College Physics for AP® Courses 2e

# C | Useful Information

This appendix is broken into several tables.

Symbol Meaning Best Value Approximate Value
$c c$ Speed of light in vacuum $2 . 99792458 × 10 8 m / s 2 . 99792458 × 10 8 m / s$ $3 . 00 × 10 8 m / s 3 . 00 × 10 8 m / s$
$G G$ Gravitational constant $6 . 67408 ( 31 ) × 10 − 11 N ⋅ m 2 / kg 2 6 . 67408 ( 31 ) × 10 − 11 N ⋅ m 2 / kg 2$ $6 . 67 × 10 − 11 N ⋅ m 2 / kg 2 6 . 67 × 10 − 11 N ⋅ m 2 / kg 2$
$N A N A$ Avogadro’s number $6.02214076 × 10 23 6.02214076 × 10 23$ $6 . 02 × 10 23 6 . 02 × 10 23$
$k k$ Boltzmann’s constant $1.380649 × 10 − 23 J / K 1.380649 × 10 − 23 J / K$ $1 . 38 × 10 − 23 J / K 1 . 38 × 10 − 23 J / K$
$R R$ Gas constant $8.3144621 ( 75 ) J / mol ⋅ K 8.3144621 ( 75 ) J / mol ⋅ K$ $8.31 J/mol ⋅ K = 1.99 cal/mol ⋅ K = 0.0821 atm ⋅ L/mol ⋅ K 8.31 J/mol ⋅ K = 1.99 cal/mol ⋅ K = 0.0821 atm ⋅ L/mol ⋅ K$
$σ σ$ Stefan-Boltzmann constant $5 . 670373 ( 21 ) × 10 − 8 W / m 2 ⋅ K 5 . 670373 ( 21 ) × 10 − 8 W / m 2 ⋅ K$ $5 . 67 × 10 − 8 W / m 2 ⋅ K 5 . 67 × 10 − 8 W / m 2 ⋅ K$
$k k$ Coulomb force constant $8 . 987551788 . . . × 10 9 N ⋅ m 2 / C 2 8 . 987551788 . . . × 10 9 N ⋅ m 2 / C 2$ $8.99 × 10 9 N ⋅ m 2 / C 2 8.99 × 10 9 N ⋅ m 2 / C 2$
$q e q e$ Charge on electron $− 1.602176634 × 10 − 19 C − 1.602176634 × 10 − 19 C$ $− 1 . 60 × 10 − 19 C − 1 . 60 × 10 − 19 C$
$ε 0 ε 0$ Permittivity of free space $8 . 854187817 . . . × 10 − 12 C 2 / N ⋅ m 2 8 . 854187817 . . . × 10 − 12 C 2 / N ⋅ m 2$ $8 . 85 × 10 − 12 C 2 / N ⋅ m 2 8 . 85 × 10 − 12 C 2 / N ⋅ m 2$
$μ 0 μ 0$ Permeability of free space $4π × 10 − 7 T ⋅ m / A 4π × 10 − 7 T ⋅ m / A$ $1 . 26 × 10 − 6 T ⋅ m / A 1 . 26 × 10 − 6 T ⋅ m / A$
$h h$ Planck’s constant $6.62607015 × 10 − 34 J ⋅ s 6.62607015 × 10 − 34 J ⋅ s$ $6 . 63 × 10 − 34 J ⋅ s 6 . 63 × 10 − 34 J ⋅ s$
Table C1 Important Constants 1
Symbol Meaning Best Value Approximate Value
$m e m e$ Electron mass $9 . 10938291 ( 40 ) × 10 − 31 kg 9 . 10938291 ( 40 ) × 10 − 31 kg$ $9 . 11 × 10 − 31 kg 9 . 11 × 10 − 31 kg$
$m p m p$ Proton mass $1 . 672621777 ( 74 ) × 10 − 27 kg 1 . 672621777 ( 74 ) × 10 − 27 kg$ $1 . 6726 × 10 − 27 kg 1 . 6726 × 10 − 27 kg$
$m n m n$ Neutron mass $1 . 674927351 ( 74 ) × 10 − 27 kg 1 . 674927351 ( 74 ) × 10 − 27 kg$ $1 . 6749 × 10 − 27 kg 1 . 6749 × 10 − 27 kg$
$u u$ Atomic mass unit $1 . 660538921 ( 73 ) × 10 − 27 kg 1 . 660538921 ( 73 ) × 10 − 27 kg$ $1 . 6605 × 10 − 27 kg 1 . 6605 × 10 − 27 kg$
Table C2 Submicroscopic Masses 2
 Sun mass $1 . 99 × 10 30 kg 1 . 99 × 10 30 kg$ average radius $6 . 96 × 10 8 m 6 . 96 × 10 8 m$ Earth-sun distance (average) $1 . 496 × 10 11 m 1 . 496 × 10 11 m$ Earth mass $5 . 9736 × 10 24 kg 5 . 9736 × 10 24 kg$ average radius $6 . 376 × 10 6 m 6 . 376 × 10 6 m$  orbital period $3 . 16 × 10 7 s 3 . 16 × 10 7 s$ Moon mass $7 . 35 × 10 22 kg 7 . 35 × 10 22 kg$ average radius $1 . 74 × 10 6 m 1 . 74 × 10 6 m$ orbital period (average) $2 . 36 × 10 6 s 2 . 36 × 10 6 s$ Earth-moon distance (average) $3 . 84 × 10 8 m 3 . 84 × 10 8 m$
Table C3 Solar System Data
Prefix Symbol Value Prefix Symbol Value
tera T $10 12 10 12$ deci d $10 − 1 10 − 1$
giga G $10 9 10 9$ centi c $10 − 2 10 − 2$
mega M $10 6 10 6$ milli m $10 − 3 10 − 3$
kilo k $10 3 10 3$ micro $μ μ$ $10 − 6 10 − 6$
hecto h $10 2 10 2$ nano n $10 − 9 10 − 9$
deka da $10 1 10 1$ pico p $10 − 12 10 − 12$
$10 0 ( = 1 ) 10 0 ( = 1 )$ femto f $10 − 15 10 − 15$
Table C4 Metric Prefixes for Powers of Ten and Their Symbols
 Alpha $Α Α$ $α α$ Eta $Η Η$ $η η$ Nu $Ν Ν$ $ν ν$ Tau $Τ Τ$ $τ τ$ Beta $Β Β$ $β β$ Theta $Θ Θ$ $θ θ$ Xi $Ξ Ξ$ $ξ ξ$ Upsilon $Υ Υ$ $υ υ$ Gamma $Γ Γ$ $γ γ$ Iota $Ι Ι$ $ι ι$ Omicron $Ο Ο$ $ο ο$ Phi $Φ Φ$ $ϕ ϕ$ Delta $Δ Δ$ $δ δ$ Kappa $Κ Κ$ $κ κ$ Pi $Π Π$ $π π$ Chi $Χ Χ$ $χ χ$ Epsilon $Ε Ε$ $ε ε$ Lambda $Λ Λ$ $λ λ$ Rho $Ρ Ρ$ $ρ ρ$ Psi $Ψ Ψ$ $ψ ψ$ Zeta $Ζ Ζ$ $ζ ζ$ Mu $Μ Μ$ $μ μ$ Sigma $Σ Σ$ $σ σ$ Omega $Ω Ω$ $ω ω$
Table C5 The Greek Alphabet
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 $J = kg ⋅ m 2 / s 2 J = kg ⋅ m 2 / s 2$ 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 C6 SI Units
 Length $1 inch ( in . ) = 2 . 54 cm ( exactly ) 1 inch ( in . ) = 2 . 54 cm ( exactly )$ $1 foot ( ft ) = 0 . 3048 m 1 foot ( ft ) = 0 . 3048 m$ $1 mile ( mi ) = 1 . 609 km 1 mile ( mi ) = 1 . 609 km$ Force $1 pound ( lb ) = 4 . 448 N 1 pound ( lb ) = 4 . 448 N$ Energy $1 British thermal unit ( Btu ) = 1 . 055 × 10 3 J 1 British thermal unit ( Btu ) = 1 . 055 × 10 3 J$ Power $1 horsepower ( hp ) = 746 W 1 horsepower ( hp ) = 746 W$ Pressure $1 lb / in 2 = 6 . 895 × 10 3 Pa 1 lb / in 2 = 6 . 895 × 10 3 Pa$
Table C7 Selected British Units
 Length $1 light year ( ly ) = 9 . 46 × 10 15 m 1 light year ( ly ) = 9 . 46 × 10 15 m$ $1 astronomical unit ( au ) = 1 . 50 × 10 11 m 1 astronomical unit ( au ) = 1 . 50 × 10 11 m$ $1 nautical mile = 1 . 852 km 1 nautical mile = 1 . 852 km$ $1 angstrom ( Å ) = 10 − 10 m 1 angstrom ( Å ) = 10 − 10 m$ Area $1 acre ( ac ) = 4 . 05 × 10 3 m 2 1 acre ( ac ) = 4 . 05 × 10 3 m 2$ $1 square foot ( ft 2 ) = 9 . 29 × 10 − 2 m 2 1 square foot ( ft 2 ) = 9 . 29 × 10 − 2 m 2$ $1 barn ( b ) = 10 − 28 m 2 1 barn ( b ) = 10 − 28 m 2$ Volume $1 liter ( L ) = 10 − 3 m 3 1 liter ( L ) = 10 − 3 m 3$ $1 U.S. gallon ( gal ) = 3 . 785 × 10 − 3 m 3 1 U.S. gallon ( gal ) = 3 . 785 × 10 − 3 m 3$ Mass $1 solar mass = 1 . 99 × 10 30 kg 1 solar mass = 1 . 99 × 10 30 kg$ $1 metric ton = 10 3 kg 1 metric ton = 10 3 kg$ $1 atomic mass unit ( u ) = 1 . 6605 × 10 − 27 kg 1 atomic mass unit ( u ) = 1 . 6605 × 10 − 27 kg$ Time $1 year ( y ) = 3 . 16 × 10 7 s 1 year ( y ) = 3 . 16 × 10 7 s$ $1 day ( d ) = 86 , 400 s 1 day ( d ) = 86 , 400 s$ Speed $1 mile per hour ( mph ) = 1 . 609 km / h 1 mile per hour ( mph ) = 1 . 609 km / h$ $1 nautical mile per hour ( naut ) = 1 . 852 km / h 1 nautical mile per hour ( naut ) = 1 . 852 km / h$ Angle $1 degree ( ° ) = 1 . 745 × 10 − 2 rad 1 degree ( ° ) = 1 . 745 × 10 − 2 rad$ $1 minute of arc ( ' ) = 1 / 60 degree 1 minute of arc ( ' ) = 1 / 60 degree$ $1 second of arc ( '' ) = 1 / 60 minute of arc 1 second of arc ( '' ) = 1 / 60 minute of arc$ $1 grad = 1 . 571 × 10 − 2 rad 1 grad = 1 . 571 × 10 − 2 rad$ Energy $1 kiloton TNT ( kT ) = 4 . 2 × 10 12 J 1 kiloton TNT ( kT ) = 4 . 2 × 10 12 J$ $1 kilowatt hour ( kW ⋅ h ) = 3 . 60 × 10 6 J 1 kilowatt hour ( kW ⋅ h ) = 3 . 60 × 10 6 J$ $1 food calorie ( kcal ) = 4186 J 1 food calorie ( kcal ) = 4186 J$ $1 calorie ( cal ) = 4 . 186 J 1 calorie ( cal ) = 4 . 186 J$ $1 electron volt ( eV ) = 1 . 60 × 10 − 19 J 1 electron volt ( eV ) = 1 . 60 × 10 − 19 J$ Pressure $1 atmosphere ( atm ) = 1 . 013 × 10 5 Pa 1 atmosphere ( atm ) = 1 . 013 × 10 5 Pa$ $1 millimeter of mercury ( mm Hg ) = 133 . 3 Pa 1 millimeter of mercury ( mm Hg ) = 133 . 3 Pa$ $1 torricelli ( torr ) = 1 mm Hg = 133 . 3 Pa 1 torricelli ( torr ) = 1 mm Hg = 133 . 3 Pa$ Nuclear decay rate $1 curie ( Ci ) = 3 . 70 × 10 10 Bq 1 curie ( Ci ) = 3 . 70 × 10 10 Bq$
Table C8 Other Units
 Circumference of a circle with radius $rr$ or diameter $dd$ $C = 2 πr = πd C = 2 πr = πd$ Area of a circle with radius $rr$ or diameter $dd$ $A = πr 2 = πd 2 / 4 A = πr 2 = πd 2 / 4$ Area of a sphere with radius $rr$ $A = 4 πr 2 A = 4 πr 2$ Volume of a sphere with radius $rr$ $V = 4 / 3 πr 3 V = 4 / 3 πr 3$
Table C9 Useful Formulae

### Footnotes

• 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 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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