Giáo trình

# College Physics

Science and Technology

## Useful Information

Tác giả: OpenStaxCollege

This appendix is broken into several tables.

 Symbol Meaning Best Value Approximate Value $c$ Speed of light in vacuum $2\text{.}\text{99792458}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{8}\phantom{\rule{0.15em}{0ex}}\text{m}/\text{s}$ $3\text{.}\text{00}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{8}\phantom{\rule{0.15em}{0ex}}\text{m}/\text{s}$ $G$ Gravitational constant $6\text{.}\text{67384}\left(\text{80}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{11}}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{kg}}^{2}$ $6\text{.}\text{67}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{11}}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{kg}}^{2}$ ${N}_{A}$ Avogadro’s number $6\text{.}\text{02214129}\left(\text{27}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}}$ $6\text{.}\text{02}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}}$ $k$ Boltzmann’s constant $1\text{.}\text{3806488}\left(\text{13}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K}$ $1\text{.}\text{38}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K}$ $R$ Gas constant $8\text{.}\text{3144621}\left(\text{75}\right)\phantom{\rule{0.15em}{0ex}}\text{J}/\text{mol}\cdot \text{K}$ $8\text{.}\text{31}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{mol}\cdot \text{K}=1\text{.}\text{99}\phantom{\rule{0.20em}{0ex}}\text{cal}/\text{mol}\cdot \text{K}=0\text{.}\text{0821}\text{atm}\cdot \text{L}/\text{mol}\cdot \text{K}$ $\text{σ}$ Stefan-Boltzmann constant $5\text{.}\text{670373}\left(\text{21}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-8}\phantom{\rule{0.15em}{0ex}}\text{W}/{\text{m}}^{2}\cdot \text{K}$ $5\text{.}\text{67}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-8}\phantom{\rule{0.15em}{0ex}}\text{W}/{\text{m}}^{2}\cdot \text{K}$ $k$ Coulomb force constant $8\text{.}\text{987551788}\text{.}\text{.}\text{.}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{9}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{C}}^{2}$ $8.99\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{9}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{C}}^{2}$ ${q}_{e}$ Charge on electron $-1\text{.}\text{602176565}\left(\text{35}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C}$ $-1\text{.}\text{60}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C}$ ${\text{ε}}_{0}$ Permittivity of free space $8\text{.}\text{854187817}\text{.}\text{.}\text{.}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{12}}\phantom{\rule{0.15em}{0ex}}{\text{C}}^{2}/\text{N}\cdot {\text{m}}^{2}$ $8\text{.}\text{85}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{12}}\phantom{\rule{0.15em}{0ex}}{\text{C}}^{2}/\text{N}\cdot {\text{m}}^{2}$ ${\text{μ}}_{0}$ Permeability of free space $4\pi \phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-7}\phantom{\rule{0.15em}{0ex}}\text{T}\cdot \text{m}/\text{A}$ $1\text{.}\text{26}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-6}\phantom{\rule{0.15em}{0ex}}\text{T}\cdot \text{m}/\text{A}$ $h$ Planck’s constant $6\text{.}\text{62606957}\left(\text{29}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s}$ $6\text{.}\text{63}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s}$
 Symbol Meaning Best Value Approximate Value $m e size 12{m rSub { size 8{e} } } {}$ Electron mass $9 . 10938291 ( 40 ) × 10 − 31 kg size 12{9 "." "10938291" \( "40" \) times "10" rSup { size 8{ - "31"} } `"kg"} {}$ $9 . 11 × 10 − 31 kg size 12{9 "." "11" times "10" rSup { size 8{ - "31"} } `"kg"} {}$ $m p size 12{m rSub { size 8{p} } } {}$ Proton mass $1 . 672621777 ( 74 ) × 10 − 27 kg size 12{1 "." "672621777" \( "74" \) times "10" rSup { size 8{ - "27"} } `"kg"} {}$ $1 . 6726 × 10 − 27 kg size 12{1 "." "6726" times "10" rSup { size 8{ - "27"} } `"kg"} {}$ $m n size 12{m rSub { size 8{n} } } {}$ Neutron mass $1 . 674927351 ( 74 ) × 10 − 27 kg size 12{1 "." "674927351" \( "74" \) times "10" rSup { size 8{ - "27"} } `"kg"} {}$ $1 . 6749 × 10 − 27 kg size 12{1 "." "6749" times "10" rSup { size 8{ - "27"} } `"kg"} {}$ $u size 12{u} {}$ Atomic mass unit $1 . 660538921 ( 73 ) × 10 − 27 kg size 12{1 "." "660538921" \( "73" \) times "10" rSup { size 8{ - "27"} } `"kg"} {}$ $1 . 6605 × 10 − 27 kg size 12{1 "." "6605" times "10" rSup { size 8{ - "27"} } `"kg"} {}$
 Sun mass $1 . 99 × 10 30 kg size 12{1 "." "99" times "10" rSup { size 8{"30"} } `"kg"} {}$ average radius $6 . 96 × 10 8 m size 12{6 "." "96" times "10" rSup { size 8{8} } `m} {}$ Earth-sun distance (average) $1 . 496 × 10 11 m size 12{1 "." "496" times "10" rSup { size 8{"11"} } " m"} {}$ Earth mass $5 . 9736 × 10 24 kg size 12{5 "." "9736" times "10" rSup { size 8{"24"} } `"kg"} {}$ average radius $6 . 376 × 10 6 m size 12{6 "." "376" times "10" rSup { size 8{6} } `m} {}$ ${}$ orbital period $3 . 16 × 10 7 s size 12{3 "." "16" times "10" rSup { size 8{7} } " s "} {}$ Moon mass $7 . 35 × 10 22 kg size 12{7 "." "35" times "10" rSup { size 8{"22"} } `"kg"} {}$ average radius $1 . 74 × 10 6 m size 12{1 "." "74" times "10" rSup { size 8{6} } `m} {}$ orbital period (average) $2 . 36 × 10 6 s size 12{2 "." "36" times "10" rSup { size 8{6} } " s"} {}$ Earth-moon distance (average) $3 . 84 × 10 8 m size 12{3 "." "84" times "10" rSup { size 8{8} } " m"} {}$
 Prefix Symbol Value Prefix Symbol Value tera T ${\text{10}}^{\text{12}}$ deci d ${\text{10}}^{-1}$ giga G ${\text{10}}^{9}$ centi c ${\text{10}}^{-2}$ mega M ${\text{10}}^{6}$ milli m ${\text{10}}^{-3}$ kilo k ${\text{10}}^{3}$ micro $μ size 12{μ} {}$ ${\text{10}}^{-6}$ hecto h ${\text{10}}^{2}$ nano n ${\text{10}}^{-9}$ deka da ${\text{10}}^{1}$ pico p ${\text{10}}^{-\text{12}}$ — — ${\text{10}}^{0}\left(=1\right)$ femto f ${\text{10}}^{-\text{15}}$
 Alpha $\text{Α}$ $\alpha$ Eta $\text{Η}$ $\eta$ Nu $\text{Ν}$ $\nu$ Tau $\text{Τ}$ $\tau$ Beta $\text{Β}$ $\beta$ Theta $\text{Θ}$ $\theta$ Xi $\text{Ξ}$ $\xi$ Upsilon $\text{Υ}$ $\upsilon$ Gamma $\text{Γ}$ $\gamma$ Iota $\text{Ι}$ $\iota$ Omicron $\text{Ο}$ $ο$ Phi $\text{Φ}$ $\varphi$ Delta $\text{Δ}$ $\delta$ Kappa $\text{Κ}$ $\kappa$ Pi $\text{Π}$ $\pi$ Chi $\text{Χ}$ $\chi$ Epsilon $\text{Ε}$ $\epsilon$ Lambda $\text{Λ}$ $\lambda$ Rho $\text{Ρ}$ $\rho$ Psi $\text{Ψ}$ $\psi$ Zeta $\text{Ζ}$ $\zeta$ Mu $\text{Μ}$ $\mu$ Sigma $\text{Σ}$ $\sigma$ Omega $\Omega$ $\omega$
 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 $N = kg ⋅ m / s 2 size 12{N="kg" cdot {m} slash {s rSup { size 8{2} } } } {}$ newton Energy $J = kg ⋅ m 2 / s 2 size 12{J="kg" cdot {m rSup { size 8{2} } } slash {s rSup { size 8{2} } } } {}$ joule Power $W = J / s size 12{W= {J} slash {s} } {}$ watt Pressure $Pa = N / m 2 size 12{"Pa"= {N} slash {m rSup { size 8{2} } } } {}$ pascal Frequency $Hz = 1 / s size 12{"Hz"= {1} slash {s} } {}$ hertz Electronic potential $V = J / C size 12{V= {J} slash {C} } {}$ volt Capacitance $F = C / V size 12{F= {C} slash {V} } {}$ farad Charge $C = s ⋅ A size 12{C=s cdot A} {}$ coulomb Resistance $Ω = V / A size 12{ %OMEGA = {V} slash {A} } {}$ ohm Magnetic field $T = N / A ⋅ m size 12{T= {N} slash { left (A cdot m right )} } {}$ tesla Nuclear decay rate $Bq = 1 / s size 12{"Bq"= {1} slash {s} } {}$ becquerel
 Length $1\phantom{\rule{0.20em}{0ex}}\text{inch}\phantom{\rule{0.20em}{0ex}}\left(\text{in}\text{.}\right)=2\text{.}\text{54}\phantom{\rule{0.20em}{0ex}}\text{cm}\phantom{\rule{0.20em}{0ex}}\left(\text{exactly}\right)$ $1\phantom{\rule{0.20em}{0ex}}\text{foot}\phantom{\rule{0.20em}{0ex}}\left(\text{ft}\right)=0\text{.}\text{3048}\phantom{\rule{0.20em}{0ex}}\text{m}$ $1\phantom{\rule{0.20em}{0ex}}\text{mile}\phantom{\rule{0.20em}{0ex}}\left(\text{mi}\right)=1\text{.}\text{609}\phantom{\rule{0.20em}{0ex}}\text{km}$ Force $1\phantom{\rule{0.20em}{0ex}}\text{pound}\phantom{\rule{0.20em}{0ex}}\left(\text{lb}\right)=4\text{.}\text{448}\phantom{\rule{0.20em}{0ex}}\text{N}$ Energy $1\phantom{\rule{0.20em}{0ex}}\text{British thermal unit}\phantom{\rule{0.20em}{0ex}}\left(\text{Btu}\right)=1\text{.}\text{055}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{J}$ Power $1\phantom{\rule{0.20em}{0ex}}\text{horsepower}\phantom{\rule{0.20em}{0ex}}\left(\text{hp}\right)=\text{746}\phantom{\rule{0.20em}{0ex}}\text{W}$ Pressure $1\phantom{\rule{0.20em}{0ex}}\text{lb}/{\text{in}}^{2}=6\text{.}\text{895}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{Pa}$
 Length $1\phantom{\rule{0.20em}{0ex}}\text{light year}\phantom{\rule{0.20em}{0ex}}\left(\text{ly}\right)=9\text{.}\text{46}×{\text{10}}^{\text{15}}\phantom{\rule{0.20em}{0ex}}\text{m}$ $1\phantom{\rule{0.20em}{0ex}}\text{astronomical unit}\phantom{\rule{0.20em}{0ex}}\left(\text{au}\right)=1\text{.}\text{50}×{\text{10}}^{\text{11}}\phantom{\rule{0.20em}{0ex}}\text{m}$ $1\phantom{\rule{0.20em}{0ex}}\text{nautical mile}=1\text{.}\text{852}\phantom{\rule{0.20em}{0ex}}\text{km}$ $1\phantom{\rule{0.20em}{0ex}}\text{angstrom}\left(\text{Å}\right)\phantom{\rule{0.20em}{0ex}}={\text{10}}^{-\text{10}}\phantom{\rule{0.20em}{0ex}}\text{m}$ Area $1\phantom{\rule{0.20em}{0ex}}\text{acre}\phantom{\rule{0.20em}{0ex}}\left(\text{ac}\right)=4\text{.}\text{05}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}$ $1\phantom{\rule{0.20em}{0ex}}\text{square foot}\phantom{\rule{0.20em}{0ex}}\left({\text{ft}}^{2}\right)=9\text{.}\text{29}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}$ $1\phantom{\rule{0.20em}{0ex}}\text{barn}\phantom{\rule{0.20em}{0ex}}\left(b\right)={\text{10}}^{-\text{28}}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}$ Volume $1\phantom{\rule{0.20em}{0ex}}\text{liter}\phantom{\rule{0.20em}{0ex}}\left(L\right)={\text{10}}^{-3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{3}$ $1\phantom{\rule{0.20em}{0ex}}\text{U.S. gallon}\phantom{\rule{0.20em}{0ex}}\left(\text{gal}\right)=3\text{.}\text{785}×{\text{10}}^{-3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{3}$ Mass $1\phantom{\rule{0.20em}{0ex}}\text{solar mass}\phantom{\rule{0.20em}{0ex}}=1\text{.}\text{99}×{\text{10}}^{\text{30}}\phantom{\rule{0.20em}{0ex}}\text{kg}$ $1\phantom{\rule{0.20em}{0ex}}\text{metric ton}={\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{kg}$ $1\phantom{\rule{0.20em}{0ex}}\text{atomic mass unit}\phantom{\rule{0.20em}{0ex}}\left(u\right)=1\text{.}\text{6605}×{\text{10}}^{-\text{27}}\phantom{\rule{0.20em}{0ex}}\text{kg}$ Time $1\phantom{\rule{0.20em}{0ex}}\text{year}\phantom{\rule{0.20em}{0ex}}\left(y\right)=3\text{.}\text{16}×{\text{10}}^{7}\phantom{\rule{0.20em}{0ex}}\text{s}$ $1\phantom{\rule{0.20em}{0ex}}\text{day}\phantom{\rule{0.20em}{0ex}}\left(d\right)=\text{86},\text{400}\phantom{\rule{0.20em}{0ex}}\text{s}$ Speed $1\phantom{\rule{0.20em}{0ex}}\text{mile per hour}\phantom{\rule{0.20em}{0ex}}\left(\text{mph}\right)=1\text{.}\text{609}\phantom{\rule{0.20em}{0ex}}\text{km}/\text{h}$ $1\phantom{\rule{0.20em}{0ex}}\text{nautical mile per hour}\phantom{\rule{0.20em}{0ex}}\left(\text{naut}\right)=1\text{.}\text{852}\phantom{\rule{0.20em}{0ex}}\text{km}/\text{h}$ Angle $1\phantom{\rule{0.20em}{0ex}}\text{degree}\phantom{\rule{0.20em}{0ex}}\left(°\right)=1\text{.}\text{745}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}\text{rad}$ $1\phantom{\rule{0.20em}{0ex}}\text{minute of arc}\phantom{\rule{0.20em}{0ex}}{\left(}^{\text{'}}\right)=1/\text{60}\phantom{\rule{0.20em}{0ex}}\text{degree}$ $1\phantom{\rule{0.20em}{0ex}}\text{second of arc}\text{}\phantom{\rule{0.20em}{0ex}}{\left(}^{\text{''}}\right)=1/\text{60}\phantom{\rule{0.20em}{0ex}}\text{minute of arc}$ $1\phantom{\rule{0.20em}{0ex}}\text{grad}=1\text{.}\text{571}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}\text{rad}$ Energy $1\phantom{\rule{0.20em}{0ex}}\text{kiloton TNT}\phantom{\rule{0.20em}{0ex}}\left(\text{kT}\right)=4\text{.}2×{\text{10}}^{\text{12}}\phantom{\rule{0.20em}{0ex}}\text{J}$ $1\phantom{\rule{0.20em}{0ex}}\text{kilowatt hour}\phantom{\rule{0.20em}{0ex}}\left(\text{kW}\cdot h\right)=3\text{.}\text{60}×{\text{10}}^{6}\phantom{\rule{0.20em}{0ex}}\text{J}$ $1\phantom{\rule{0.20em}{0ex}}\text{food calorie}\phantom{\rule{0.20em}{0ex}}\left(\text{kcal}\right)=\text{4186}\phantom{\rule{0.20em}{0ex}}\text{J}$ $1\phantom{\rule{0.20em}{0ex}}\text{calorie}\phantom{\rule{0.20em}{0ex}}\left(\text{cal}\right)=4\text{.}\text{186}\phantom{\rule{0.20em}{0ex}}\text{J}$ $1\phantom{\rule{0.20em}{0ex}}\text{electron volt}\phantom{\rule{0.20em}{0ex}}\left(\text{eV}\right)=1\text{.}\text{60}×{\text{10}}^{-\text{19}}\phantom{\rule{0.20em}{0ex}}\text{J}$ Pressure $1\phantom{\rule{0.20em}{0ex}}\text{atmosphere}\phantom{\rule{0.20em}{0ex}}\left(\text{atm}\right)=1\text{.}\text{013}×{\text{10}}^{5}\phantom{\rule{0.20em}{0ex}}\text{Pa}$ $1\phantom{\rule{0.20em}{0ex}}\text{millimeter of mercury}\phantom{\rule{0.20em}{0ex}}\left(\text{mm}\phantom{\rule{0.20em}{0ex}}\text{Hg}\right)=\text{133}\text{.}3\phantom{\rule{0.20em}{0ex}}\text{Pa}$ $1\phantom{\rule{0.20em}{0ex}}\text{torricelli}\phantom{\rule{0.20em}{0ex}}\left(\text{torr}\right)=1\phantom{\rule{0.20em}{0ex}}\text{mm}\phantom{\rule{0.20em}{0ex}}\text{Hg}=\text{133}\text{.}3\phantom{\rule{0.20em}{0ex}}\text{Pa}$ Nuclear decay rate $1\phantom{\rule{0.20em}{0ex}}\text{curie}\phantom{\rule{0.20em}{0ex}}\left(\text{Ci}\right)=3\text{.}\text{70}×{\text{10}}^{\text{10}}\phantom{\rule{0.20em}{0ex}}\text{Bq}$
 Circumference of a circle with radius $r$ or diameter $d$ $C=2\pi r=\mathrm{\pi d}$ Area of a circle with radius $r$ or diameter $d$ $A={\mathrm{\pi r}}^{2}={\mathrm{\pi d}}^{2}/4$ Area of a sphere with radius $r$ $A=4{\pi r}^{2}$ Volume of a sphere with radius $r$ $V=\left(4/3\right)\left({\mathrm{\pi r}}^{3}\right)$