$M_{e}$	Mass of the earth	$5.98 \times 10^{24} kg$
$R_{e}$	Radius of the earth	$6.37 \times 10^{6}$ m
$g$	Free-fall acceleration on earth	$9.80 m / s^{2}$
$G$	Gravitational constant	$6.67 \times 10^{- 11} N m^{2} / k g^{2}$
$k_{B}$	Boltzmann’s constant	$1.38 \times 10^{- 23} J / K$
$R$	Gas constant	$8.31 J / mol K$
$N_{A}$	Avogadro’s number	$6.02 \times 10^{23} particles / m o l$
$T_{0}$	Absolute zero	$- 273 ° C$
$σ$	Stefan-Boltzmann constant	$5.67 \times 10^{- 8} W / m^{2} K^{4}$
$p_{atm}$	Standard atmosphere	101,300 Pa
$v_{sound}$	Speed of sound in air at $20 ° C$	$343 m / s$
$m_{p}$	Mass of the proton (and the neutron)	$1.67 \times 10^{- 27} kg$
$m_{e}$	Mass of the electron	$9.11 \times 10^{- 31} kg$
$K$	Coulomb’s law constant $(1 / 4 π ε_{0})$	$8.99 \times 10^{9} N m^{2} / C^{2}$
$ε_{0}$	Permittivity constant	$8.85 \times 10^{- 12} C^{2} / N m^{2}$
$μ_{0}$	Permeability constant	$1.26 \times 10^{- 6} T m / A$
$e$	Fundamental unit of charge	$1.60 \times 10^{- 19} C$
$c$	Speed of light in vacuum	$3.00 \times 10^{8} m / s$
$h$	Planck’s constant	$6.63 \times 10^{- 34} J s$	$4.14 \times 10^{- 15} e V s$
$ℏ$	Planck’s constant	$1.05 \times 10^{- 34} J s$	$6.58 \times 10^{- 16} e V s$
$a_{B}$	Bohr radius	$5.29 \times 10^{- 11} m$

Common Prefixes

Prefix	Meaning
femto-	$10^{- 15}$
pico-	$10^{- 12}$
nano-	$10^{- 9}$
micro-	$10^{- 6}$
milli-	$10^{- 3}$
centi-	$10^{- 2}$
kilo-	$10^{3}$
mega-	$10^{6}$
giga-	$10^{9}$
terra-	$10^{12}$

Conversion Factors

Length

$1 in = 2.54 cm$

$1 mi = 1.609 km$

$1 m = 39.37 in$

$1 km = 0.621 mi$

Velocity

$1 mph = 0.447 m / s$

$1 m / s = 2.24 mph = 3.28 ft / s$

Mass and energy

$1 u = 1.661 \times 10^{- 27} kg$

$1 cal = 4.19 J$

$1 eV = 1.60 \times 10^{- 19} J$

Time

$1 day = 86, 400 s$

$1 year = 3.16 \times 10^{7} s$

Pressure

$1 atm = 101.3 kPa = 760 mm of Hg$

$1 atm = 14.7 lb / i n^{2}$

Rotation

$1 rad = 180 ° / π = 57.3 °$

$1 rev = 360 ° = 2 π rad$

$1 rev / s = 60 rpm$

Mathematical Approximations

Binomial approximation: $(1 + x)^{n} \approx 1 + n x if x ≪ 1$

Small-angle approximation: $sin θ \approx t a n θ \approx θ a n d c o s θ \approx 1 i f θ ≪ 1 r a d i a n$

Greek Letters Used in Physics

Alpha		$α$	Mu		$μ$
Beta		$β$	Pi		$π$
Gamma	$Γ$	$γ$	Rho		$ρ$
Delta	$Δ$	$δ$	Sigma	$\sum$	$σ$
Epsilon		$ε$	Tau		$τ$
Eta		$η$	Phi	$Φ$	$ϕ$
Theta	$Θ$	$θ$	Psi		$ψ$
Lambda		$λ$	Omega	$Ω$	$ω$

Astronomical Data

Planetary body	Mean distance from sun (m)	Period (years)	Mass (kg)	Mean radius (m)
Sun	—	—	$1.99 \times 10^{30}$	$6.96 \times 10^{8}$
Moon	$3.84 \times 10^{8}$ ^*	27.3 days	$7.36 \times 10^{22}$	$1.74 \times 10^{6}$
Mercury	$5.79 \times 10^{10}$	0.241	$3.18 \times 10^{23}$	$2.43 \times 10^{6}$
Venus	$1.08 \times 10^{11}$	0.615	$4.88 \times 10^{24}$	$6.06 \times 10^{6}$
Earth	$1.50 \times 10^{11}$	1.00	$5.98 \times 10^{24}$	$6.37 \times 10^{6}$
Mars	$2.28 \times 10^{11}$	1.88	$6.42 \times 10^{23}$	$3.37 \times 10^{6}$
Jupiter	$7.78 \times 10^{11}$	11.9	$1.90 \times 10^{27}$	$7.15 \times 10^{7}$
Saturn	$1.43 \times 10^{12}$	29.5	$5.68 \times 10^{26}$	$6.02 \times 10^{7}$
Uranus	$2.87 \times 10^{12}$	84.0	$8.68 \times 10^{25}$	$2.33 \times 10^{7}$
Neptune	$4.50 \times 10^{12}$	165	$1.03 \times 10^{26}$	$2.21 \times 10^{7}$

*Distance from earth

Typical Coefficients of Friction

Material	Static $μ_{s}$	Kinetic $μ_{k}$	Rolling $μ_{r}$
Rubber on dry concrete	1.00	0.80	0.02
Rubber on wet concrete	0.30	0.20	0.002
Steel on steel (dry)	0.80	0.60	0.002
Steel on steel (lubricated)	0.10	0.05
Wood on wood	0.50	0.20
Wood on snow	0.12	0.06
Ice on ice	0.10	0.03

Heats of Transformation

Substance	$T_{m} (° C)$	$L_{f} (J/kg)$	$T_{b} (° C)$	$L_{v} (J/kg)$
Water	0	$3.33 \times 10^{5}$	100	$22.6 \times 10^{5}$
Nitrogen $(N_{2})$	$- 210$	$0.26 \times 10^{5}$	$- 196$	$1.99 \times 10^{5}$
Ethyl alcohol	$- 114$	$1.09 \times 10^{5}$	78	$8.79 \times 10^{5}$
Mercury	$- 39$	$0.11 \times 10^{5}$	357	$2.96 \times 10^{5}$
Lead	328	$0.25 \times 10^{5}$	1750	$8.58 \times 10^{5}$

Properties of Materials

Substance	$ρ (kg / m^{3})$	$c (J/kg K)$	$η$ (Pas)
Air at 0°C and 1 atm	1.29		$1.7 \times 10^{- 5}$
Air at 20°C and 1 atm	1.20		$1.8 \times 10^{- 5}$
Ethyl alcohol	790	2400	$1.3 \times 10^{- 3}$
Glycerin	1260
Mercury	13,600	140
Oil (typical)	900
Olive oil (20°C)	910		$8.4 \times 10^{- 2}$
Seawater	1030
Water (20°C)	1000	4190	$1.0 \times 10^{- 3}$
Water (40°C)	1000	4190	$6.5 \times 10^{- 4}$
Aluminum	2700	900
Copper	8920	385
Gold	19,300	129
Ice	920	2090
Iron	7870	449
Lead	11,300	128

Coefficients of Thermal Expansion

Material	$α (° C^{- 1})$
Aluminum	$2.3 \times 10^{- 5}$
Brass	$1.9 \times 10^{- 5}$
Concrete	$1.2 \times 10^{- 5}$
Steel	$1.1 \times 10^{- 5}$
Invar	$0.09 \times 10^{- 5}$

Material	$β (° C^{- 1})$
Gasoline	$9.6 \times 10^{- 4}$
Mercury	$1.8 \times 10^{- 4}$
Ethyl alcohol	$1.1 \times 10^{- 4}$

Thermal Conductivities

Material	$k (W/m K)$
Diamond	2000
Silver	430
Copper	400
Aluminum	240
Iron	80
Stainless steel	14
Ice	1.7
Concrete	0.8
Glass	0.8
Styrofoam	0.035
Air $(20 ° C, 1 atm)$	0.023

Molar Specific Heats of Gases

Gas	$C_{P} (J/mol K)$	$C_{V} (J/mol K)$
Monatomic Gases
He	20.8	12.5
Ne	20.8	12.5
Ar	20.8	12.5
Diatomic Gases
$H_{2}$	28.7	20.4
$N_{2}$	29.1	20.8
$O_{2}$	29.2	20.9

Resistivity and Conductivity of Conductors

Metal	Resistivity $(Ω m)$	Conductivity $(Ω^{- 1} m^{- 1})$
Aluminum	$2.8 \times 10^{- 8}$	$3.5 \times 10^{7}$
Copper	$1.7 \times 10^{- 8}$	$6.0 \times 10^{7}$
Gold	$2.4 \times 10^{- 8}$	$4.1 \times 10^{7}$
Iron	$9.7 \times 10^{- 8}$	$1.0 \times 10^{7}$
Silver	$1.6 \times 10^{- 8}$	$6.2 \times 10^{7}$
Tungsten	$5.6 \times 10^{- 8}$	$1.8 \times 10^{7}$
Nichrome	$1.5 \times 10^{- 6}$	$6.7 \times 10^{5}$
Carbon	$3.5 \times 10^{- 5}$	$2.9 \times 10^{4}$

Indices of Refraction

Material	Index of refraction
Vacuum	1 exactly
Air	1.00
Water	1.33
Ethyl alcohol	1.36
Oil	1.46
Glass (typical)	1.50
Polystyrene plastic	1.59
Cubic zirconia	2.18
Diamond	2.42

Atomic and Nuclear Data

Atom	Z	Mass (u)	Mass $(M e V / c^{2})$
Electron	—	0.000 548	0.51
Proton	—	1.007 276	938.28
Neutron	—	1.008 665	939.57
$^{1} H$	1	1.007 825	938.79
$^{2} H$	1	2.014 102
$^{4} He$	2	4.002 602
$^{12} C$	6	12.000 000
$^{14} C$	6	14.003 242
$^{14} N$	7	14.003 074
$^{16} O$	8	15.994 915
$^{20} Ne$	10	19.992 435
$^{27} Al$	13	26.981 538
$^{40} Ar$	18	39.962 384
$^{207} Pb$	82	206.975 871
$^{238} U$	92	238.050 784

Hydrogen Atom Energies and Radii

$n$	$E_{n} (e V)$	$r_{n} (n m)$
1	$- 13.60$	0.053
2	$- 3.40$	0.212
3	$- 1.51$	0.476
4	$- 0.85$	0.848
5	$- 0.54$	1.322

Work Functions of Metals

Metal	$E_{0} (e V)$
Potassium	2.30
Sodium	2.36
Aluminum	4.28
Tungsten	4.55
Iron	4.65
Copper	4.70
Gold	5.10

Problem-Solving Strategies and Model Boxes

Note for users of the three-volume edition:

Volume 1 (pp. 1–628) includes Chapters 1–21.

Volume 2 (pp. 629–1092) includes Chapters 22–36.

Volume 3 (pp. 1051–1270) includes Chapters 36–42.

PROBLEM-SOLVING STRATEGY		PAGE
1.1	Motion diagrams	12
1.2	General problem-solving strategy	20
2.1	Kinematics with constant acceleration	47
4.1	Projectile motion problems	88
6.1	Newtonian mechanics	134
7.1	Interacting-objects problems	171
8.1	Circular-motion problems	199
10.1	Energy-conservation problems	249
11.1	Conservation of momentum	276
12.1	Rotational dynamics problems	315
17.1	Interference of two waves	492
19.1	Work in ideal-gas processes	536
19.2	Calorimetry problems	546
21.1	Heat-engine problems	607
22.1	Electrostatic forces and Coulomb’s law	642
23.1	The electric field of multiple point charges	661
23.2	The electric field of a continuous distribution of charge	667
24.1	Gauss’s law	703
25.1	Conservation of energy in charge interactions	727
25.2	The electric potential of a continuous distribution of charge	735
28.1	Resistor circuits	810
29.1	The magnetic field of a current	833
30.1	Electromagnetic induction	879
36.1	Relativity	1074
40.1	Quantum-mechanics problems	1176

MODEL		PAGE
2.1	Uniform motion	35
2.2	Constant acceleration	46
4.1	Projectile motion	88
4.2	Uniform circular motion	97
4.3	Constant angular acceleration	99
5.1	Ball-and-spring model of solids	114
6.1	Mechanical equilibrium	132
6.2	Constant force	136
6.3	Friction	142
8.1	Central force with constant r	190
9.1	Basic energy model	213
11.1	Collisions	283
12.1	Rigid-body model	301
12.2	Constant torque	316
12.3	Static equilibrium	317
14.1	Molecular model of gases and liquids	365
14.2	Ideal fluid	380
15.1	Simple harmonic motion	418
16.1	The wave model	454
18.1	Solids, liquids, and gases	507
19.1	Thermodynamic energy model	540
22.1	Charge model	632, 634
22.2	Electric field	647
23.1	Four key electric fields	660
26.1	Charge escalator model of a battery	753
29.1	Three key magnetic fields	832
33.1	Wave model of light	979
34.1	Ray model of light	991
38.1	Photon model of light	1123
38.2	The Bohr model of the atom	1130

Useful Data