# A | Reference Tables

### A | Reference Tables

Figure A1 Periodic Table of Elements
Prefix Symbol Value Prefix Symbol Value
tera T 1012 deci d 10–1
giga G 109 centi c 10–2
mega M 106 milli m 10–3
kilo k 103 micro µ 10–6
hecto h 102 nano n 10–9
deka da 101 pico p 10–12
___ 100 femto f 10–15
Table A1 Metric Prefixes for Powers of Ten and Their Symbols
Entity Abbreviation Name
Fundamental units Length m meter
Mass kg kilogram
Time s second
Current A ampere
Derived units Force $N=kg· m s 2 N=kg· m s 2$ newton
Energy $J=kg· m 2 J=kg· m 2$ joule
Power $W= J s W= J s$ watt
Pressure $Pa= N m 2 Pa= N m 2$ pascal
Frequency $Hz= 1 s Hz= 1 s$ hertz
Electronic potential $V= J C V= J C$ volt
Capacitance $F= C V F= C V$ farad
Charge $C=s⋅A C=s⋅A$ coulomb
Resistance $Ω= V A Ω= V A$ ohm
Magnetic field $T= N A·m T= N A·m$ tesla
Nuclear decay rate $Bq= 1 s Bq= 1 s$ becquerel
Table A2 SI Units
 Length 1 inch (in.) = 2.54 cm (exactly) 1 foot (ft) = 0.3048 m 1 mile (mi) = 1.609 km Force 1 pound (lb) = 4.448 N Energy 1 British thermal unit (Btu) = 1.055 × 103 J Power 1 horsepower (hp) = 746 W Pressure 1 lb/in2 = 6.895 × 103 Pa
Table A3 Selected British Units
 Length 1 light year (ly) = 9.46 × 1015 m 1 astronomical unit (au) = 1.50 × 1011 m 1 nautical mile = 1.852 km 1 angstrom(Å) = 10-10 m Area 1 acre (ac) = 4.05 × 103 m2 1 square foot (ft2) 9.29 × 10-2 m3 1 barn (b) = 10-28 m2 Volume 1 liter (L) = 10-3 m3 1 U.S. gallon (gal) = 3.785 × 10-3 m3 Mass 1 solar mass = 1.99 × 1030 kg 1 metric ton = 103 kg 1 atomic mass unit (u) = 1.6605 × 10-27 kg Time 1 year (y) = 3.16 × 107 s 1 day (d) = 86,400 s Speed 1 mile per hour (mph) = 1.609 km / h 1 nautical mile per hour (naut) = 1.852 km / h Angle 1 degree (°) = 1.745x10-2 rad 1 minute of arc (') = 1 / 60 degree 1 second of arc ('') = 1 / 60 minute of arc 1 grad = 1.571 × 10-2 rad Energy 1 kiloton TNT (kT) = 4.2 × 1012 J 1 kilowatt hour (kW $⋅ ⋅$ h) = 3.60 × 106 J 1 food calorie (kcal) = 4186 J 1 calorie (cal) = 4.186 J 1 electron volt (cV) = 1.60 × 10-19 J Pressure 1 atmosphere (atm) = 1.013 × 105 Pa 1 millimeter of mercury (mm Hg) = 133.3 Pa 1 torricelli (torr) = 1 mm Hg = 133.3 Pa Nuclear decay rate 1 curie (Ci) = 3.70 × 1010 Bq
Table A4 Other Units
 Circumference of a circle with radius r or diameter d $C=2π=πd C=2π=πd$ Area of a circle with radius r or diameter d $A=π r 2 =π d 2 /4 A=π r 2 =π d 2 /4$ Area of a sphere with radius r $A=4π r 2 A=4π r 2$ Volume of a sphere with radius r $V=( 4/3 )(π r 3 ) V=( 4/3 )(π r 3 )$
Table A5 Useful formulae
Symbol Meaning Best Value Approximate Value
c Speed of light in vacuum
G Gravitational constant
k Boltzmann’s constant
R Gas constant
σ Stefan-Boltzmann Constant
k Coulomb force constant
qe Charge on electron
ε0 Permittivity of free space
µ0 Permeability of free space
h Planck’s constant
Table A6 Important Constants
 Alpha $Α Α$ $α α$ Beta $Β Β$ $β β$ Gamma $Γ Γ$ $γ γ$ Delta $Δ Δ$ $δ δ$ Epsilon $Ε Ε$ $ε ε$ Zeta $Ζ Ζ$ $ζ ζ$ Eta $Η Η$ $η η$ Theta $Θ Θ$ $θ θ$ Iota $Ι Ι$ $ι ι$ Kappa $Κ Κ$ $κ κ$ Lambda $Λ Λ$ $λ λ$ Mu $Μ Μ$ $μ μ$ Nu $Ν Ν$ $ν ν$ Xi $Ξ Ξ$ $ξ ξ$ Omicron $Ο Ο$ $ο ο$ Pi $Π Π$ $π π$ Rho $Ρ Ρ$ $ρ ρ$ Sigma $Σ Σ$ $σ σ$ Tau $Τ Τ$ $τ τ$ Upsilon $ϒ ϒ$ $υ υ$ Phi $Φ Φ$ $ϕ ϕ$ Chi $Χ Χ$ $χ χ$ Psi $Ψ Ψ$ $ψ ψ$ Omega $Ω Ω$ $ω ω$
Table A7 The Greek Alphabet
 Sun mass 1.99 × 1030 kg average radius 6.96 × 108 m Earth-sun distance (average) 1.496 × 1011 m Earth mass 5.9736 × 1024 kg average radius 6.376 × 106 m orbital period 3.16 × 107 s Moon mass 7.35 × 1022 kg average radius 1.74 × 106 s orbital period (average) 2.36 × 106 s Earth-moon distance (average) 3.84 × 108 m
Table A8 Solar System Data
Atomic number, Z Name Atomic Mass Number, A Symbol Atomic Mass (u) Percent Abundance or Decay Mode Half-life, t1/2
0 neutron 1 n 1.008 665 β 10.37 min
1 Hydrogen 1 1H 1.007 825 99.985%
Deuterium 2 2H or D 2.014 102 0.015%
Tritium 3 3H or T 3.016 050 β 12.33 y
2 Helium 3 3He 3.016 030 1.38 × 10−4 %
4 4He 4.002 603 ≈100%
3 Lithium 6 6Li 6.015 121 7.5%
7 7Li 7.016 003 92.5%
4 Beryllium 7 7Be 7.016 928 EC 53.29 d
9 9Be 9.012 182 100%
5 Boron 10 10B 10.012 937 19.9%
11 11B 11.009 305 80.1%
6 Carbon 11 11C 11.011 432 EC, β+
12 12C 12.000 000 98.90%
13 13C 13.003 355 1.10%
14 14C 14.003 241 β 5730 y
7 Nitrogen 13 12N 13.005 738 β+ 9.96 min
14 13N 14.003 074 99.63%
15 14N 15.000 108 0.37%
8 Oxygen 15 15O 15.003 065 EC, β+ 122 s
16 16O 15.994 915 99.76%
18 18O 17.999 160 0.200%
9 Fluorine 18 18F 18.000 937 EC, β+ 1.83 h
19 19F 18.998 403 100%
10 Neon 20 20Ne 19.992 435 90.51%
22 22Ne 21.991 383 9.22%
11 Sodium 22 22Na 21.994 434 β+ 2.602 y
23 23Na 22.989 767 100%
24 24Na 23.990 961 β 14.96 h
12 Magnesium 24 24Mg 23.985 042 78.99%
13 Aluminum 27 27Al 26.981 539 100%
14 Silicon 28 28Si 27.976 927 92.23% 2.62h
31 31Si 30.975 362 β
15 Phosphorus 31 31P 30.973 762 100%
32 32P 31.973 907 β 14.28 d
16 Sulfur 32 32S 31.972 070 95.02%
35 35S 34.969 031 β 87.4 d
17 Chlorine 35 35Cl 34.968 852 75.77%
37 37Cl 36.965 903 24.23%
18 Argon 40 40Ar 39.962 384 99.60%
19 Potassium 39 39K 38.963 707 93.26%
40 40K 39.963 999 0.0117%, EC, β 1.28 × 109 y
20 Calcium 40 40Ca 39.962 591 96.94%
21 Scandium 45 45Sc 44.955 910 100%
22 Titanium 48 48Ti 47.947 947 73.8%
23 Vanadium 51 51V 50.943 962 99.75%
24 Chromium 52 52Cr 51.940 509 83.79%
25 Manganese 55 55Mn 54.938 047 100%
26 Iron 56 56Fe 55.934 939 91.72%
27 Cobalt 59 59Co 58.933 198 100%
60 60Co 59.933 819 β 5.271 y
28 Nickel 58 58Ni 57.935 346 68.27%
60 60Ni 59.930 788 26.10%
29 Copper 63 63Cu 62.939 598 69.17%
65Cu 64.927 793 30.83%
30 Zinc 64 64Zn 63.929 145 48.6%
66 66Zn 65.926 034 27.9%
31 Gallium 69 69Ga 68.925 580 60.1%
32 Germanium 72 72Ge 71.922 079 27.4%
74 74Ge 73.921 177 36.5%
33 Arsenic 75 75As 74.921 594 100%
34 Selenium 80 80Se 79.916 520 49.7%
35 Bromine 79 79Br 78.918 336 50.69%
36 Krypton 84 84Kr 83.911 507 57.0%
37 Rubidium 85 85Rb 84.911 794 72.17%
38 Strontium 86 86Sr 85.909 267 9.86%
88 88Sr 87.905 619 82.58%
90 90Sr 89.907 738 β 28.8 y
39 Yttrium 89 89Y 88.905 849 100%
90 90Y 89.907 152 β 64.1 h
40 Zirconium 90 90Zr 89.904 703 51.45%
41 Niobium 93 93Nb 92.906 377 100%
42 Molybdenum 98 98Mo 97.905 406 24.13%
43 Technetium 98 98Tc 97.907 215 β 4.2 × 106 y
44 Ruthenium 102 102Ru 101.904 348 31.6%
45 Rhodium 103 103Rh 102.905 500 100%
46 Palladium 106 106Pd 105.903 478 27.33%
47 Silver 107 107Ag 106.905 092 51.84%
109 109Ag 108.904 757 48.16%
48 Cadmium 114 114Cd 113.903 357 28.73%
49 Indium 115 115In 114.903 880 95.7%, β 4.4 × 1014 y
50 Tin 120 120Sn 119.902 200 32.59%
51 Antimony 121 121Sb 120.903 821 57.3%
52 Tellurium 130 130Te 129.906 229 33.8%, β 2.5 × 1021 y
53 Iodine 127 127I 126.904 473 100%
131 131I 130.906 114 β 8.040 d
54 Xenon 132 132Xe 131.904 144 26.9%
136 136Xe 135.907 214 8.9%
55 Cesium 133 133Cs 132.905 429 100%
134 134Cs 133.906 696 EC, β 2.06 y
56 Barium 137 137Ba 136.905 812 11.23%
138 138Ba 137.905 232 71.70%
57 Lanthanum 139 139La 138.906 346 99.91%
58 Cerium 140 140Ce 139.905 433 88.48%
59 Praseodymium 141 141Pr 140.907 647 100%
60 Neodymium 142 142Nd 141.907 719 27.13%
61 Promethium 145 145Pm 144.912 743 EC, α 17.7 y
62 Samarium 152 152Sm 151.919 729 26.7%
63 Europium 153 153Eu 152.921 225 52.2%
64 Gadolinium 158 158Gd 157.924 099 24.84%
65 Terbium 159 159Tb 158.925 342 100%
66 Dysprosium 164 164Dy 163.929 171 28.2%
67 Holmium 165 165Ho 164.930 319 100%
68 Erbium 166 166Ho 165.930 290 33.6%
69 Thulium 169 169Tm 168.934 212 100%
70 Ytterbium 174 174Yb 173.938 859 31.8%
71 Lutecium 175 175Lu 174.940 770 97.41%
72 Hafnium 180 180Hf 179.946 545 35.10%
73 Tantalum 181 181Ta 180.947 992 99.98%
74 Tungsten 184 184W 183.950 928 30.67%
75 Rhenium 187 187Re 186.955 744 62.6%, β 4.6 × 1010y
76 Osmium 191 191Os 190.960 920 β 15.4 d
192 192Os 191.961 467 41.0%
77 Iridium 191 191Ir 190.960 584 37.3%
193 193Ir 192.962 917 62.7%
78 Platinum 195 195Pt 194.964 766 33.8%
79 Gold 197 197Au 196.966 543 100%
198 198Au 197.968 217 β 2.696 d
80 Mercury 199 199Hg 198.968 253 16.87%
202 202Hg 201.970 617 29.86%
81 Thallium 205 205Tl 204.974 401 70.48%
82 Lead 206 206Pb 205.974 440 24.1%
207 207Pb 206.975 872 22.1%
208 208Pb 207.976 627 52.4%
210 210Pb 209.984 163 α, β 22.3 y
211 211Pb 210.988 735 β 36.1 min
212 212Pb 211.991 871 β 10.64 h
83 Bismuth 209 209Bi 208.980 374 100%
211 211Bi 210.987 255 α, β 2.14 min
84 Polonium 210 210Po 209.982 848 α 138.38 d
85 Astatine 218 218At 218.008 684 α, β 1.6 s
86 Radon 222 222Rn 222.017 570 α 3.82 d
87 Francium 2 223 223Fr 223.019 733 α, β 21.8 min
88 Radium 226 226Ra 226.025 402 α 1.60 × 103 y
89 Actinium 227 227Ac 227.027 750 α, β 21.8 y
90 Thorium 228 228Th 228.028 715 α 1.91 y
232 232Th 232.038 054 100%, α 1.41 × 1010 y
91 Protactinium 231 231Pa 231.035 880 α 3.28 × 104 y
92 Uranium 233 233U 233.039 628 α 1.59 × 103 y
235 235U 235.043 924 0.720%, α 7.04 × 108 y
236 236U 236.045 562 α 2.34 × 107 y
238 238U 238.050 784 99.2745%, α 4.47 × 109 y
239 239U 239.054 289 β 23.5 min
93 Neptunium 239 239Np 239.052 933 β 2.355 d
94 Plutonium 239 239Pu 239.052 157 α 2.41 × 104 y
95 Americium 243 243Am 243.061 375 α, fission 7.37 × 103 y
96 Curium 245 245Cm 245.065 483 α 8.50 × 103 y
97 Berkelium 245 247Bk 247.070 300 α 1.38 × 103 y
98 Californium 249 249Cf 249.074 844 α 351 y
99 Einsteinium 254 254Es 254.088 019 α, β 276 d
100 Fermium 253 253Fm 253.085 173 EC, α 3.00 d
101 Mendelevium 255 255Md 255.091 081 EC, α 27 min
102 Nobelium 255 255No 255.093 260 EC, α 3.1 min
103 Lawrencium 257 257Lr 257.099 480 EC, α 0.646 s
104 Rutherfordium 261 261Rf 261.108 690 α 1.08 mim
105 Dubnium 262 262Db 262.113 760 α, fission 34 s
106 Seaborgium 263 263Sg 263.11 86 α, fission 0.8 s
107 Bohrium 262 262Bh 262.123 1 α 0.102 s
108 Hassium 264 264Hs 264.128 5 α 0.08 ms
108 Meitnerium 266 266Mt 266.137 8 α 3.4 ms
Table A9 Atomic Masses and Decay
Isotope t1/2 Decay Mode Energy(MeV) Percent T-Ray Energy(MeV) Percent
3H 12.33 y β 0.0186 100%
14C 5730 y β 0.156 100%
13N 9.96 min β+ 1.20 100%
22Na 2.602 y β+ 1.20 90% γ 1.27 100%
32P 14.28 d β 1.71 100%
35S 87.4 d β 0.167 100%
36Ci 3.00 × 105 y β 0.710 100%
40K 1.28 × 109 y β 1.31 89%
43K 22.3 h β 0.827 87% γs 0.373 87%
0.618 87%
45Ca 165 d β 0.257 100%
51Cr 27.70 d EC γ 0.320 10%
52Mn 5.59d β+ 3.69 28% γ s 1.33 28%
1.43 28%
52Fe 8.27 h β+ 1.80 43% 0.169 43%
0.378 43%
59Fe 44.6 d β s 0.273 45% γ s 1.10 57%
0.466 55% 1.29 43%
60Co 5.271 y β 0.318 100% γ s 1.17 100%
1.33 100%
65Zn 244.1 d EC γ 1.12 51%
67Ga 78.3 h EC γ s 0.0933 70%
0.185 35%
0.300 19%
others
75Se 118.5 d EC γ s 0.121 20%
0.136 65%
0.265 68%
0.280 20%
others
86Rb 18.8 d β s 0.69 9% γ 1.08 9%
1.77 91%
85Sr 64.8 d EC γ 0.514 1 100%
90Sr 28.8 y β 0.546 100%
90Y 64.1 h β 2.28 100%
99mTc 6.02 h IT γ 0.142 100%
113mIn 99.5 min IT γ 0.392 100%
123I 13.0 h EC γ 0.159 ≈100%
131I 8.040 d β s 0.248 7% γ s 0.364 85%
0.607 93% others
others
129Cs 32.3 h EC γ s 0.0400 35%
0.372 32%
0.411 25%
others
137Cs 30.17 y β s 0.511 95% γ 0.662 95%
1.17 5%
140Ba 12.79 d β 1.035 ≈100% γ s 0.030 25%
0.044 65%
0.537 24%
others
198Au 2.696 d β 1.161 ≈100% γ 0.412 ≈100%
197Hg 64.1 h EC γ 0.0733 100%
210Po 138.38 d α 5.41 100%
226Ra 1.60 × 103 y αs 4.68 5% γ 0.186 1 100%
4.87 95%
235U 7.038 × 108 y α 4.68 ≈100% γ s Numerous 0.400%
238U 4.468 × 109 y αs 4.22 23% γ 0.050 23%
4.27 77%
237Np 2.14 × 106 y αs numerous γ s numerous 0.250%
4.96 (max.)
239Pu 2.41 × 104 y αs 5.19 11% γ s 7.5 × 10-5 73%
5.23 15% 0.013 15%
5.24 73% 0.052 15%
others
243Am 7.37 × 103 y αs Max. 5.44 γ s 0.075
5.37 88% others
5.32 11%
others
Symbol Meaning Best Value Approximate Value
me Electron mass 9.10938291(40) × 10–31 kg 9.11 × 10–31 kg
mp Proton mass 1.672621777(74) × 10–27 kg 1.6726 × 10–27 kg
mn Neutron mass 1.674927351(74) × 10–27 kg 1.6749 × 10–27 kg
u Atomic mass unit 1.660538921(73) × 10–27 kg 1.6605 × 10–27 kg
Table A11 Submicroscopic masses
Substance p(kg/m3) Substance p(kg/m3)
Air 1.29 Iron 7.86 × 103
Air (at 20°C and Atmospheric pressure) 1.20 Lead 11.3 × 103
Aluminum 2.70 × 103 Mercury 13.6 × 103
Benzene 0.879 × 103 Nitrogen gas 1.25
Brass 8.4 × 103 Oak 0.710 × 103
Copper 8.92 × 103 Osmium 22.6 × 103
Ethyl alcohol 0.806 × 103 Oxygen gas 1.43
Fresh water 1.00 × 103 Pine 0.373 × 103
Glycerin 1.26 × 103 Platinum 21.4 × 103
Gold 1.93 × 103 Seawater 1.03 × 103
Helium gas 1.79 × 10–1 Silver 10.5 × 103
Hydrogen gas 8.99 × 10–2 Tin 7.30 × 103
Ice 0.917 × 103 Uranium 18.7 × 103
Table A12 Densities of common substances (including water at various temperatures)
Substance Specific Heat (J/kg $⋅ ⋅$ °C) Substance Specific Heat (J/kg $⋅ ⋅$ °C)
Elemental solids Other solids
Aluminum 900 Brass 380
Beryllium 1830 Glass 837
Cadmium 230 Ice (–5 °C) 2090
Copper 387 Marble 860
Germanium 322 Wood 1700
Gold 129 Liquids
Iron 448 Alcohol (ethyl) 2400
Silicon 703 Water (15 °C) 4186
Silver 234 Gas
Steam (100 °C) 2010
Note: To convert values to units of cal/g $⋅⋅$ °C, divide by 4186
Table A13 Specific heats of common substances
Substance Melting Point (°C) Latent Heat of Fusion (J/kg) Boiling Point (°C) Latent Heat of Vaporization (J/kg)
Helium –272.2 5.23 × 103 –268.93 2.09 × 104
Oxygen –218.79 1.38 × 104 –182.97 2.13 × 105
Nitrogen –209.97 2.55 × 104 –195.81 2.01 × 105
Ethyl Alcohol –114 1.04 × 105 78 8.54 × 105
Water 0.00 3.33 × 105 100.00 2.26 × 106
Sulfur 119 3.81 × 104 444.60 2.90 × 105
Lead 327.3 3.97 × 105 1750 8.70 × 105
Aluminum 660 3.97 × 105 2516 1.05 × 107
Silver 960.80 8.82 × 104 2162 2.33 × 106
Gold 1063.00 6.44 × 104 2856 1.58 × 106
Copper 1083 1.34 × 105 2562 5.06 × 106
Table A14 Heats of fusion and vaporization for common substances
Materials (Solids) Average Linear Expansion Coefficient (a)(°C)–1 Material (Liquids and Gases) Average Volume Expansion Coefficient (B)(°C)–1
Aluminum 24 × 10–6 Acetone 1.5 × 10–4
Brass and Bronze 19 × 10–6 Alcohol, ethyl 1.12 × 10–4
Concrete 12 × 10–6 Benzene 1.24 × 10–4
Copper 17 × 10–6 Gasoline 9.6 × 10–4
Glass (ordinary) 9 × 10–6 Glycerin 4.85 × 10–4
Glass (Pyrex) 3.2 × 10–6 Mercury 1.82 × 10–4
Invar (Ni-Fe alloy) 1.3 × 10–6 Turpentine 9.0 × 10–4
Lead 29 × 10–6 Air* at 0°C 3.67 × 10–3
Steel 13 × 10–6 Helium* 3.665 × 10–3
* The values given here assume the gases undergo expansion at constant pressure. However, the expansion of gases depends on the pressure applied to the gas. Therefore, gases do not have a specific value for the volume expansion coefficient.
Table A15 Coefficients of thermal expansion for common substances
Medium v(m/s) Medium v(m/s) Medium v(m/s)
Gases Liquids at 25°C Solids*
Hydrogen 1286 Glycerol 1904 Pyrex glass 5640
Helium 972 Seawater 1533 Iron 5950
Air 343 Water 1493 Aluminum 5100
Air 331 Mercury 1450 Brass 4700
Oxygen 317 Kerosene 1324 Copper 3560
Methyl Alcohol 1143 Gold 3240
Carbon tetrachloride 926 Lucite 2680
Rubber 1600
*Values given here are for propagation of longitudinal waves in bulk media. However, speeds for longitudinal waves in thin rods are slower, and speeds of transverse waves in bulk are even slower.
Table A16 Speed of sound in various substances
Source of Sound B(dB)
Nearby jet airplane 150
Jackhammer machine gun 130
Siren; rock concert 120
Subway; power lawn mower 100
Busy traffic 80
Vacuum cleaner 70
Normal Conversation 60
Mosquito buzzing 40
whisper 30
Rustling leaves 10
Threshold of hearing 0
Table A17 Conversion of sound intensity to decibel level
Wavelength Range (nm) Color Description
400-430 Violet
430-485 Blue
485-560 Green
560-590 Yellow
590-625 Orange
625-700 Red
Table A18 Wavelengths of visible light
Substance Index of Refraction Substance Index of Refraction
Solids at 20°C Liquids at 20°C
Cubic zirconia 2.15 Benzene 1.501
Diamond (C) 2.419 Carbon disulfide 1.628
Flourite (CaF2) 1.434 Carbon tetrachloride 1.461
Fused quartz (SiO2) 1.458 Ethyl alcohol 1.361
Gallium phosphide 3.50 Glycerin 1.473
Glass, crown 1.52 Water 1.333
Glass, flint 1.66
Ice (H2O) 1.309 Gases at 0°C, 1 atm
Polystyrene 1.49 Air 1.000 293
Sodium chloride (NaCl) 1.544 Carbon dioxide 1.000 45
Note: These values assume that light has a wavelength of 589 nm in vacuum.
Table A19 Indices of refraction
 Hoop or thin cylindrical shell $I CM =M R 2 I CM =M R 2$ Hollow cylinder $I CM = 1 2 M( R 1 2 + R 2 2 ) I CM = 1 2 M( R 1 2 + R 2 2 )$ Solid cylinder or disk $I CM = 1 2 M R 2 I CM = 1 2 M R 2$ Rectangular plane $I CM = 1 12 M( a 2 + b 2 ) I CM = 1 12 M( a 2 + b 2 )$ Long, thin rod with rotation axis through center $I CM = 1 12 M L 2 I CM = 1 12 M L 2$ Long, thin rod with rotation axis through end $I CM = 1 3 M L 2 I CM = 1 3 M L 2$ Solid sphere $I CM = 2 5 M R 2 I CM = 2 5 M R 2$ Thin spherical shell $I CM = 2 3 M R 2 I CM = 2 3 M R 2$
Table A20 Moments of inertia for different shapes
μs μk
Rubber on dry concrete 1.0 0.8
Steel on steel 0.74 0.57
Aluminum on steel 0.61 0.47
Glass on glass 0.94 0.4
Copper on steel 0.53 0.36
Wood on wood 0.25-0.5 0.2
Waxed wood on wet snow 0.14 0.1
Waxed wood on dry snow 0.1 0.04
Metal on metal (lubricated) 0.15 0.06
Teflon on Teflon 0.04 0.04
Ice on ice 0.1 0.03
Synovial joints in humans 0.01 0.003
Note: All values are approximate. In some cases, the coefficient of friction can exceed 1.0.
Table A21 Coefficients of friction for common objects on other objects
Material Dielectric Constant ĸ Dielectric Strength* (106V/m)
Air (dry) 1.000 59 3
Bakelite 4.9 24
Fused quartz 4.3 8
Mylar 3.2 7
Neoprene rubber 6.7 12
Nylon 3.4 14
Paper 3.7 16
Paraffin-impregnated paper 3.5 11
Polystyrene 2.56 24
Polyvinyl chloride 3.4 40
Porcelain 6 8
Pyrex glass 5.6 14
Silicone oil 2.5 15
Strontium titanate 233 8
Teflon 2.1 60
Vacuum 1.000 00
Water 80 3
Table A22 Dielectric constants