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College Physics for AP® Courses 2e

C | Useful Information

College Physics for AP® Courses 2eC | 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
Supplementary unit Angle rad radian
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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