Index
- Page ID
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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