Physics For Scientists And Engineers 6E - part 342

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 (v

rms

), 645t,

656–657

Root-mean-square voltage (#V

rms

), 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, 5
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 (R

p

), 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

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 (#7), 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

I.18

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 (C

P

),

646–649, 647t

molar, at constant volume (C

V

),

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 (v

(

), 27, 656–657

average angular (&

(

), 293–296, 294

and dimensional analysis, 11t
distribution of molecular, 655–657
drift (v

d

), 834, 841–842

escape (v

esc

), 407–408t

exhaust (v

e

), 278

instantaneous (v), 28–30, 29
instantaneous angular (&), 293–296,

294

most probable (v

mp

), 656–657

relative (v"), 522–523
root-mean-square (v

rms

), 645t, 656–657

of sound waves, 513–514t, 665
terminal (v

T

), 163, 165t

transverse (v

y

), 495

Speed (v)(Continued)

units of, A.1t
vs. velocity, 27
of waves (v), 492–493

Speed of light (c), 5

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

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, 4

of amount of substance, 4
of electric current, 4
of length, 4–5t
of luminous intensity, 4
of mass, 4–5t
of temperature, 4
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

Index

I.19

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 (4), 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), 4

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

(a

t

), 94–96, 298

Tangential forces (F

t

), 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 (T

c

), 844–845t

Curie (T

Curie

), 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

Tension (T )(Continued)

and speed of wave propagation, 488,

496–499, 554

Terminal speed (v

T

), 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

I.20

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 (5). 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 (5), 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 (15), 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 (a

y

), 495

Transverse speed (v

y

), 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

Unit vectors (iˆ, jˆ, kˆ), 66–70

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, 5
Unstable equilibrium, 237
Uranus, 399t. See also Planetary motion

escape speed from, 408t

U.S. customary system of units, 7

Van Allen belts, 910
Van de Graaff, Robert J., 782
Van de Graaff generators, 782–783
Vaporization

latent heat of, 611-612t

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

average (v

(

), 26–27

of center of mass (v

CM

), 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 (v"), 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 (

0

), 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

Index

I.21