260–261

    see also cooking three dimensions 277

    banknotes 248

    barbell 293

    barrels, oil 14

    bar-tailed godwit 134, 135

    basal metabolism 23, 271

    batteries

    typical 168

    9-volt 23, 139

    Bayes’ theorem 237–238, 245

    Bayesian interpretation

    see probability, Bayesian

    Bayesian probability

    see probability, Bayesian

    beautiful people 268

    beauty, mathematical 117

    bel 63, 243

    belief, degree of

    see probability, Bayesian

    bending beam

    musical note 325–330

    stiffness 326–328

    bending stiffness 326

    bicycle spoke 355

    bicycling

    see cycling

    binding energy 179, 189, 191

    heavy atoms 315

    hydrogen 307

    physical model 301–305

    binomial theorem 323

    birthday paradox 123–125, 280–281

    bisection 75

    black hole 290, 291, 345

    blackbody radiation 107, 181–186, 306

    blackbody temperature 306

    Earth 186

    blackjack (card game) 259

    blood doping 22

    blue skies 174

    blue–green light 352

    Bode plot 299

    body temperature 270

    Boeing 747

    coefficient of lift 133

    cross-sectional area 120–121

    cruising altitude 120

    cruising speed 99

    drag coefficient 128, 132

    flight range 122, 131–133

    fuel capacity 122

    fuel consumption 119–122

    fuel efficiency 16

    maximum takeoff mass 98

    passenger capacity 122

    runway length 100

    takeoff power 98

    technical data 99, 122

    thrust 99

    wingspan 98

    Bohr radius xvii, 176, 178, 179, 187, 233, 301, 318

    see also hydrogen, size

    Boltzmann’s constant xvii, 68, 165, 167, 267, 307

    bon voyage 358

    bonds

    chemical

    abstraction 28

    energy scale 180

    participating electrons 168

    simplest 187

    energies 29, 187–188

    nitrogen 351

    typical xvii, 187, 191

    gravitational 304

    length 305

    result of competition 304

    spring model 304, 317–319

    bone 355

    bookend regimes 282

    bookkeeping 326

    books 138

    Boston 76, 122

    boundary layer 262–263, 265, 296

    Reynolds number 263

    thickness 262, 278

    turbulence 263

    box models 75–83

    atmosphere 80

    average solar flux 79–80

    drag 84

    rainfall 80–82

    residence time 82–83

    running in rain 58–59

    surface temperature 107

    taxis in Boston 75–77

    brachistochrone 220

    brain

    mass 138

    power consumption 138

    brand name 333

    Brans–Dicke theory 159

    breaking the bank 259

    brittle materials 193, 355

    Brody, Carlos xiii

    broken symmetry

    see symmetry, breaking

    brute-force analysis compared to proportional reasoning 105

    finding dimensionless groups 182

    fuel consumption 119

    heat loss 271

    orbital period 112

    surface temperature 108, 109

    temperature distribution 73

    bubble sort 125

    Buckingham Pi theorem 145, 147, 159, 171, 176, 184

    Buckingham, Edgar 145

    buckling 355

    buoyancy 40, 316

    bureaucracy 279

    burst power output 21

    butter, energy density of 23

     

    cake, eating and having 63

    calculus 265

    as elephant gun 70

    hindering insight 209

    leaving magic 113

    maxima and minima without 70

    turning into algebra 321, 339

    calculus of variations 220

    California, population of 127

    Calliope hummingbird 95

    calorie 266, 274

    Calorie

    see kilocalorie

    Caltech xiv

    Cambridge University xiv, 150, 158

    capacitance

    dimensions 169

    thermal 49

    capacitor 36, 38, 44

    Cape Town 51, 122

    capillaries 253

    car ownership 13

    carbohydrates, combustion energy 31

    Caro, Robert 6

    Carpenter, Thomas 199

    carrying capacity

    highway lane 6, 57

    train line 7

    cars

    fuel efficiency 90–92

    nocturnal activities in 121

    cartoon 290

    cataclysm 175

    causal sequence 346

    caveat 306

    cd

    see drag coefficient

    Census Bureau 215

    center of mass 205, 330, 342

    centripetal acceleration 343

    see also circular acceleration

    chance

    see prepared mind

    change, handling 58, 74, 103, 138, 204, 347

    changing units

    see units, changing

    characteristic values 203–212, 354

    acceleration 208, 224, 321

    distance 208, 223, 232, 249, 305

    energy 322

    force 321

    gravitational energy 305

    kinetic energy 322, 323

    Mach number 341

    potential energy 322, 323

    scale height 300

    speed 322

    strain 226

    stress 225

    time 209

    circular motion 210

    demographic 215

    diffusion 260

    radiation 334

    random-walk timestep 250

    sound propagation 321

    spring–mass system 322

    charge 39

    acoustic 331–332

    radiated power 333–337

    capacitor 36

    conservation 338

    density 78

    dimensional analysis 168–171

    gravitational 39

    point 40

    chemical bonds

    see bonds, chemical

    chemical enhancement 96

    chessboard tiling

    see solitaire, chessboard tiling

    chewing gum 294

    chunks, fluid 219

    CH2 unit

    burning 29

    circuits

    inductor–capacitor (LC) 36

    low-pass RC 46, 169, 299, 349

    LRC 169

    circular acceleration

    dimensional analysis 139–144

    electron 177

    lumping 209–210

    planet 110

    train 139

    using angular frequency 146

    using period 147

    circulatory systems 249, 253

    city driving 299

    classical electrodynamics 182

    classical electron radius 180, 187, 350

    see also electron, size

    Classical Mechanics 174

    classical mechanics 310–312

    clock ticks 250

    clothing 249, 267

    clouds 80

    clutter 219

    CM

    see center of mass

    coaxial cable 54, 194

    coefficient of lift 133

    coin game 31–33

    coin toss 291

    color 346

    high frequency 349

    combustion energy 28

    comfortable temperature 271

    commutativity 71

    comparison

    meaningful 137, 155, 158, 254, 271, 307, 334

    nonsense 138

    competition 233, 291, 299–307

    attraction vs. repulsion 304

    drag vs. surface tension 316

    electrostatics vs. quantum mechanics 233, 317–318

    gravity vs. quantum mechanics 230, 232

    gravity vs. thermal motion 167, 299– 301, 305–307

    thermal motion vs. intermolecular attraction 299

    complex amplitude 169

    complex number 45

    compound pendulum

    see pendulum, compound

    compression, adiabatic vs. isothermal 166

    Compton wavelength 187

    concentration gradient 265

    concrete thinking 39

    conduction 267

    cone

    see also terminal speed, cone

    drag coefficient 163

    free fall 217–218

    template 85

    taping 119

    confidence in estimates 16

    confinement energy 230, 232

    hydrogen 301–304

    neutron star 230

    conjecture

    Atwood-machine acceleration 286

    birthday paradox 123, 125

    coin game 32

    electromagnetic radiated power 338

    random-walk dispersion 251, 252

    rolling motion 292

    conscience 122

    conservation 75, 107

    charge 188

    energy 84, 152, 294, 297

    momentum 219, 330

    Consider a Spherical Cow 212

    consistency 297, 335

    constant acceleration 208, 229

    constraints

    boundary 262

    chain of 144

    diffusion of 262

    dimensional validity 140, 328

    eliminating an easy-cases regime 287–290

    from optimization 130

    geometric 288

    no slip 262

    on dimensionless functions 157

    contact radius 225

    from easy cases 288

    monotonicity 157

    sign 157

    viscous drag 296

    contact

    area 356

    force 228, 356

    radius 193, 225

    time 193, 228

    continued fraction 54

    contour lines 73, 74

    contour plot 74

    contradiction 160

    convection 267

    conventions 145

    conversion factor

    see units, changing

    cooking

    egg 261

    fish

    see baking

    meat 260

    coordinate axes 249

    copyright license, open xv

    correlation 273

    coulomb 172

    Coulomb’s law 170, 175

    courage xiv, 13, 77, 149, 197, 312, 334

    Coyote, Wile E. 290

    Creative Commons xv

    credibility 236

    critical probability 357

    critical wavelength 316

    crooked made straight 220

    cross section

    see scattering cross section

    cross-sectional area 68, 84, 189

    car 91, 121

    cone 118

    cyclist 88

    molecule 220

    plane (747) 120–121, 128, 129

    cross-sectional radius 117

    cruising speed

    see flight speed

    cube

    for easy cases 313

    for lumping 207

    solitaire 60

    cubic lattice 230

    current 24, 37, 168

    as flow 44

    current density 78

    curvature 247

    cycling

    drag power 87–89

    to keep warm 271

    1-hour record 89

    damped oscillation 353

    damped spring–mass system 353, 354

    damping

    coefficient 353

    constant 193

    force 353

    linear 353

    ratio 193

    dB

    see decibel

    decade (factor of 10) 116, 206

    decency 270

    decibel 243, 337

    acoustic 63, 244

    deed, good 184

    degree of belief

    see probability, Bayesian

    degree of freedom 58, 152

    Delaware

    government budget 127

    population 127

    delta-function potential 195

    demand

    see also supply energy 269

    estimating 10–16

    oil 75

    Democritus 175

    density

    air 122

    effect on sound speed 191

    instead of mass 115

    instead of sound speed 328

    salt 21

    solids and liquids 212–214

    water 122

    derivatives

    dimensionless 339

    lumping 209–210

    desert of the real 207

    diamond

    specific heat 277

    speed of sound 277

    thermal conductivity 275, 277

    differential equations

    avoiding 208, 218, 225, 321

    solving 218

    turning into algebra 277

    differential quantities 259

    differentiation, dimensionless 339

    diffraction 181

    diffusion

    see also thermal diffusivity; kinematic viscosity; viscosity constant 160, 251

    types 254–255

    flux 264–267

    speed 263–264

    time 261, 263

    dimensional analysis 253

    lumping 252

    neurotransmitter 254

    dimensional analysis 80, 328

    see also dimensionless groups; universal constants; universal functions atmosphere scale height 167

    atomic-bomb yield 150–151

    blackbody radiation 181–186

    charge 168–171

    circular acceleration 139–144

    contact radius 193

    delta-function potential 195

    diffraction 181

    drag 159–164

    electric field of uniform sheet 172

    electric field, energy density in 170

    ground-state energies 181

    hydrogen 176–180

    impact speed 146

    in simpler unit system 182

    light bending by gravity 153–159

    low-pass RC circuit 169

    LRC circuit 169

    magnetic field 172

    pendulum period 147

    radiated power 172–174

    rolling speed 153

    spring–mass system, period of 149

    temperature 165–167

    thermal speed 165

    wave speed 146

    with easy cases 283, 287

    Young’s modulus 189

    dimensionless derivative 339, 341

    dimensionless function 152

    Atwood machine 284

    contact radius 225, 227

    drag 163

    guessing 285

    projectile range 288

    rolling speed 292

    dimensionless groups 139–145

    as abstractions 144

    choosing 156

    counting 144–145, 146

    extending definition 285

    finding 139–144

    independent 141

    waves 309

    dimensionless numbers

    Froude number Fr 143

    Mach number M

    see Mach number

    Prandtl number Pr 255

    Reynolds number Re

    see Reynolds number

    dimensionless parameter 50

    dimensionless prefactor 110, 172, 190, 205, 296, 298

    beam vibration 330

    binding energy, hydrogen 180

    blackbody flux 185

    circular acceleration 210

    drag 92, 118

    energy density, electric field 171

    gravitational radiation 343

    ignoring 118, 247

    natural frequency, spring–mass system 322

    projectile range 289

    pyramid volume 313

    specific heat 268

    time aloft 113

    dimensionless ratio 291

    atmosphere scale height 300

    binding energy, hydrogen 301

    floating on water 298

    inharmonicity 355

    Mach number 341, 343

    radiation 334

    speaker size 336

    water depth 308

    water waves 309, 316

    dimensionless size 336

    dimensionless temperature 261

    dimensions

    capacitance 169

    charge 168

    current 168

    independent 145, 171

    inductance 169

    resistance 168

    temperature 165

    voltage 168

    dipole field 338

    moment 338

    oscillating 338

    radiation 337–340, 346

    dirty dishes 263

    discrepancy

    diffusion constants in water 255

    explaining 116

    learning from 216, 257

    disjoint sets, comparing 11

    displaced fluid 69

    dissipation 218

    divide-and-conquer reasoning 39

    beam vibration 326, 327

    cycling speed 88

    dimensional analysis 153

    dollar bill, volume of 3

    energy density 266, 273

    energy minimization 72

    fuel consumption 120

    gravitational radiation 342

    increasing accuracy of 241

    Karatsuba multiplication 126

    mental arithmetic 222, 307, 336

    merge sort 125

    probabilistic analysis of 239–248

    supply and demand 77, 205

    temperature signals 52

    thermal conductivity 267, 272

    dollar bill, volume of 3

    double bond 30

    double counting, avoiding 124, 188, 191

    doubling question 109

    see also proportional reasoning beam vibration 330

    flux 77

    gravitational acceleration 126

    orbits 112

    pipe flow 195

    projectile range 113

    terminal speed 117

    drag 117, 217, 218

    box model 84–92

    dimensional analysis 159–164

    dimensionless prefactor 118

    easy cases 295–298

    energy 128, 129

    flight 71

    high Reynolds number 296–297

    jumping fleas 207

    low Reynolds number 295–296

    on cyclist 87

    Stokes 265

    drag coefficient 68, 92, 118, 128

    as dimensionless group 160

    as ratio of energies 69

    based on squared wingspan 128, 132

    based on wing area 132

    cone 163

    easy cases 295–298

    high Reynolds number 296–297

    low Reynolds number 295–296, 297

    neglecting 89

    nonstreamlined objects 118

    sphere 164

    drag force

    see drag

    dressing warmly 270–271

    drift 259

    drift speed 214

    driven spring–mass system 354

    driving frequency 347

    natural frequency 347

    dry water 84

    dynamic range 337

     

    e

    see electron charge

    Earth

    as black hole 291

    bending starlight 158

    blackbody temperature 186

    density 116

    gravitational radiation from 342

    greenhouse effect 186

    mass xvii, 26

    oblateness 192

    orbital speed 203

    precession of the equinoxes 234

    radius xvii

    rainfall 80

    solar flux 79

    solar power reaching 138

    surface temperature 186

    earthquakes 150

    Earth–Sun distance xvii, 203, 343

    easy cases 331

    acoustic field 333–334

    Atwood machine 283

    birthday paradox 280

    choosing regime 297

    compound pendulum 313

    drag 295–298

    driven spring–mass system 347

    ellipse 283

    fields of physics 310–312

    high Reynolds number 296

    light bending 289–290

    low Reynolds number 295

    projectile range 287–289

    rolling 291–294

    variance 290

    waves 308–310

    eccentricity (orbital) 314

    eclipse expedition 158

    Eddington, Arthur 158

    effective potential 194

    efficiency

    see also engine efficiency

    animal metabolism 95, 271

    cooling 269

    effort variable 37, 43

    see also flow variable

    egg, boiling 261

    Einstein, Albert 158, 159

    as traffic policeman 311

    elastic modulus

    see Young’s modulus

    elders 270

    electric field 37, 39, 169, 331, 350

    energy density in 170

    spherical shell 222

    uniform sheet 172, 222

    electromagnetic field 255

    electromagnetic radiation 40, 177

    electron

    charge xvii, 176, 346

    mass 176, 348

    rest energy xvii, 178, 183, 187

    size 177

    electron shells 179

    electron volt 29, 67, 168

    electrostatic energy 233

    electrostatic potential energy

    see electrostatics, energy

    electrostatics 181

    charge 39

    energy 179

    hydrogen 301–304

    elegance 108

    elephant gun, calculus as 70

    ellipse 313

    area 283

    length parameters 313

    planetary orbits 112

    empires 3

    energy

    confinement

    see confinement energy

    green-light photon 68

    spring models 321–330

    energy conservation

    see conservation, energy

    energy consumption 138

    energy density 190, 266, 350

    acoustic field 334

    atomic blast 211

    butter 23

    dimensions 189

    electric field 170, 332, 339

    fat 134

    fields 39, 331

    fuel 131, 134

    gasoline 90

    gradient 265

    kinetic 332

    magnetic field 172

    muscle 205

    peanut butter 31

    sunlight 348

    TNT 151

    energy flow 48, 333

    energy flux 79, 182

    acoustic 63

    electromagnetic 174

    sunlight 349

    energy loss 160

    energy signature 318, 321, 324

    Engel, Arthur 58

    engine efficiency 92, 132, 134

    English dialects

    American 216

    British 216

    envelope, back of 214, 215

    enzymes 271

    \(\epsilon_{0}\)

    see permittivity of free space

    equality, kinds of 5

    equating energies 324

    equations, not getting buried in 47

    equilibrium 73, 317

    equinoxes, precession of 234

    equivalence, mathematical vs. psychological 67, 156, 214

    errors

    cancellation 92

    worthwhile 231

    estimates, confidence in 16

    Euler, Leonhard 45

    evaporation 80

    evaporative cooling 268–270

    evidence 236

    exact calculation 199

    birthday paradox 125

    too difficult 117, 215, 218, 224

    exhortation 258

    expansion, adiabatic vs. isothermal 166

    expected position 250

    expected value 290

    explanatory power 237

    see also likelihood

    exponential decay

    atmospheric density 234

    atmospheric pressure 167

    temperature 49

    voltage 47

    exponents 54

    mental arithmetic with 200

    tree representations 9, 111

    extensive quantities 116

    extreme case 226, 241

    see also easy cases

     

    false negative 238

    false positive 238

    far field 334

    Fermi velocity 257

    The Feynman Lectures on Physics 175

    Feynman, Richard 84, 175

    fiat 183

    fiber-optic cable 354

    Fick’s law 265, 266

    fine-structure constant xvii, 178, 179, 257

    fleas, drag on 207

    flexural rigidity 326

    flight range

    bar-tailed godwit 134

    Boeing 747 131–133

    effect of size 134

    plane (747) 122

    flight speed

    bar-tailed godwit 135

    effect of air density 135

    effect of mass 135

    optimization 128–134

    plane 71

    flight, airplane

    see Boeing 747

    flight, hovering

    see hovering

    floating 298

    flow variable 43, 44

    see also effort variable

    fluid, as an abstraction 28

    Fluid-Dynamic Drag 164

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