Appendix C Useful Information

This appendix is broken into several tables.

Table 3. Important Constants1

Symbol Meaning Best Value Approximate Value
[latex]c[/latex] Speed of light in vacuum [latex]2.99792458 \times 10^8 \text{m/s}[/latex] [latex]3.00 \times 10^8 \text{m/s}[/latex]
[latex]G[/latex] Gravitational constant [latex]6.67408(31) \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2[/latex] [latex]6.67 \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2[/latex]
[latex]N_A[/latex] Avogadro’s number [latex]6.02214129(27) \times 10^{23}[/latex] [latex]6.02 \times 10^{23}[/latex]
[latex]k[/latex] Boltzmann’s constant [latex]1.3806488(13) \times 10^{-23} \;\text{J} / \text{K}[/latex] [latex]1.38 \times 10^{-23} \;\text{J} / \text{K}[/latex]
[latex]R[/latex] Gas constant [latex]8.3144621(75) \;\text{J} / \text{mol} \cdot \text{K}[/latex] [latex]8.31 \;\text{J} / \text{mol} \cdot \text{K} = 1.99 \text{cal} / \text{mol} \cdot \text{K} = 0.0821 \text{atm} \cdot \text{L} / \text{mol} \cdot \text{K}[/latex]
[latex]\sigma[/latex] Stefan-Boltzmann constant [latex]5.670373(21) \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}[/latex] [latex]5.67 \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}[/latex]
[latex]k[/latex] Coulomb force constant [latex]8.987551788 \dots \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2[/latex] [latex]8.99 \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2[/latex]
[latex]q_e[/latex] Charge on electron [latex]-1.602176565(35) \times 10^{-19} \;\text{C}[/latex] [latex]-1.60 \times 10^{-19} \;\text{C}[/latex]
[latex]\varepsilon _0[/latex] Permittivity of free space [latex]8.854187817 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \cdot \text{m}^2[/latex] [latex]8.85 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \text{m}^2[/latex]
[latex]\mu _0[/latex] Permeability of free space [latex]4 \pi \times 10^{-7} \;\text{T} \cdot \;\text{m}/ \text{A}[/latex] [latex]1.26 \times 10^{-6} \;\text{T} \cdot \text{m} / \text{A}[/latex]
[latex]h[/latex] Planck’s constant [latex]6.62606957(29) \times 10^{-34} \;\text{J} \cdot \text{s}[/latex] [latex]6.63 \times 10^{-34} \;\text{J} \cdot \text{s}[/latex]
Symbol Meaning Best Value Approximate Value
[latex]m_e[/latex] Electron mass [latex]9.10938291(40) \times 10^{-31} \text{kg}[/latex] [latex]9.11 \times 10^{-31} \text{kg}[/latex]
[latex]m_p[/latex] Proton mass [latex]1.672621777(74) \times 10^{-27} \text{kg}[/latex] [latex]1.6726 \times 10^{-27} \text{kg}[/latex]
[latex]m_n[/latex] Neutron mass [latex]1.674927351(74) \times 10^{-27} \text{kg}[/latex] [latex]1.6749 \times 10^{-27} \text{kg}[/latex]
[latex]\text{u}[/latex] Atomic mass unit [latex]1.660538921(73) \times 10^{-27} \text{kg}[/latex] [latex]1.6605 \times 10^{-27} \text{kg}[/latex]
Table 4. Submicroscopic Masses2
Sun mass [latex]1.99 \times 10^{30} \text{kg}[/latex]
average radius [latex]6.96 \times 10^8 \text{m}[/latex]
Earth-sun distance (average) [latex]1.496 \times 10^{11} \text{m}[/latex]
Earth mass [latex]5.9736 \times 10^{24} \text{kg}[/latex]
average radius [latex]6.376 \times 10^6 \text{m}[/latex]
orbital period [latex]3.16 \times 10^7 \text{s}[/latex]
Moon mass [latex]7.35 \times 10^{22} \text{kg}[/latex]
average radius [latex]1.74 \times 10^6 \text{m}[/latex]
orbital period (average) [latex]2.36 \times 10^6 \text{s}[/latex]
Earth-moon distance (average) [latex]3.84 \times 10^8 \text{m}[/latex]
Table 5. Solar System Data
Prefix Symbol Value Prefix Symbol Value
tera T [latex]10^{12}[/latex] deci d [latex]10^{-1}[/latex]
giga G [latex]10^{9}[/latex] centi c [latex]10^{-2}[/latex]
mega M [latex]10^{6}[/latex] milli m [latex]10^{-3}[/latex]
kilo k [latex]10^{3}[/latex] micro [latex]\mu[/latex] [latex]10^{-6}[/latex]
hecto h [latex]10^{2}[/latex] nano n [latex]10^{-9}[/latex]
deka da [latex]10^{1}[/latex] pico p [latex]10^{-12}[/latex]
— — [latex]10^{0} (= 1)[/latex] femto f [latex]10^{-15}[/latex]
Table 6. Metric Prefixes for Powers of Ten and Their Symbols
Alpha A [latex]\alpha[/latex] Eta Η [latex]\eta[/latex] Nu Ν [latex]\nu[/latex] Tau Τ [latex]\tau[/latex]
Beta Β [latex]\beta[/latex] Theta Θ [latex]\theta[/latex] Xi Ξ [latex]\xi[/latex] Upsilon Υ [latex]\upsilon[/latex]
Gamma Γ [latex]\gamma[/latex] Iota Ι [latex]\iota[/latex] Omicron Ο [latex]\omicron[/latex] Phi Φ [latex]\phi[/latex]
Delta Δ [latex]\delta[/latex] Kappa Κ [latex]\kappa[/latex] Pi Π [latex]\pi[/latex] Chi Χ [latex]\chi[/latex]
Epsilon Ε [latex]\epsilon[/latex] Lambda Λ [latex]\lambda[/latex] Rho Ρ [latex]\rho[/latex] Psi Ψ [latex]\psi[/latex]
Zeta Ζ [latex]\zeta[/latex] Mu Μ [latex]\mu[/latex] Sigma Σ [latex]\sigma[/latex] Omega Ω [latex]\omega[/latex]
Table 7. The Greek Alphabet
Entity Abbreviation Name
Fundamental units Length [latex]\text{m}[/latex] meter
Mass [latex]\text{kg}[/latex] kilogram
Time [latex]\text{s}[/latex] second
Current [latex]\text{A}[/latex] ampere
Supplementary unit Angle [latex]\text{rad}[/latex] radian
Derived units Force [latex]\text{N} = \text{kg} \cdot \text{m} / \text{s}^2[/latex] newton
Energy [latex]\text{J} = \text{kg} \cdot \text{m}^2 / \text{s}^2[/latex] joule
Power [latex]\text{W} = \text{J} / \text{s}[/latex] watt
Pressure [latex]\text{Pa} = \text{N} / \text{m}^2[/latex] pascal
Frequency [latex]\text{Hz} = 1/ \text{s}[/latex] hertz
Electronic potential [latex]\text{V} = \text{J} / \text{C}[/latex] volt
Capacitance [latex]\text{F} = \text{C} / \text{V}[/latex] farad
Charge [latex]\text{C} = \text{s} \cdot \text{A}[/latex] coulomb
Resistance [latex]\Omega = \text{V} / \text{A}[/latex] ohm
Magnetic field [latex]\text{T} = \text{N} / (\text{A} \cdot \text{m})[/latex] tesla
Nuclear decay rate [latex]\text{Bq} = 1 / \text{s}[/latex] becquerel
Table 8. SI Units
Length [latex]1 \;\text{inch} \; (\text{in.}) = 2.54 \;\text{cm} \; (\text{exactly})[/latex]
[latex]1 \;\text{foot} \; (\text{ft}) = 0.3048 \;\text{m}[/latex]
[latex]1 \;\text{mile} \; (\text{mi}) = 1.609 \;\text{km}[/latex]
Force [latex]1 \;\text{pound} \; (\text{lb}) = 4.448 \;\text{N}[/latex]
Energy [latex]1 \;\text{British thermal unit} \; (\text{Btu}) = 1.055 \times 10^3 \text{J}[/latex]
Power [latex]1 \;\text{horsepower} \; (\text{hp}) = 746 \;\text{W}[/latex]
Pressure [latex]1 \;\text{lb} / \text{in}^2 = 6.895 \times 10^3 \;\text{Pa}[/latex]
Table 9. Selected British Units
Length [latex]1 \;\text{light year} \; (\text{ly}) = 9.46 \times 10^{15} \; \text{m}[/latex]
[latex]1 \; \text{astronomical unit} \;(\text{au}) = 1.50 \times 10^{11} \; \text{m}[/latex]
[latex]1 \;\text{nautical mile} = 1.852 \;\text{km}[/latex]
[latex]1 \;\text{angstrom}\; (Å) = 10^{-10} \text{m}[/latex]
Area [latex]1 \;\text{acre} \;(\text{ac}) = 4.05 \times 10^3 \text{m}^2[/latex]
[latex]1 \;\text{square foot} \; (\text{ft}^2) = 9.29 \times 10^{-2} \;\text{m}^2[/latex]
[latex]1 \;\text{barn} \;(b) = 10^{-28} \;\text{m}^2[/latex]
Volume [latex]1 \;\text{liter} \;(L) = 10^{-3} \; \text{m}^3[/latex]
[latex]1 \;\text{U.S. gallon} \;(\text{gal}) = 3.785 \times 10^{-3} \;\text{m}^3[/latex]
Mass [latex]1 \;\text{solar mass} = 1.99 \times 10^{30} \; \text{kg}[/latex]
[latex]1 \;\text{metric ton} = 10^3 \;\text{kg}[/latex]
[latex]1 \;\text{atomic mass unit} \;(u)= 1.6605 \times 10^{-27} \;\text{kg}[/latex]
Time [latex]1 \;\text{year} \;(\text{y}) = 3.16 \times 10^7 \;\text{s}[/latex]
[latex]1 \;\text{day} \;(\text{d}) = 86,400 \;\text{s}[/latex]
Speed [latex]1 \;\text{mile per hour} \;(\text{mph}) = 1.609 \;\text{km} / \text{h}[/latex]
[latex]1 \;\text{nautical mile per hour} \;(\text{naut}) = 1.852 \;\text{km} / \text{h}[/latex]
Angle [latex]1 \;\text{degree} \;(^{\circ}) = 1.745 \times 10^{-2} \;\text{rad}[/latex]
[latex]1 \;\text{minute of arc} \; ([/latex]‘ [latex]) = 1/60 \;\text{degree}[/latex]
[latex]1 \;\text{second of arc} \; (") = 1/60 \;\text{minute of arc}[/latex]
[latex]1 \;\text{grad} = 1.571 \times 10^{-2} \;\text{rad}[/latex]
Energy [latex]1 \;\text{kiloton TNT} \;(\text{kT}) = 4.2 \times 10^{12} \;\text{J}[/latex]
[latex]1 \; \text{kilowatt hour} \;(\text{kW} \cdot h) = 3.60 \times 10^6 \;\text{J}[/latex]
[latex]1 \;\text{food calorie} \;(\text{kcal}) = 4186 \;\text{J}[/latex]
[latex]1 \;\text{calorie} \;(\text{cal}) = 4.186 \;\text{J}[/latex]
[latex]1 \;\text{electron volt} \;(\text{eV}) = 1.60 \times 10^{-19} \;\text{J}[/latex]
Pressure [latex]1 \;\text{atmosphere} \;(\text{atm}) = 1.013 \times 10^5 \;\text{Pa}[/latex]
[latex]1 \;\text{millimeter of mercury} \;(\text{mm Hg}) = 133.3 \;\text{Pa}[/latex]
[latex]1 \;\text{torricelli} \;(\text{torr}) = 1 \;\text{mm Hg} = 133.3 \;\text{Pa}[/latex]
Nuclear decay rate [latex]1 \;\text{curie} \;(\text{Ci}) = 3.70 \times 10^{10} \; \text{Bq}[/latex]
Table 9. Other Units
[latex]\text{Circumference of a circle with radius} \; \text{r} \; \text{or diameter} \;\text{d}[/latex] [latex]C = 2 \pi r = \pi d[/latex]
[latex]\text{Area of a circle with radius} \; r \;\text{or diameter} d[/latex] [latex]A = \pi r^2 = \pi d^{2}/4[/latex]
[latex]\text{Area of a sphere with radius} \; r[/latex] [latex]A = 4 \pi r^2[/latex]
[latex]\text{Volume of a sphere with radius} \; r[/latex] [latex]V = (4/3)( \pi r^3)[/latex]
Table 10. Useful Formulae

Footnotes

  1. 1 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
  2. 2 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.

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College Physics Copyright © August 22, 2016 by OpenStax is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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