APPENDIX I

ENERGY AND POWER SPECTRA

10"

10'0

lO" } 1010

10'

10- 10

10- 1'

10-'0

Rotational kinetic energy of the Earth

Solar energy incident on Earth in one year

World's energy consumption in one year

Range of nuclear explosions

One liter of gasoline

Flashlight battery

Walking person's kinetic energy

Stored in a 1-I'F capacitor at I volt

Fission of one 235U

nucleus

Needed to ionize one Hatom·

One molecule's kinetic energy at room temperature

Figure 1.1. Some approximate energies, on a logarithmic scale. The already huge range exhibited here could still be greatly expanded by inclusion of stellar, galactic, and cosmic energy values.

(Watts)

10 18

10 17

1016

101'

10' --+--10'

10'

106

10' --;.--

10'

103 --'-'--

10' _-+ __

Solar power incident on whole Earth

World power consumption

Output ofa generating plant

Automobile's consumption at40MPH

Solar power incident on one square meter

One person's metabolism

Flashlight

Figure 1.2. Some approximat~ power values, on a logarithmic scale. The data are from R. H. Romer, Energy (W. H. Freeman & Co., San Francisco, 1976).

669

APPENDIX II

THE VECTOR CROSS PRODUCT

The vector cross product is often used in physics. In this book, it occurs in connection with angular momentum and torque (notes at end of Chap. 7); magnetic forces [Sees. Band C of Chap. 18, as well as its Note (ii)]; magnetic fields from currents [Sec. A of Chap. 19]; and the energy flow in an electromagnetic wave [Sec. B of Chap. 22]. This appendix serves as a common summary for those scattered discussions.

i. Definition

Let A, B denote two arbitrary vectors, of magnitudes A, B; see Fig. 11.1. The cross product A x B is defined as a vector with (1) Magnitude

IA x BI =AB sin e (11.1)

where f) is the angle between A and B when they are displayed tail to tail; and (2) Direction perpendicular to the plane through A andB:

A x B perpendicular to A

A x B perpendicular to B (II.2)

in accordance with the right-hand rule. Several versions of this rule are explained in the text. They are all equivalent to that of Fig. 11.1.

[We see that A x B = 0 when A and Bare mutually parallel or antiparallel (in particular, A x A = 0); also, IA x BI = AB when A and Bare mutually perpendicular.]

ii. Some Important Properties

Two remarkable features of Ax B are its non­commutativity,

AxB= -(BxA) (IIJ)

and its nonassociativity,

A x (B x C) =F (A x B) x C (II.4)

(in general).

~~. (Y. A \A

(c)

Figure 11.1. (a) The cross product, A x B. (b) The right-hand rule, here based on a right-handed corkscrew. (Are there left-handed corkscrews'?) As the handle turns from A to B, the screw advances along + (A x B). (c) The handle must tum through the smaller of the two available angles.

671

672

Illustrations Consider the three orthogonal unit vectors i, j, k

of Fig. 11.2. We see, for example, that

ixj=k, whereas j xi = -k

Also,

(i xj) xj = k xj = -i,

whereas

ix(jxj)=ixO=O

More conventional-looking properties of the cross product are its behavior under multiplication by an ordinary number ("scalar") n:

Appendix II

Note how the order of factors is preserved across these equalities. We shall not go into the proofs of (11.5)--(11.7).

iii. Application of the Distributive Rule

Two uses of Eqs. (11.6), (11.7) deserve special mention.

(1) Note (iii) at the end of Chap. 7 introduces the differentiation rule (supposing that A and B both depend on time, t)

d (dA) ( dB) -(AxB)= -xB + Ax-dt dt dt

(11.8)

n(A x B) = (nA) x B = A x (nB) (11.5) where the order of the factors must be preserved. The reader may derive (11.8) along the following

as well as the distributive rule lines. Use the definition

A x(B+C) =(AxB) +(A x C) (11.6)

and, similarly,

(B+C)xA=(BxA)+(C xA) (11.7)

k

j

Figure 11.2. Three orthogonal unit vectors.

~(AxB)= lim A(AxB) dt 41-0 .1t

(11.9)

and similarly for A and B individually. Set

.1(A x B) = (A +.1A) x (B +.1B) -(A xB)

(11.10)

and work this out with use of (11.6); neglect the .1A x LIB term in the limit.

(2) Note (ii) at the end of Chap. 18 points out, on the basis of the distributive rule, that the magnetic force on the drifting electrons in a wire is calculated as if all electrons had the same velocity (their average velocity).

APPENDIX III

MATHEMATICAL FORMULAS

Special Numbers

Algebra

Let

Then

J2 ~ 1.414214

1l~3.l41593

e~2.718282

ax2 +bx+c=0 (a #=0)

X= -b ± (b2 _4aC)I/2

2a

Small x (x ~ 1) Approximations

1 _ -l-~l+x ±x

(1 +x)n~ 1 +nx

In(1 +x)~x

sinx~tanx~x

Trigonometry

1l = 1l rad = 1800

sin2 (X + cos2 (X = 1

sin 2(X = 2 sin (X cos (X

sin2 (X = !<1 - cos 2(X)

cos2 (X =!(1 + cos 2(X)

sin( (X + P) = sin (X cos P + cos (X sin P cos( (X + P) = cos (X cos P - sin (X sin P

(X+P (X-P cos (X + cos P = 2 cos --cos --

2 2

P 2 · (X+P . P-(X cos (X - cos = sm --sm --

2 2

. . P 2' (X+P (X-P sm (X + sm = sm --cos --2 2

. . P 2 (X+p. (X-P sm (X - sm = cos -2- sm -2-

Differentiation

d dxf(x) = J'(x)

d dxf(ax) =aJ'(ax)

d dx (fg) = J'g+ fg'

~ (l\ =J'g - fg' dx g) g2

d - xn=nxn- 1

dx

d -ex=ex dx

673

674

Integration

Let

d 1 -d In Ixl =-x x

d . dxsmx=cosx

d dx cos x = -sin x

d 1 -tanx=--dx cos2 x

d -1 -cotx=-­dx sin2 x

dF(x) -=f(x)

dx

Appendix III

Then

f f(x) dx = F(x) + const

r f(x) dx =F(x) I: =F(b) -F(a)

f xn dx = _1_ xn + I + const n+l

fdx ~=ln Ixl +const

(n"l -1)

f sin x dx = -cos x + const

f cos x dx = sin x + const

f eX dx = eX + const

APPENDIX IV

CONVERSION FACTORS*

Conversion Factors to International-System Units

One unit of Equals

Acceleration

ft/sec2 3.048 x 10-1 meter/sec2 (exact) standard g 9.80665 meters/sec2 (exact)

Area

acre 4.047 x 103 meters2 barn (nuclear cross section) 10-8 meter2 (exact) ft2 9290 x 10-2 meter2

Density

Ib mass/ft 3 1.602 x W kg/meter3

slug/ft 3 (British system) 5.154 x 102 kg/meter3

Distance, see Length

Energy

BTU (thermochemical) 1.054 x 103 joules kcal (thermochemical) 4.184 x 103 joules (exact) electron volt 1.6021917 x 10- 19 joule erg 10-7 joule (exact) ft Ib 1.356 joules kW hr. 3.6 x 106 joules (exact) kiloton (nuclear explosion) 420 x 1012 joules

Force

dyne 10-5 newton (exact) Ib 4.448 newtons

Length

A (=Angstrom unit) 10- 10 meter (exact) AU (=astronomical unit) 1.496 x 1011 meters fermi ( = femtometer) 10- 15 meter (exact) ft 3.048 x 10-1 meter (exact) light year 9.46055 x W5 meters micron ( = micrometer) 10-6 meter (exact) mil 2.54 x 10-5 meter (exact) mile (U.S. statute) 1.609 x 103 meters

• For a more extensive table, see The International System of Units, by E. A. Mechtly (National Aeronautics and Space Publication SP-7012, 1973).

675

676 Appendix IV

Conversion Factors to International-System Units

One unit of Equals

Mass

carat 2 x 10-4 kg (exact) gram 10-1 kg (exact) Ib-mass 4.536 x 10- 1 kg slug (British system) 1.459 x W kg ton (metric) 101 kg (exact) u ( = amu = atomic mass

unit = dalton) 1.66053 x 10 -27 kg

Power

electric horsepower 7.46 x 102 watts (exact)

Pressure

atmosphere 1.01325 x WS Pa (exact) bar 105 Pa (exact) inch of mercury (60°F) 3.377 x W Pa Ib/in.2 (psi) 6.895 x 101 Pa millibar 102 Pa (exact) torr ( =mm of Hg, O°C) 1.333 X 102 Pa

Speed

ft/sec 3.048 x 10-1 meter/sec (exact) km/h 2.778 x 10-1 meter/sec mile/h (U.S. statute) 4.4704 x 10- 1 meter/sec (exact)

Temperature

Co ( = Celsius degree) 1 K (exact) FO (=Fahrenheit degree) 5/9 K (exact)

Time

day 8.640 x 104 sec (exact) hour 3.6 x 101 sec (exact) minute 6x 101 sec (exact) year 3.1536 x 107 sec

Velocity, see Speed

Volume

barrel (=42 gal petroleum) 1.590 x 10- 1 meter1 ft1 2.832 x 10-2 meter1 gallon (U.S., liquid) 3.785 x 10-1 meter1 liter 10-1 meter1 (exact) ounce (U.S., liquid) 2.957 x 10-5 meter1 quart (U.S., liquid) 9.464 x 10-4 meter1 ton (ship displacement) 2.832 meters1

APPENDIX V

NUMERICAL CONSTANTS*

The following constants are selected for their importance in this book:

Quantity Symbol Value Unit

Permittivity of the vacuum eo 8.854 188 x 10 -12 C 2 N- I m- 2

Coulomb's law factor 1/41teo ( =K) 8.987 552 x 109 C- 2 Nm2

Permeability of the vacuum (exact) Po (=41tK') 41t x 10-7 A2 N Speed of light in vacuum (exact) c 2.997 924 58 x 108 msec- I

Gravitational constant G 6.6732 x 10- 11 Nm2 kg- 2

Avogadro's number (for I kmole) .AlA 6.022 169 x 1026

Boltzmann's constant k 1.380 622 x 10 - 23 IK- I

Gas constant R 8.314 34x W 1 kmole- I K- I

Volume of ideal gas, standard conditions (for I kmole) 'iSTP 224136 x 101 m3

Atomic mass unit I u 1.660 531 x 10-27 kg Planck's constant h 6.626 196 x 10 -34 Is

h/21t ( = Ii) 1.054591 9 x 10 -34 Is Electron charge e 1.6021917 x 10- 19 C Electron rest mass me 9.109558 x 10-31 kg

5.485 930 x 10-4 u Proton rest mass mp 1.672 614 x 10-27 kg

1.00727661 u Neutron rest mass mn 1.674920 x 10 -27 kg

1.00866520 u Electron charge to mass ratio elme 1.758 802 8 x 10 11 Ckg- I

Standard acceleration of gravity (exact) gst 9.80665 ms-2

Mass of the Earth ME 5.976 x 1024 kg Earth's radius (sea level, equatorial) 'Ee 6.378 160 x 106 m

(Sea level, polar) 'Ep 6.356775 x 106 m

• After E. A Mechtly, The International System of Units (National Aeronautics and Space Publication SP 7012, 1983).

677

APPENDIX VI

THE GREEK ALPHABET

A,o: alpha I, I iota P,p rho B,p beta K,K kappa E, (1 sigma r, y gamma A, A. lambda T,r tau A,c5,a delta M,j.l mu I,V upsilon E,G epsilon N, v nu tP, ifJ, rp phi Z,( zeta E,e Xl X,X chi H,,, eta 0,0 OmIcron 'P, Vt psi 8, () theta II,n pI Q,W omega

679

APPENDIX VII

LIST OF TABLES AND SPECTRA

(Numerical)

Chapter Reference (Roman Item Chapter label numerals refer to Reference Atomic weights (average) 11 Table 11.1

Item Appendix) label Vibration frequencies 13 Fig. 13.26 Speed of sound 14 Table 14.1

Energies and powers I Intensity levels (sound) 14 Table 14.2 Conversion factors IV Electric field strengths 15 Fig. 15.13 Numerical constants V Potential diiferences 16 Fig. 16.11 Distances I Fig. 1.1 Resistivities 17 Table 17.1 Time intervals 1 Fig. 1.3 Magnetic field strengths 18 Fig. 18.8 Speeds 2 Fig. 2.2 Electromagnetic spectrum, Accelerations (gravity) 2 Fig. 2.7 including photon energies 22 Figs. 22.13, 22.14 Masses 3 Fig. 3.4 Transparency of atmosphere 22 Fig. 22.16 Forces 3 Fig. 3.5 Indices of refraction 23 Table 23.1 Circular frequencies 6 Fig. 6.10 Dispersion in glass 23 Fig. 23.9 Angular momenta 7 Fig. 7.33 Photoemission thresholds 26 Table 26.1 Astronomical data 8 Table 8.1 X-ray spectrum 26 Fig. 26.6 Pressures 9 Fig. 9.7 Hydrogen spectrum 27 Fig. 27.1, Densities 9 Table 9.1 Table 27.1 Temperatures 10 Figs. 10.6, 10.7 Fraunhofer lines 27 Fig. 27.8 Specific heats 10 Table 10.1 Electron configuration in atoms 27 Figs. 27.21, 27.22,

11 Fig. 11.8 Table 27.3 Fusion and vaporization 10 Table 10.2 Periodic table of elements 27 Figs. 27.23, 27.24 Thermal expansion 10 Fig. 10.11, Stable nuclides 28 Fig. 28.2

Table 10.3 Atomic masses up to carbon 28 Table 28.1 Heats of combustion 10 Table 10.4 Charge density in nucleus 28 Fig.28.3

681

INDEX

A (musical note), 9, 287 Aberration, stellar, 591 Absolute value, 24; see also Magnitude Absolute zero, 212 Absorption, 503 Absorption lines, 623 ac,478

motor, 469, 486 power, 480

Acceleration, 17, 46 angular, 144, 148, 163 centripetal, 130 gravity, 19

spectrum, 19 radial, 134, 136 tangential, 134, 136 uniform, 19 vector, 33

Acoustic spectrum, 286 Action, line of, 152 Action, 597

and reaction, 53, 162,428,439 Activity, 656 Adiabatic enclosure, 209 Adiabatic expansion, 253 Airy disc, 562 Alpha decay, 653 Alpha particles, 652, 663 Alternating current: see ac Alternating voltage, 457 Altitude, maximum, 22, 23 Ammeter, 375 Ampere (unit), 372 Ampere's law, 429, 440, 490 Amplitude, 279, 281, 300

current, 478 voltage, 478

Angle deviation, 537 incidence, 514 rellection, 517 refraction, 514 total rellection, 518

Angstrom (unit), 502, 507

Angular acceleration, 144, 148, 163 coordinate, 125 displacement, 282 frequency, 300 magnification, 531, 541 momentum, 160 momentum, conservation, 160, 166, 184

quantized, 629 momentum, spectrum, 163 momentum, vector, 164 position, 126 velocity, 127

Annihilation, 654 Anode, 360, 362, 601 Antenna, 501 Antimatter, 583 Antineutrino, 653 Antinode, 309 Antirellective coating, 545 Archimedes' principle, 198 Astronomical data, 175, 177, 185 Astronomical unit, 177 Astronomy, 175 Atmosphere, 195, 202, 246, 269

absorption, 503 refraction, 538 transmission, 503

Atom, 227 Bohr model, 624 Rutherford model, 663 size, 229 Thomson model, 663

Atomic mass, 229, 659 mass unit, 229, 648 number, 634, 640, 648 shells, 635 structure, 617 table, 231 weight, 230

Atwood's machine, 57 Avogadro's law, 232, 234 Avogadro's number, 230, 385, 657, 666

Axis, coordinate, 8 optic, 521, 529

Azimuthal: see Orbital

B field: see Magnetic field Back emf, 467 Balance

Cavendish, 181, 295 current, 433 equal-arm, 155 spring, 47 torsion, 181, 295 unequal-arm, 169

Ballistic galvanometer, 467 Ballistic pendulum, 120 Ballistics: see Projectiles Balloon, 200 Balmer series, 618 Banking of road, 140 Bar (unit), 195 Bar magnet, 391, 394, 438 Barlow's wheel, 407 Battery, 371

emf,378 internal resistance, 378 See also Cell

Beam: collimated, 512 electron, 360, 361, 401, 461 light, 512 particle, 400, 401, 663 photon, 600, 603 proton, 405 splitter, 548

Beats, 287 Becquerel (unit), 657 Bel (unit), 313 Bernoulli's principle, 202 Beta decay, 653 Betatron, 461, 467 Bifilar pendulum, 283 Bifilar torsion pendulum, 171 Bimetallic thermometer, 209 Binoculars, 519

683

684

Biot-Savart law, 421 Black hole, 188 Block-and-tackle, 56 Blue shift, 588 Bohr model, 624 Bohr radius, 627 Bohr periodic table, 637 Boiling point, 219

table, 220 Boltzmann constant, 238 Bomb, hydrogen, 661 Bomb, nuclear, 662 Boyle's law, 234 Brackett series, 619 Bradley's measurement of light speed, 591 Bragg's diffraction condition, 550 Bremsstrahlung, 601 British thermal unit (Btu), 215 Brownian motion, 228 Btu: see British thermal unit Buoyancy, 198

Cable, coaxial, 431 Calorie: see Kilocalorie Calorimeter, 218 Camera, 524, 562

pinhole, 562 Capacitance, 355 Capacitor, 353, 479

circuits: see CR loop, CL loop, CRL loop

electrolytic, 355 energy of, 358 series of parallel, 357

Carbon dating, 657 Carnot cycle, 260 Cathode, 360, 599, 601 Cathode rays, 361 Cathode tube, 361 Cavendish experiment, 181, 295 Cell,384 Celsius temperature scale, 213 Center of curvature, 521 Center of gravity, 154 Center of lens, 521 Center of mass, lll, 158, 160

frame: see Collision, zero-momentum for various shapes, 113, 114 motion of, 114, 117

Centigrade scale, 213 Centrifugal force, I3I Centrifuge, 133, 139 Centripetal acceleration, 130

at the equator, 132 Centripetal force, 130 Cgs system (energy), 77 Charge, 319

conservation of, 321, 378, 652 electric force on, 322, 326 electron, 324, 362, 385

Charge (Cont.) hollow spherical, 334, 363 induced, 325, 352 infinite sheet, 340 long straight wire, 355 magnetic force on, 397 quantized, 324, 362

Charge-to-mass ratio, 400, 401 electron, 401 proton, 402

Charles' law, 212, 234 Chemical energy, 384 Circuit, 375

ac, 469, 478 dc, 371 oscillating, 475 resonant, 481, 483 See also Coil; Loop (current)

Circuital law: see Am~re's law Circular motion, 125

nonuniform, 132, 134 uniform, 127, 279

Circular aperture, 562 Circular polarization, 495 CL loop, 475, 482 Classical physics, 595, 611 Clock,8

cesium, 9 CLR loop, 477, 480, 481, 483 Coaxial cable, 431 Coefficient

of expansion, 221 table, 222

of friction, 59, 61 of performance, 270

Coherent wave, 560 Coil, 409, 456

Helmholtz, 445 search,467 snatch,467 toroidal, 448, 474 torque on, 410

Collimated beam, 512 Collision

elastic, 107 head-on, 108 inelastic, 106, 218 off -center, 11 0 zero-momentum, 107

Color, 503 Combustion, heat of, 221

table, 222 Commutator, 412, 457 Compass, 392, 396,411 Component of a vector, 28 Compressibility, 197, 227, 246 Compression: see Expansion Compton effect, 603, 611 Compton scattering, 603 Compton wavelength, 605 Concave, 521

Conduction electric, 381 thermal, 215, 265, 386

Index

Conduction electrons, 349, 382, 408, 413 Conductivity

electric, 382 thermal, 386

Conductors, 321, 349 Conic section, 184 Conical pendulum, 132 Conservation

angular momentum, 160, 166, 184 charge, 321, 378, 652 energy, 75, 78, 87,91,95,216,378,

452, 605, 658 linear momentum, 103, 605 mass, 48 nucleons, 652

Conservative force, 84 Constants, table, 677 Constructive interference, 544 Convection, 216 Converging lens, 521 Converging mirror, 529 Conversion table, units, 675 Convex, 521 Coordinate, 8 Core, iron, 439, 454, 458 Correspondence principle, 628, 645 Cosmic rays, 657 Coulomb (unit), 323 Coulomb's law

electric, 322, 326 magnetic, 392

Couple, 157 Covalent radius, 229 CR loop, 380 Creation, 654 Critical force, 165 CRL loop, 477, 480, 481, 483 Cross product, 165, 398, 408, 423, 671 Crystal, 227

lattice, 550 Curie (unit), 657 Current, 371

alternating: see ac amplitude, 478 balance, 433 density, 383 direct: see dc ,direction of, 372, 379 displacement, 489 eddy, 453 element, 407, 421 induced, 451, 453 rms,481 rule, 378

Curvature, 533 center of, 521 radius of, 521

Cutoff frequency, 602

Index

Cycle, 279

Carnot,26O Cyclic process, 256 Cyclotron, 405

frequency, 404

D'Arsonvai galvanometer, 411 Ds (also dees) of cyclotron, 406 Dalton's law, 236 Damped oscillations, 477, 483 Damped resonance, 482 Damping, 291

circuit, 477, 481 Daniell cell, 384 Data, 1 Dating, radiocarbon, 657 Daughter nucleus, 652 Davisson-Germer experiment, 607 Day, mean solar, 10 dc, 371

circuit, 371 generator: see Faraday's wheel motor, 412

De Broglie wavelength, 606 Decay

alpha, 653 beta, 653 constant, 655 exponential, 381, 474, 478, 656 gamma, 654

Deceleration, 20 Decibel, 313

table, 314 Dees of cyclotron: see Ds of cyclotron Deflection, by a prism, 516, 537, 538 Density, 196

current, 383 energy

electric, 359 magnetic, 472

lines, 329, 394 mean, 205 table, 198 water, 221

Derivative, 16 second, 18 vector, 33, 129

Destructive interference, 544 Determinism, 64 Deuterium, 648, 660 Deuteron, 660 Deviation: see Deflection Diatomic gas, 241 Dichroism, 566 Dietary calorie, 222 Diffraction, 552, 563

Bragg, 550 circular aperture, 562 electron, 607 Fraunhofer, 555 Fresnel, 555

Diffraction (Cont.)

fringes, 546, 549, 558, 562 grating, 555 one-slit, 558 two-slit, 553 Young, 553 x-ray, 550

Dilation, time, 585 Dimensions, 22, 300 Dipole

electric, 327, 338 magnetic, 396, 410

Direct current: see dc Direction (vector), 29 Dirod, 325 Disc dynamo: see Faraday's wheel Discharge, gas, 617, 622, 623 Dispersion, 300, 516 Displacement

angular, 282 current, 489 linear, 15, 273 vector, 24

Dissipation, Joule, 375 Dissipative force, 86 Distance, 4

spectrum, 6 Diverging

lens, 521 mirror, 532

Doppler effect, 306, 588, 589 Dot product, 79 Drag, magnetic, 453 Drift velocity, 382 Driving frequency, 290 Duration, 10 Dynamics, 45 Dynamo, 456, 467

disc: see Faraday's wheel Dyne, 47

E field: see Electric field Earth

weighing the, 181 circumference of, 4 magnetic field, 395

Eddy currents, 453 Effective

gravity, 62, 133 weight, 63

Efficiency of a heat engine, 258, 260, 261 Einstein's equation

mass-energy, 583, 658 photoelectric, 597

Elastic collision, 107 Elastic force, 273 Elastic limit, 275 Elastic potential energy, 275 Electric and magnetic fields, motion in,

399 Electric field, 326

Electric field (Cont.)

energy, 359 hollow sphere, 334 induced, 459 infinite sheet, 340 line, 328 long straight wire, 335 motional, 450 point charge, 326 uniform, 331

Electric battery, 371 cell, 384 charge, 319 conductivity, 382 current, 371 dipole, 327, 338 field: see Electric field flux, 330 force, 319, 323 intensity: see Electric field potential, 343 power, 374 resistivity, 382

table, 382 shielding, 341

Electrical: see Electric Electricity, 319 Electrode, 360, 384, 596 Electrodynamics, 491 Electrolyte, 384 Electrolytic capacitor, 355 Electromagnet, 439 Electromagnetic

induction: see Magnetic induction theory, 491 waves, 489

energy, 495 intensity, 497 momentum, 498 spectrum, 500, 502, 503 speed, 413, 494

Electrometer, 356 Electromotive force

back,467 battery, 378 induced, 451, 454 motional, 451

Electron, 163, 322 charge, 324, 362, 385 charge-to-mass ratio, 400, 401 conduction, 349, 382, 408, 413 diffraction, 607 drift velocity, 382 emission, 360, 596 gun, 360 magnetic moment, 438 microscope, 615 momentum, 361 shells, 634, 638 smallness, 641

685

686

Electron (Cont.) spin,437 states, 628 volt, 360 wave, 606

Electroscope, 321 Electrostatic

generator, 325, 353 induction, 325 See also Electric

Electrostatics, 319 Elements, periodic table, 636, 637 Ellipse, 184 Elongation, 273 Emf: see Electromotive force Energy, 75

capacitor, 358 conservation, 75, 78, 87, 91, 95, 216,

375, 378, 452, 605, 658 density, electric, 359 density, magnetic, 472 elastic, 275 'electromagnetic, 495 fission, 661 fusion, 659 general definition, 95 gravitational, 76, 185, 188 harmonic oscillator, 283 inductor, 472 internal, 158, 241 ionization, 624 kinetic, 76, 84, 145 level,620

hydrogen, 623 mass, 583, 658 metastable, 622

mechanical, 76 nuclear, 658 potential, 76, 116, 275 rotational, 158, 164, 241 spectrum, 669 translational, 158, 164, 238, 241 vibrational, 241, 283

Engine heat, 256 reversible, 259, 260

Entropy, 262 mixing, 271

Equation of state, ideal gas, 235 Equilibrium, 50, 154

neutral, 95 rotational, 154 stable, 95, 116 thermal, 209 translational, 154 unstable, 95

Equipartition of energy, 239 Equipotential surface, 347 Equivalence, principle of, 19 Erect image, 52!! Erg, 77

Escape, speed of, 187 Ether, 577 Excited state, 629, 654 Exclusion principle, 635 Expansion

adiabatic, 253, 254 free, 255, 266 isothermal, 234, 251 thermal, 212, 221

table, 222 water, 221 work from, 249 See also Process

Explosion, 107, 115 Exponential, 202

decay, 381, 474, 478, 656 External force, 105 Eye, resolution of, 574 Eyepiece, 527

Newtonian mounting, 531

Fahrenheit scale, 213 Fall

vertical free, 18 nonvertical free, 34

Farad,355 Faraday (unit), 385 Faraday's ice pail, 352 Faraday's law, 454, 460 Faraday's wheel, 465 Fermi (unit), 6, 647, 650 Fermi's reactor, 662 Ferromagnetism, 438 Fiber optics, 519 Field: see Electric field; Magnetic field Field ion microscope, 228, 359 Field line

electric, 328 magnetic, 394

Films, thin, 544, 547, 560 nonreflective, 545

Filter, polarizing, 565 Fine-structure constant, 628 First law

of Newton, 45 of thermodynamics, 251

Fission, nuclear, 661 Fizeau's measurement of light speed, 592 Flow diagram (heat engine), 257 Fluid, 193 Fluorescent lamp, 623 Flux

electric, 330 line: see Field line magnetic, 394, 437, 455

Flywheel, 148, 161, 163 Focal length

lens, 522, 534 mirror, 529, 535 thin lenses in combination, 526

Focal plane, 524

Focal point lens, 523 mirror, 529, 530

Focus, 184 Foot: see Inch Foot-pound, 77 Force, 46

addition, 50 centrifugal, 131 centripetal, 130 combination, 50, 156 conservative, 84 critical, 61 dissipative, 86 elastic, 273 equilibrium, 50, 157 external, 105 fluid, 193 hydrostatic, 194 line of: see Field line nonconservative, 86 normal, 58, 193 restoring, 273 shearing, 193 spectrum, 50 transmission of, 54 transverse, 85

Force between bar magnet and coil, 425 bar magnet and loop, 428 capacitor plates, 356 magnet poles, 391 parallel wires, 427 point charges, 322 solenoid and loop, 438

Force constant: see Spring constant Force on

current element, 407 moving charge, 397

Index

Forced harmonic motion: see Resonance Forcemeter, 48 Formulas, mathematical, 673 Fourier's theorem, 286 Frame

inertial, 46 reference, 45

Fraunhofer diffraction, 555 Fraunhofer lines, 623 Free expansion, 255, 256 Free fall, vertical, 18 Free path, mean, 247 Freezing point, 213, 214; see also Ice

point; Melting point Frequency, 127, 279, 299, 310, 500

acoustic, spectrum, 287 angular, 279, 300 circular, spectrum, 133 cutoff,602 cyclotron, 404 driving, 290 LC loop, 476

Index

Frequency (Cont.) natural, 280, 290, 310 resonant, 290 threshold, 597

table, 598 Fresnel diffraction, 555 Friction, 59, 61, 86, 89 Frictionless plane (or surface), 46, 58 Fringes, 546

width of, 558 'Wung's, 553

Fundamental frequency, 286, 310 Fusion

heat of, 219 table, 220

nuclear, 659 controlled, 660 Sun, 660

g, 19 spectrum, 19

Galilean relativity, 38 Galvanometer, 379, 411

ballistic, 467 d'Arsonval, 411

Gamma decay, 654 Gamma rays, 502 Gas

constant, 234 discharge, 560, 617, 622, 623 thermometer, 211

Gases diatomic, 241 heat capacity, 242, 252 ideal, 210, 233 kinetic theory, 236, 243 monatomic, 241 polyatomic, 241

Gauge, tire, 245 Gauge pressure, 195 Gauss (unit), 395 Gauss' law

electric, 332 magnetic, 436

Gay-Lussac's law, 235 General relativity, 188 Generator

ac: see Dynamo dc: see Faraday's wheel electrostatic, 325, 353 homopolar, 465 MHD,450 Van de Graaff, 353

Geometrical optics, 511 Geosynchronous, 190 Governor, 140 Graph, linear, 15 Grating

diffraction, 555 reflection, 557 replica, 556

Grating (Cont.) resolution of, 573 spectrometer, 557

Gravitation, Newton's law of, 177 Gravitational

constant, 178, 176, 181 potential energy, 76, 185, 188

Gravity, 19, 85, 175 acceleration of, 19 artificial, 133 center of, 154 effective, 62, 133 specific, 197 from spheres, 179

Greek alphabet, 679 Ground state, 621 Gun

electron, 360 rail, 436

Half-life, 655 Harmonic motion, 278

angular: see Rotational oscillation forced: see Resonance linear, 278

Harmonics, 285, 310 Head-to-tail method, 24 Heat, 215, 217, 251

capacity, 218, 242, 252 combustion, 221

table, 222 engine, 256 fusion, 219

table, 220 mechanical equivalent, 216 pump, 261, 270 specific, 217

table, 218 vaporization, 220

Heating, Joule, 375 Heisenberg uncertainty principle, 609 Helical motion in B field, 406 Helmholtz coils, 445 Henry (unit), 462, 471 Hertz (unit), 128, 279 Homopolar

generator, 465 motor, 407

Hooke's law, 273, 280 Horizontal range, 37 Horsepower, 83 Hour, 9, 10 Hovercraft, 205 Humidity, relative, 247 Huygens'

construction, 553 wavelets, 553

Hydraulic jack, 206 Hydrogen

atom, 338 atom model, 624

Hydrogen (Cont.) bomb,66O levels, 623, 624, 636 spectrum, 617

Hydrometer, 207 Hydrostatic force, 194

Ice point, 213 Ideal gas, 210, 233 Image, 519

distance, 522 erect, 525 intensity, 539 inverted, 524 point, 520 real,520 virtual, 520

Impact parameter, 110 Impedance, 480 Impulse, 119, 237 Incandescent lamp, 374, 375, 481 Inch, 5 Incidence

angle of, 514 plane of, 513, 517

Incident ray, 513 Inclination, magnetic, 391 Inclined plane, 58, 60 Incoherent: see Noncoherent Indeterminacy: see Uncertainty Index of refraction, 514

table, 515 gas, 571

Induced charge, 325, 352 current, 451, 453 electric field, 459 emf, 451, 454

Inductance, 470 mutual, 457, 462 self-, 470

Induction electrostatic, 325 Faraday's law of, 454, 460 magnetic, 449, 459

Inductor, 470, 479 energy in, 472

687

series and parallel connection, 472 Inelastic collision, 106, 218 Inertia, 47

law of, 45 moment of, 144, 159, 162

for various shapes, 146 Inertial frame, 46 Infrared, 502 Initial value, 13, 64

projectile, 35, 36 Inner product, 79 Insulator, 321 Integral, 82

688

Intensity, 313 electric: see Electric field image, 539 level, 313

table, 314 light, 498, 504 magnetic: see Magnetic field reflection, 569 wave, 497

Interactions, weak, strong, 654 Interference, 287

films, 544, 547, 560 fringes, 546 slits: see Diffraction

Interferometer, Michelson, 548, 578 Internal combustion, 256 Internal energy, 241 Internal reflection, total, 518 Internal resistance, 378 International System (of units), 5 Inverse-square law, 175, 177, 180 Inverted image, 524 Ion microscope, field, 359 Ionization

energy, 624 potential, 624

Iron core, 439, 458 spectrum, 620

Irreversible, 264 Isothermal process, 234, 252, 254 Isotherms, 234, 254 Isotope, 229, 648

Jack, hydraulic, 206 Jerk, 18 Jet propulsion, 110 Joule (unit), 77 Joule's experiment, 216 Joule

dissipation, 375 heating, 375

Junction rule, 378 Jupiter, 183

Kelvin temperature scale, 230, 262 Kepler's rules, 182, 184 Kilocalorie, 215, 216 Kilogram, 47 Kilometer, 5 Kilomole, 232 Kilowatt-hour, 83 Kinematics, 13 Kinetic energy, 76, 158

translational, 158, 238 Kinetic theory of gases, 236 Kirchhoff's rules, 378 Kundt tube, 318

Laminar flow: see Streamline flow Laminated core, 454, 459

Lamp fluorescent, 623 incandescent, 374, 375, 481

Laser, 553, 560, 622 Latent heat: see Fusion; Vaporization Lateral magnification, 524 Lattice, crystal, 550 LC loop, 475, 482 LCR loop, 477, 480, 481, 483 Leiden jar, 353 Length measurement, 550 Lens, 519, 521

center of, 521 converging, 521 diverging, 521 equation, 522, 533 focal length of, 522, 534 focal point of, 523 power of, 522, 526 thin, 522, 526

Lensmaker's formula, 534 Lenz's rule, 456, 470 Levels

energy, 620 hydrogen, 623 metastable, 622

Lever, 93, 168 arm,151

Life, mean, 655, 666 Light, speed of, 413, 492, 514, 581, 591,

592, 593 Light year, 6 Light

bulb: see Lamp, incandescent intensity, 498, 504 ray, 51l wave, 500

Limit of resolution: see Resolution Line, spectral, 617 Line of action, 152 Linear

expansion, coefficient of, 221 table, 222

graph, 15 motion: see One-dimensional motion polarization, 495, 565

Load,374 Logarithmic scale, 7 Longitudinal waves, 303 Loop (current), 409

circular, 423 hexagonal, 446 LC, 475, 482 RC,380 rectangular, 409, 446 RL,473 RLC,477 rule, 378 square, 446 torque on, 410

Loop (wave), 309

LR loop, 473 LRC loop, 477, 480, 481, 483 Lyman series, 618, 619

Macroscopic, 227 Magnet

bar, 391, 394, 438 permanent, 392

Index

Magnetic and electric fields, motion in, 399

Magnetic field, 393, 398 bar, 394 current, 421 curved wire, 427 Earth,395 line, 394 long straight wire, 425, 439 loop, 423 motion in, 402 moving point charge, 507 rotating, 486 uniform, 396

Magnetic bottle, 406 dipole, 396, 410 drag, 453 energy density, 472 field: see separate entry flux, 394,437, 455 force on charge, 397 force on current, 407 inclination, 391 induction, 449, 459 intensity: see Magnetic field lens, 407 moment, 396, 410 monopoles, 393 poles, 391, 392, 397, 436 pressure, 435 quantum number, 631

Magnetism, 391, 437 Magnetohydrodynamic generator, 540 Magnification, 524, 527, 530

angular, 531, 541 lateral, 524 microscope, 527 magnifier, 524 telescope, 531, 541

Magnifier, 524 Magnifying glass, 524 Magnitude

order of, 7 vector, 24, 28

Malus' law, 565 Manometer, 194, 206 Mass, 47

center of, Ill, 158, 160 conservation, 48 dynamic comparison, 48 Earth, 181 spectrometer, 400, 404

Index

Mass (Cont.)

spectrum, 49 standard, 47

Mass-energy relation, 583, 658 Mathematical formulas, 673 Matter, amount, 48 Maxwell

displacement current, 489 electromagnetic theory, 491

Mean free path, 247 Mean life, 655, 666 Measurement, 1 Mechanical

advantage, 57 equivalent of heat, 216

Mechanics, 45 Medium of propagation, 303 Megawatt, 83 Melting point, 219

table, 220 Mendeleyev table, 637 Mercury

barometer, 201 millimeter of, 201 thermometer, 209

Meter, 4 defined, 582

Metric System, 4 MHD generator, 450 Michelson interferometer, 548, 578 Michelson-Morley experiment, 577 Microscope, 527

electron, 615 field ion, 229, 359 resolution of, 528, 565, 615 scanning tunneling, 228, 229

Microscopic, 227 Microwaves, 502 Millikan's experiment, 362 Minimum defiection, 538 Mirror

converging, 529 diverging, 532 equation, 530 focal length of, 529, 535 focal point of, 529, 530 parabolic, 531 plane, 528 spherical, 529

Mixing, 271 Mks: see Units Moderator, 662 Modern physics, 595 Moire pattern, 288 Mole: see Kilomole Molecular

speed,239 weight, 230

Molecules, 227 Moment

arm, 152

Moment (Cont.)

inertia, 144, 159, 162 for various shapes, 146

magnetic, 396, 410 electron, 438

Momentum, 103 angular, 161, 164

conservation, 161, 166 spectrum, 163 vector, 165

electromagnetic, 498 electron, 361, 605, 607 linear (= ordinary), 103

conservation, 103, 605 uncertainty, 609

Monatomic gas, 241 Monochromatic wave, 504 Monochromatic x rays, 552 Monopoles, magnetic, 393 Moon, 133, 138, 180 Moseley's law, 638 Motion

Brownian, 228 circular, 125 harmonic, 278 linear: see Motion, one-dimensional nonuniform circular, 132, 134 one-dimensional, 15 perpetual, 70, 171, 206 in a plane, 30 planetary, 182 projectile, 34 uniform, 13, 34 uniform circular, 127, 279 uniformly accelerated, 19

Motional emf, 451 Motional electric field, 450 Motor

ac, 469, 486 dc, 412 homopolar, 407

Muon, 593 Mutual inductance, 457, 462 Myopia: see Nearsightedness

Nanometer, 6 Natural frequency, 280, 289

string, 310 Natural period, 280 Near distance, 525 Nearsightedness, 526 Neutral equilibrium, 95 Neutrino, 653 Neutron, 647, 648

mass, 650 number, 648 star, 19, 197

Newton (unit), 47 Newton

first law, 45 law of gravitation, 177

Newton (Cont.)

pail, 136 rings, 546 second law, 46, 104, 117 third law, 53, 162

Newtonian eyepiece mounting, 531 Node, 309 Nonconservati ve force, 86 Nonrefiecting films, 545

689

Nonuniform circular motion, 132, 134 Normal (line), 513 Normal force, 58, 193 Nuclear

bomb,662 energy, 658 fission, 661 fusion, 659 reactions, 658 reactor, 647, 662 structure, 647 See also Nucleus

Nucleon, 648, 651 Nucleons, conservation of, 652 Nucleus

charge; 648 charge density, 651 density, 650 mass, 648, 659

table, 650 size, 649, 663 See also Nuclear

Nuclides, 648 stable, chart, 649

Null experiment, 52 Numerical constants, table, 677

Object distance, 522 point, 520 virtual, 529

Objective, 527 Octave, 286 Ocular: see Eyepiece Ohm (unit), 373 Ohm's law, 372

thermal, 386 Oil drop experiment, 338, 362 Omegatron, 417 Optic

axis, 521, 529 fiber, 519

Optics geometrical, 511 quantum, 595 wave, 543

Orbit Bohr model, 627 circular, 182 elliptic, 184 in E and B fields, 399, 402

Orbital quantum number, 631

690 Index

Order of magnitude, 7 Photon, 595, 598, 605 Pressure (Cont.) Organ pipe, 311 beam, 600, 603 atmospheric, 195, 197,202,269 Oscillating circuit, 475 energy, 599, 600 gauge, 195

damped, 477, 483 momentum, 605, 606 magnetic, 435 steady-state, 478 rest mass, 603 partial, 236

Oscillation, 273 Physical pendulum, 295 sound, 305 rotational, 282 Pinch effect, 428 spectrum, 197

Overhead projector, 541 Pinhole, 512 Primary winding, 459 Overtones: see Harmonics camera, 562 Principal quantum number, 631

Pipe, vibration in, 311 Principle of equivalence, 19 P.s.i., 195 Pitch, 286 Prism Parabola, 16, 21, 35, 136, 184 Pitot tube, 204 deflection by, 516, 537, 538 Paraboloid, 136 Planck's constant, 595, 597 dispersion by, 516

Parallel Plane reflecting, 519 resistors in, 376 frictionless, 46, 58 Process (gas, summary), 256

capacitors in, 357 incidence, 513, 517 Projectiles, 34 inductors in, 472 mirror, 528 initial value problem, 36

Parallel-axis theorem, 159 vibration, 494 Projector, overhead, 541 Parallelogram method, 25 wave, 493 Proton, 402, 405, 407, 624, 648 Paraxial rays, 523 Planetary motion, 182 Pulley, 56 Parent nucleus, 652 Plasma, 428, 660 PV diagram, 234 Partial pressure, 236 Points, effect of, 353 Particle, 8, 56 Polarization of wave, 494, 565 Quantization

beam, 400, 401, 663 circular, 495 of angular momentum, 629 Pascal (unit), 195 linear, 495, 565 condition for hydrogen, 625 Pascal's principle, 200 partial, 565 energy, 620

Paschen series, 618, 619 Polarizing filter, 565 Quantum, 595

Pauli exclusion principle, 635 Polaroid, 565 action, 597 Pellat current balance, 433 Poles, magnetic, 391, 392, 397,436 charge, 324, 362

Pendulum Polyatomic gas, 241 efficiency, 601 ballistic, 120 Position, 7 mechanics, 608 bifilar, 283 angular, 126 number, 626, 628

conical, 132 uncertainty, 609, 610 magnetic, 631

physical, 295 vector, 30 orbital, 631 simple, 277, 282, 295 Positron, 418, 654, 667 principal, 631 torsion, 171, 295 Potential spin, 632

Performance, coefficient of, 270 absolute measurement, 356 state, 628 Period, 128,177,279,280,299 difference, 345, 354 transition, 620

natural, 280 ionization, 624 Quark, 324, 651 Periodic table, 637 point charge, 343 Permanent magnet, 392 spherical shell, 347 Radar, 502 Perpendicular-axis theorem, 171 stopping, 596 Radial acceleration, 134, 136 Perpetual motion, 70, 171, 206 Potential energy, 76, 116, 275 Radian, 126

Pfund series, 619 elastic, 275 Radiation, 216; see also Decays; Rays;

Phase gravitational, 76, 185, 188 Waves

angle, 279 Potentiometer, 379 Radio waves, 501, 502 difference, 544 Pound force, 47 Radioactivity, 652 relative, 287 Power, 82, 149 Radiocarbon dating, 657 shift, 478 ac,480 Radius transition, 219 dc, 374 of curvature, 521 vector, 129, 280 from dynamo, 467 gyration, 167

Phasor, 129 electric, 374 orbit, 403, 627 Photocathode, 596 factor, 481 Rail gun, 436

Photocurrent, 596 lens, 522, 526 Range of a projectile, 37 Photoelasticity, 569 spectrum, 669 Rate of change, 17 Photoelectric effects, 596 wave, 306, 312 vector, 33, 129 Photoelectric equation, 597, 599 Powers of ten, 3 See also Derivative Photoelectric tube, 596 Poynting vector, 496 Ray, 511 Photoelectron, 596 Precision, 3 diagram for lens, 523 Photoemission, 596, 644 Prediction, 2 diagram for mirror, 529

table of thresholds, 598 Pressure, 194, 305 incident, 513

Index 691

Ray (Cont.) Resolution (Cont.) Series optics, 511 electron microscope, 615 capacitors in, 357 retlected, 517 eye, 574 inductors in, 472 refracted, 513 grating, 573 resistors in, 376 See also Rays light microscope, 565 spectral, 617

Rayleigh's criterion, 563 telescope, 563 triboelectric, 320 Rays Resonance, 288, 481, 483 Shells, atomic, 635

alpha, 653 Resultant, 50 Shielding, electric, 341 beta, 653 Reversible, 259, 260, 262, 263 Shift cathode, 361 Revolution, 125, 128 blue, 588 cosmic, 657 Right-hand rule, 397, 422, 494, 671 Doppler, 588, 589 gamma, 502, 654 Rigid body, 91, 96, 144 phase, 478 Roentgen, 601 RL loop, 473 red,588 x,601 RLC loop, 477, 480, 481, 483 violet, 588

RC loop, 380 Rrns,239 SI, 5; see also Units RCL loop, 477, 480, 481, 483 Rocket, 52, 110 Significant figures, 2 Reaction, 53, 162 Rod, 54 Simple pendulum, 277, 282, 295 Reactions, nuclear, 658 Roemer's measurement of light speed, 593 Slit Reactor, 657, 662 Roentgen rays: see X rays double, 553 Real image, 520 Rolling, 61, 158, 172 single, 558 Red shift, 588 Root-mean-square, 239, 481 Slope of a graph, 15, 16 Reference Rotating Snatch coil, 467

frame, 45, 46 B field, 486 Snell's law, 513 level, 76 drum experiment, 241 Solenoid, 432, 438, 471, 473

Retlected pail, 136 Sonogram, 574 ray, 517 Rotation, 143 Sound, 284, 304, 313 intensity, 569 Rotational intensity, 313

Retlecting energy, 145, 158, 164, 241 level, 313 prism, 519 equation of motion, 165 frequency spectrum, 287 telescope, 530, 541 equilibrium, 154 power, 306

Retlection, 517 oscillation, 282 pressure, 305 angle of, 517 Rough surface, 59 speed, 14, 305 grating, 557 Rpm, 128 Special relativity, 577 intensity, 569 Rutherford postulates, 581 total internal, 518 atom model, 663 Specific gravity, 197 waves, 308 scattering, 663 Specific heat, 217

Refracted ray, 513 Rydberg constant, 643 table, 218 Refraction, 512 gases, 242, 252

angle of, 514 Saccadic movement, 169 Specific impulse, III atmospheric, 538 Sagittal theorem, 533 Spectra, 681 index of, 514 Satellite, 131, 139, 190 Spectral: see Spectrum

table, 515 geosynchronous, 190 Spectrograph: see Spectrometer gas, 571 Saturated vapor, 247 Spectrometer, 504

Refrigerator, 259, 261 Scalar, 26 grating, 557 Relative product, 79 mass, 400, 404

humidity, 247 Scale, logarithmic, 7 Spectroscope: see Spectrometer velocity, 32, 581, 590 Scanning tunneling microscope, 228, 229 Spectrum

Relativity, 577 Scattering, 503 absorption, 623 Galilean, 38 alpha particles, 663 electromagnetic, 500, 502, 503 general, 188 Compton, 603 hydrogen, 617 postulates, 581 photons, 603 iron, 620 special, 577 Thomson, 642 line, 617

Replica grating, 556 Rutherford, 663 series, 617 Resistance, 373 Schwarzschild radius, 188 visible, 503 Resistivity, 382 Search coil, 467 x-ray, 602, 640

table, 382 Second, 8, 10, 620 Speed, 14 thermal, 386 Second law electromagnetic waves, 413, 494

Resistor, 373 of Newton, 46, 104, 117 escape, 187 series or parallel connection, 376 of thermodynamics, 258, 265 radio signal, 14

Resolution Secondary winding, 459 sound, 14, 239, 305 of camera, 563 Self-inductance, 470 spectrum, 14

692

Speed (Cont.) light, 14, 413, 492, 514, 581, 591, 592,

593 Spin

of electron, 437 quantum number, 632

Spring balance, 47 constant, 273, 277 ideal, 273 loaded, 274, 290 scale, 47

Stable equilibrium, 95, 116 nuclides, chart, 649

Standard distance, 4 length, 4 mass, 47 temperature and pressure, 233

Standing wave, 308, 311, 507, 610, 622 State, quantum, 628 Steam engine, 256 Stopping potential, 596 STp, 233 Streamline flow, 203 String, 54

natural frequencies, 310 waves in, 297

Strong interaction, 654 Sublimation, 219 Sun, 49, 50, 133, 138, 163, 176, 183, 197 Superconductivity, 382 Superposition, 178, 236, 285, 308, 311,

324,327,344,347,421 Surface

concave, 521 convex, 521 equipotential, 347 frictionless, 46, 58 rough,59

Symbols, 3 Synchronization, 586 Systeme international, 5

Tables, 681 Tangential

acceleration, 134, 136 velocity, 127

Telescope angular magnification of, 531, 541 reflecting, 530, 541 refracting, 540 resolution of, 563

Temperature, 209, 212 absolute or Kelvin, 213, 238, 262 spectrum, 214

Tension, 54 Tesla (unit), 394 Theories, 1 Thermal conductivity, 386

Thermal expansion, 212, 221 table, 222

Thermal resistivity, 386 Thermodynamic temperature, 262 Thermodynamics, 209

first law, 251 second law, 256, 265 zeroth law, 210

Thermometer, 209. bimetallic, 209 gas, 211 mercury, 209

Thick wire, 431, 441 Thin lens, 522, 526 Thin film, 544, 547, 560 Third law of Newton, 53, 162 Thomson

atom model, 663 elm determination, 401 scattering, 642

Threshold of hearing, 314 Thrust, 52, 110 Time, 8

flight, 22 spectrum of intervals, 9

Time constant of RC loop, 380 of RL loop, 474

Time dilation, 585 Tire gauge, 245 Toroidal coil, 448, 474 Torque, 148, 150

bar magnet, 396 coil, 410 electric dipole, 338 gravity, 153 loop, 409 restoring, 277 vector, 164

Torr, 201 Torricellian vacuum, 197 Torsion

balance, 181, 295 pendulum, 171, 295

Torsional wave, 304 Total internal reflection, 518 Trajectory, 35; see also Orbit Transient, 478 Transition, quantum, 620 Translational energy, 158, 164, 238, 241 Translational equilibrium, 154 Transmission grating: see Grating Transmission

of force, 54 of torque, 168

Transverse force, 85 Transverse magnification: see Lateral

magnification Transverse waves, 303 Threshold frequency, 597

table, 598

Triboelectric series, 320 l1"iple point, 212 1Htium, 648, 653 Thrbine, 120, 122 1\vin paradox, 587

Ultracentrifuge, 133 Ultraviolet, 502 Uncertainty, 3

principle, 609 Uniform

circular motion, 127, 279 field, 331, 396 motion, 13, 34

Uniformly accelerated motion, 19 Units, 5, 22

British gravitational, 77 cgs, 77 conversion table, 675

Index

electric and magnetic, 412, 444, 455 International System, 5

Universe, age, 9 Unpolarized light, 567 Unstable equilibrium, 95

Vacuum, Torricellian, 197 Van Allen belts, 407 Van de Graaff generator, 353 Van der Waals radius, 229 Vaporization, heat of, 220 Vector, 23

acceleration, 33 angular momentum, 164 cross product, 165, 398, 408, 423, 671 derivative of, 33, 129 difference, 25 displacement, 24 dot product, 79 force, 47 momentum, 103 phase, 129, 280 position, 30 sum, 25 torque, 164 unit, 98 velocity, 30, 129

Velocity, 13, 30 angular, 127 average, 41 drift, 382 instantaneous, 17 relative, 32, 581, 590 tangential, 127 vector, 30, 129 See also Speed

Vertical free fall, 18 Very Large Array, 564 Very long baseline interferometry, 574 Vibration, 273

plane of, 494 Vibrational energy, 241, 283

Index 693

Violet shift, 588 Wave (Cont.) Waves (Cont.) Virtual image, 520 packet, 560 ultraviolet, 402 Virtual object, 529 period,299 See also Wave Visible spectrum, 503 plane, 305, 493 Weak interaction, 654 Volt, 344, 346 polarized, 494, 565 Weber (unit), 395 Voltage, 354 power, 306, 312 Weighing, 51

amplitude, 478 pressure, 305 Weight, 48 rule, 378 reflection, 308 effective, 63

Voltmeter, 375 speed, 299, 300 Width, fringe, 558 standing, 308, 311, 507, 610, 622 Winch,99

Waste, 262 torsional, 304 Wire, thick, 431, 441 Water transverse, 303 Work, 78, 83, 149

changes of phase, 219 traveling, 297 energy theorem, 84 density of, 197, 221 water, 303 expansion, 249 waves, 303 See also Waves integral, 82

Watt (unit), 82, 374 Wavelength, 299, 500 Wave, 492 de Broglie, 606, 610 X rays, 502, 601

coherent, 560 threshold, table, 598 diffraction, 550 equation, 302 Wavelets, Huygens, 553 spectrum, 602, 640 frequency, 299 Waves, 492 front, 511 electromagnetic, 492 Yard,5 function, 606 spectrum, 502 Year, 9 intensity, 498, 504 electron, 606 Young longitudinal, 303 infrared, 502 experiment, 553 noncoherent, 560 light, 489, 543 fringes, 553 number, 643 radar, 502 optics, 543 radio, 502 Zero, absolute, 212