Appendix BPhysical Constants, Units, and Symbols
Physics writing is built from symbols such as $c$ (the speed of light), $k_{\mathrm B}$ (the Boltzmann constant), and $\rho$ (rho); from units such as $\mathrm{N}$ (newton) and $\mathrm{Pa}$ (pascal); and from hundreds of technical terms. This appendix is a “quick reference” that gathers all of them in one place. When you come across an unfamiliar letter, unit, or word while reading the main text, open this appendix first. Most entries come with their reading and a one-line meaning, and every entry has a link to the chapter and section where the main text first explains it properly. If you follow the link back, you can reread the definition and the worked examples.
Many readers probably memorized values in high school physics, such as “$g=9.8\ \mathrm{m/s^2}$” and “$k=9.0\times10^9\ \mathrm{N\,m^2/C^2}$.” In university physics, the connections among the constants (for example $R=N_{\mathrm A}k_{\mathrm B}$ and $c=1/\sqrt{\varepsilon_0\mu_0}$) come into view, and you also begin to wonder how precisely each value is known. The table in B.1 distinguishes the constants that became defined values with zero uncertainty in the 2019 revision of the SI (International System of Units) from the constants that are measured in experiments.
What you will be able to do with this appendix
- Look up the physical constants used in this book (CODATA 2018 recommended values), together with their values, units, meanings, and the chapters where they first appear (B.1).
- Learn the seven base units of the SI units, and write the derived units with special names in terms of the base units. You can also look up how the prefixes are read, and unit conversions (B.2).
- Check how the 24 Greek letters are read and how this book uses them (B.3).
- In the list of symbols for each part, look up each symbol, how it is read, its meaning, its unit, and the chapter where it first appears. Cautions for cases where the same symbol takes a different meaning are also listed (B.4).
- Use the index of terms of this book (in alphabetical order) to jump to the chapter and section where a technical term is defined (B.5).
Prerequisites: None in particular. From any chapter of this book, you can simply look things up here at the point where you need them.
Source notes: This appendix supplements material not in the notes. Its symbols and numerical values agree with those of the whole book (Yasuhide Mochizuki's eight volumes of “Physics Notes” reorganized with unified notation).
Source notes: This appendix supplements material not in the notes. Its symbols and numerical values agree with those of the whole book (Yasuhide Mochizuki's eight volumes of “Physics Notes” reorganized with unified notation).
B.1 Table of Physical Constants
The values are the 2018 CODATA (Committee on Data for Science and Technology) recommended values. A constant marked exact (defined) value is one that the May 2019 revision of the SI decided to “set to that value,” and it carries no uncertainty (it is not a quantity determined by measurement; rather, the meter and the kilogram are determined from these values). A “value determined by the defined values” is a quantity that can be computed exactly from a combination of defined values (for example $R=N_{\mathrm A}k_{\mathrm B}$); in this book we show its leading digits and indicate the continuation with $\ldots$. All the other values were measured in experiments, and the number in parentheses at the end denotes the standard uncertainty: $8.854\,187\,8128(13)\times10^{-12}$ means that the last two digits, “28,” have an uncertainty of about $\pm13$.
| Quantity | Symbol (reading) | Value | Unit | In a word | First appearance in this book (main chapters) |
|---|---|---|---|---|---|
| Speed of light in vacuum | $c$ (cee) | $299\,792\,458$ exact (defined) value | $\mathrm{m/s}$ | The speed at which light travels in vacuum. It is used in the definition of the meter. It has the same value when measured in any inertial frame of reference (Chapter 54). | Section 1.3 (mainly Section 54.4) |
| Planck constant | $h$ (aitch) | $6.626\,070\,15\times10^{-34}$ exact (defined) value | $\mathrm{J\,s}$ | The constant of proportionality connecting the energy and the frequency of light or of a particle ($E=h\nu$). It is used in the definition of the kilogram. | Section 1.3 (mainly Section 53.3) |
| Reduced Planck constant (Dirac constant) | $\hbar=\dfrac{h}{2\pi}$ (h-bar) | $1.054\,571\,817\ldots\times10^{-34}$ (value determined by the defined values) | $\mathrm{J\,s}$ | The quantity $h$ divided by $2\pi$. The energy of a quantum of angular frequency $\omega$ is $\hbar\omega$ (the same as $h\nu$). | Section 17.6 (mainly Section 58.1) |
| Elementary charge | $e$ (ee) | $1.602\,176\,634\times10^{-19}$ exact (defined) value | $\mathrm{C}$ | The magnitude of the charge of one electron (the charge of an electron is $-e$, and that of a proton is $+e$). | Section 1.4 (mainly Section 37.1) |
| Boltzmann constant | $k_{\mathrm B}$ (k-B) | $1.380\,649\times10^{-23}$ exact (defined) value | $\mathrm{J/K}$ | The “energy per 1 K of temperature” for one molecule. $k_{\mathrm B}T$ serves as a rough measure of the energy of thermal motion. | Section 24.3 |
| Avogadro constant | $N_{\mathrm A}$ (N-A) | $6.022\,140\,76\times10^{23}$ exact (defined) value | $\mathrm{mol^{-1}}$ | The number of particles contained in 1 mol of a substance. | Section 23.6 (mainly Section 24.2) |
| Gas constant | $R$ (ar) | $8.314\,462\,618\ldots$ (value determined by the defined values) | $\mathrm{J/(mol\,K)}$ | The constant of proportionality in the equation of state of an ideal gas, $pV=nRT$. It is determined by $R=N_{\mathrm A}k_{\mathrm B}$. | Section 23.6 |
| Faraday constant | $F$ (eff) | $96\,485.332\,12\ldots$ (value determined by the defined values) | $\mathrm{C/mol}$ | The magnitude of the electric charge carried by 1 mol of electrons. $F=N_{\mathrm A}e$. It is used for batteries and electrolysis. | Section 30.5 |
| Vacuum permittivity | $\varepsilon_0$ (epsilon-zero) | $8.854\,187\,8128(13)\times10^{-12}$ | $\mathrm{F/m}$ | The constant of proportionality that connects the electric field $\bm E$ and the electric displacement (electric flux density) $\bm D$ in vacuum ($\bm D=\varepsilon_0\bm E$). The constant of proportionality in Coulomb's law is $1/(4\pi\varepsilon_0)$. | Section 13.4 (mainly Section 35.1) |
| Vacuum permeability | $\mu_0$ (mu-zero) | $1.256\,637\,062\,12(19)\times10^{-6}$ | $\mathrm{N/A^2}$ | The constant of proportionality that connects the magnetic field $\bm H$ and the magnetic flux density $\bm B$ in vacuum ($\bm B=\mu_0\bm H$). It satisfies $\mu_0=1/(\varepsilon_0c^2)$ and is extremely close to $4\pi\times10^{-7}$ (a measured value since 2019). | Section 14.6 (mainly Section 38.1) |
| Gravitational constant | $G$ (gee) | $6.674\,30(15)\times10^{-11}$ | $\mathrm{N\,m^2/kg^2}$ | The constant of proportionality for the strength of universal gravitation ($F=GMm/r^2$). Among the fundamental constants it is the least precisely known; only about five significant figures are known. | Section 5.5 (mainly Section 8.1) |
| Electron mass | $m_{\mathrm e}$ (m-e) | $9.109\,383\,7015(28)\times10^{-31}$ | $\mathrm{kg}$ | The mass of one electron. Its rest energy is $m_{\mathrm e}c^2=0.510\,998\,950\,00(15)\ \mathrm{MeV}$. | Section 1.4 (mainly Section 57.5) |
| Proton mass | $m_{\mathrm p}$ (m-p) | $1.672\,621\,923\,69(51)\times10^{-27}$ | $\mathrm{kg}$ | The mass of one proton (about 1836 times the mass of the electron). $m_{\mathrm p}c^2=938.272\,088\,16(29)\ \mathrm{MeV}$. | Section 39.4 (mainly Section 57.5) |
| Neutron mass | $m_{\mathrm n}$ (m-n) | $1.674\,927\,498\,04(95)\times10^{-27}$ | $\mathrm{kg}$ | The mass of one neutron (slightly heavier than the proton). $m_{\mathrm n}c^2=939.565\,420\,52(54)\ \mathrm{MeV}$. The calculations in this book use $939.565\ \mathrm{MeV}$. | Not used in the calculations of this book (it appears in Section 57.6, in an example that expresses masses in $\mathrm{MeV}$) |
| Atomic mass unit | $u$ (you) | $1.660\,539\,066\,60(50)\times10^{-27}$ | $\mathrm{kg}$ | $1/12$ of the mass of one carbon-12 atom. $1\ \mathrm u\,c^2=931.494\,102\,42(28)\ \mathrm{MeV}$. | Section 39.6 |
| Electronvolt | $\mathrm{eV}$ (electronvolt) | $1.602\,176\,634\times10^{-19}$ exact (defined) value | $\mathrm{J}$ | The energy an electron gains when it is accelerated through a potential difference of $1\ \mathrm V$. It is used as a unit for the energies of atoms, molecules, and electrons. | Section 24.3 |
| Stefan–Boltzmann constant | $\sigma$ (sigma) | $5.670\,374\,419\ldots\times10^{-8}$ (value determined by the defined values) | $\mathrm{W\,m^{-2}K^{-4}}$ | The coefficient for which the power radiated from $1\ \mathrm{m^2}$ of the surface of a black body is $\sigma T^4$. $\sigma=2\pi^5k_{\mathrm B}^4/(15h^3c^2)$. | Section 53.5 |
| Constant of Wien's displacement law (Wien constant) | $b$ (bee) | $2.897\,771\,955\ldots\times10^{-3}$ (value determined by the defined values) | $\mathrm{m\,K}$ | The product $\lambda_{\max}T=b$ of the wavelength $\lambda_{\max}$ at which the intensity of black-body radiation is maximum and the temperature $T$. | Section 53.4 |
| Standard gravitational acceleration | $g_{\mathrm n}$ (g-n) | $9.806\,65$ exact (defined) value | $\mathrm{m/s^2}$ | The internationally fixed standard value of the gravitational acceleration. In the examples of this book, we use $g=9.8\ \mathrm{m/s^2}$ unless otherwise stated. | Section 1.5 |
| Standard atmospheric pressure (1 atmosphere) | $1\ \mathrm{atm}$ (one atmosphere) | $101\,325$ exact (defined) value | $\mathrm{Pa}$ | The standard value of atmospheric pressure near sea level. It is also true that $1\ \mathrm{atm}=760\ \mathrm{mmHg}$. | Section 23.5 |
| Origin of the Celsius temperature scale ($0\ {}^\circ\mathrm{C}$) | $0\ {}^\circ\mathrm{C}$ (zero degrees Celsius) | $273.15$ exact (defined) value | $\mathrm{K}$ | $t\ [{}^\circ\mathrm{C}]=T\ [\mathrm K]-273.15$. The Celsius temperature and the absolute temperature have the same spacing of the scale; only the origin is shifted. | Section 23.1 |
| Fine-structure constant | $\alpha$ (alpha) | $7.297\,352\,5693(11)\times10^{-3}$ | dimensionless | A dimensionless number that expresses the strength of the electromagnetic interaction. $\alpha=e^2/(4\pi\varepsilon_0\hbar c)\approx1/137.036$. | Section 58.1 |
Why are there “defined values”?
In the past, the kilogram was a single lump of metal called the “International Prototype of the Kilogram,” and the meter was fixed by “the length of the Earth's meridian” or by a “prototype bar.” Artifacts get scratched and dirty, so there was a danger that their values would change every time they were measured. So in 2019 the system was revised: the numerical values were fixed for quantities that nature itself determines (the speed of light, the Planck constant, the elementary charge, the Boltzmann constant, the Avogadro constant, and so on), and the units are determined from them. Fixing $c=299\,792\,458\ \mathrm{m/s}$ determines “1 m,” and fixing $h=6.626\,070\,15\times10^{-34}\ \mathrm{J\,s}$ determines “1 kg.” The same measuring stick can be reproduced in any laboratory in any country. On the other hand, $\varepsilon_0,\mu_0,G,m_{\mathrm e}$, and so on are still quantities measured in experiments, so they have uncertainties. Note that the relation $\mu_0=1/(\varepsilon_0c^2)$ still holds, but $\mu_0$ is no longer exactly $4\pi\times10^{-7}\ \mathrm{N/A^2}$ (the relative difference is about $5\times10^{-10}$).
Illustration B.1: Checking the connections among the constants
Compute the values of (a) $R=N_{\mathrm A}k_{\mathrm B}$, (b) $F=N_{\mathrm A}e$, and (c) $\mu_0\varepsilon_0c^2$ from the numerical values in the table.
Solution. (a) $R=6.022\,140\,76\times10^{23}\ \mathrm{mol^{-1}}\times1.380\,649\times10^{-23}\ \mathrm{J/K}=8.314\,462\,618\ldots\ \mathrm{J/(mol\,K)}$ (the exponents cancel: $10^{23}\times10^{-23}=1$). (b) $F=6.022\,140\,76\times10^{23}\times1.602\,176\,634\times10^{-19}\ \mathrm{C/mol}=9.648\,533\,212\ldots\times10^{4}\ \mathrm{C/mol}=96\,485.332\,12\ldots\ \mathrm{C/mol}$. (c) $\mu_0\varepsilon_0c^2=1.256\,637\,062\,12\times10^{-6}\times8.854\,187\,8128\times10^{-12}\times\left(2.997\,924\,58\times10^{8}\right)^2$. Using $c^2=8.987\,551\,787\times10^{16}$ gives $\mu_0\varepsilon_0=1.112\,650\,056\times10^{-17}$, and the product is $0.999\,999\,999\,999\,96\ldots$, which equals 1 to a precision better than $10^{-11}$. Therefore $c=1/\sqrt{\varepsilon_0\mu_0}$ is confirmed numerically as well (the speed of an electromagnetic wave; see Section 42.3). As for units, in (a) we get $\mathrm{mol^{-1}\,J\,K^{-1}}$, which agrees with $\mathrm{J/(mol\,K)}$, and in (b) we get $\mathrm{mol^{-1}\,C}$, which agrees with $\mathrm{C/mol}$. (The calculations were checked with Python.)
B.2 SI Units, Prefixes, and Conversions
The SI (International System of Units; in French, Le Système international d'unités) is the system of units used in common by science and industry throughout the world. Every unit is built from the seven base units and the derived units formed by multiplying and dividing them. In this book, every physical quantity is accompanied by its SI unit.
B.2.1 The Seven Base Units
| Quantity | Unit name | Symbol | Key point of the definition (fixes the exact value of this constant) | First appearance in this book |
|---|---|---|---|---|
| Time | second | $\mathrm{s}$ | Frequency of the transition between the two hyperfine levels of the ground state of the cesium-133 atom, $\Delta\nu_{\mathrm{Cs}}=9\,192\,631\,770\ \mathrm{Hz}$ | Section 1.3 |
| Length | meter | $\mathrm{m}$ | Speed of light in vacuum $c=299\,792\,458\ \mathrm{m/s}$ (the distance light travels in $1/299\,792\,458\ \mathrm s$ is $1\ \mathrm m$) | Section 1.3 |
| Mass | kilogram | $\mathrm{kg}$ | Planck constant $h=6.626\,070\,15\times10^{-34}\ \mathrm{J\,s}$ (since $\mathrm{J\,s}=\mathrm{kg\,m^2\,s^{-1}}$, once $\mathrm m$ and $\mathrm s$ are fixed, $\mathrm{kg}$ is determined) | Section 1.3 |
| Electric current | ampere | $\mathrm{A}$ | Elementary charge $e=1.602\,176\,634\times10^{-19}\ \mathrm C$ ($\mathrm C=\mathrm{A\,s}$) | Section 37.1 |
| Thermodynamic temperature | kelvin | $\mathrm{K}$ | Boltzmann constant $k_{\mathrm B}=1.380\,649\times10^{-23}\ \mathrm{J/K}$ | Section 23.1 |
| Amount of substance | mole | $\mathrm{mol}$ | The amount of substance containing $6.022\,140\,76\times10^{23}$ elementary entities is $1\ \mathrm{mol}$ (this fixes the value of the Avogadro constant $N_{\mathrm A}$) | Section 23.6 |
| Luminous intensity | candela | $\mathrm{cd}$ | Luminous efficacy $K_{\mathrm{cd}}=683\ \mathrm{lm/W}$ of monochromatic light of frequency $540\times10^{12}\ \mathrm{Hz}$ (the unit of brightness as seen by the human eye; rarely used in this book) | Section 1.3 |
B.2.2 Derived Units with Special Names
Among the derived units formed as products and quotients of base units, the frequently used ones have special names (a unit named after a person has its symbol written with a capital letter). As the “Expression in base units” column shows, every one of them can be rewritten as a product of powers of $\mathrm{m},\mathrm{kg},\mathrm{s},\mathrm{A},\mathrm{K},\mathrm{mol},\mathrm{cd}$. If the units in the middle of a calculation can be put into this form, that serves as a check on whether the dimensions of the equation match (the dimensional analysis in Section 1.3).
| Quantity | Name | Symbol | Expression in other units | Expression in base units | First appearance in this book |
|---|---|---|---|---|---|
| Plane angle | radian | $\mathrm{rad}$ | $\mathrm{m/m}$ | 1 (dimensionless) | Section 3.1 |
| Solid angle | steradian | $\mathrm{sr}$ | $\mathrm{m^2/m^2}$ | 1 (dimensionless) | Section 35.3 |
| Frequency | hertz | $\mathrm{Hz}$ | — | $\mathrm{s^{-1}}$ | Section 7.1 |
| Force | newton | $\mathrm{N}$ | — | $\mathrm{kg\,m\,s^{-2}}$ | Section 1.3 |
| Pressure, stress | pascal | $\mathrm{Pa}$ | $\mathrm{N/m^2}$ | $\mathrm{kg\,m^{-1}\,s^{-2}}$ | Section 18.3 |
| Energy, work, quantity of heat | joule | $\mathrm{J}$ | $\mathrm{N\,m}$ | $\mathrm{kg\,m^2\,s^{-2}}$ | Section 1.3 |
| Power, electric power | watt | $\mathrm{W}$ | $\mathrm{J/s}$ | $\mathrm{kg\,m^2\,s^{-3}}$ | Section 4.6 |
| Electric charge (quantity of charge) | coulomb | $\mathrm{C}$ | — | $\mathrm{A\,s}$ | Section 35.1 |
| Potential difference, voltage, electromotive force | volt | $\mathrm{V}$ | $\mathrm{W/A}=\mathrm{J/C}$ | $\mathrm{kg\,m^2\,s^{-3}\,A^{-1}}$ | Section 36.1 |
| Capacitance | farad | $\mathrm{F}$ | $\mathrm{C/V}$ | $\mathrm{kg^{-1}\,m^{-2}\,s^4\,A^2}$ | Section 36.6 |
| Electrical resistance | ohm | $\Omega$ | $\mathrm{V/A}$ | $\mathrm{kg\,m^2\,s^{-3}\,A^{-2}}$ | Section 37.3 |
| Conductance | siemens | $\mathrm{S}$ | $\mathrm{A/V}=\Omega^{-1}$ | $\mathrm{kg^{-1}\,m^{-2}\,s^3\,A^2}$ | Section 37.3 |
| Magnetic flux | weber | $\mathrm{Wb}$ | $\mathrm{V\,s}$ | $\mathrm{kg\,m^2\,s^{-2}\,A^{-1}}$ | Section 38.1 |
| Magnetic flux density | tesla | $\mathrm{T}$ | $\mathrm{Wb/m^2}$ | $\mathrm{kg\,s^{-2}\,A^{-1}}$ | Section 38.1 |
| Inductance | henry | $\mathrm{H}$ | $\mathrm{Wb/A}$ | $\mathrm{kg\,m^2\,s^{-2}\,A^{-2}}$ | Section 40.5 |
| Celsius temperature | degree Celsius | ${}^\circ\mathrm{C}$ | $\mathrm K$ (the scale intervals are the same) | $t\ [{}^\circ\mathrm{C}]=T\ [\mathrm K]-273.15$ | Section 23.1 |
| Luminous flux | lumen | $\mathrm{lm}$ | $\mathrm{cd\,sr}$ | $\mathrm{cd}$ ($\mathrm{sr}$ is dimensionless) | not used in this book |
| Illuminance | lux | $\mathrm{lx}$ | $\mathrm{lm/m^2}$ | $\mathrm{cd\,m^{-2}}$ | not used in this book |
| Radioactivity | becquerel | $\mathrm{Bq}$ | — | $\mathrm{s^{-1}}$ | not used in this book |
| Absorbed dose | gray | $\mathrm{Gy}$ | $\mathrm{J/kg}$ | $\mathrm{m^2\,s^{-2}}$ | not used in this book |
| Dose equivalent | sievert | $\mathrm{Sv}$ | $\mathrm{J/kg}$ | $\mathrm{m^2\,s^{-2}}$ | not used in this book |
| Catalytic activity (enzyme activity) | katal | $\mathrm{kat}$ | — | $\mathrm{mol\,s^{-1}}$ | not used in this book |
Illustration B.2: Converting units to base units to check the dimensions of an equation
Express the unit $\mathrm F$ of the capacitance $C=Q/V$ in terms of the base units. Also verify that the unit of the energy $U=\tfrac12CV^2$ stored in a capacitor is $\mathrm J$.
Solution. The unit of $Q$ is $\mathrm C=\mathrm{A\,s}$, and the unit of $V$ is $\mathrm V=\mathrm{kg\,m^2\,s^{-3}\,A^{-1}}$, so $$ \mathrm F=\frac{\mathrm C}{\mathrm V}=\frac{\mathrm{A\,s}}{\mathrm{kg\,m^2\,s^{-3}\,A^{-1}}}=\mathrm{kg^{-1}\,m^{-2}\,s^{4}\,A^{2}} $$ (when $\mathrm{s^{-3}A^{-1}}$ in the denominator is moved up to the numerator, it becomes $\mathrm{s^{1+3}A^{1+1}}$). For the energy we have $$ [CV^2]=\mathrm{kg^{-1}m^{-2}s^{4}A^{2}}\cdot\left(\mathrm{kg\,m^2\,s^{-3}\,A^{-1}}\right)^2=\mathrm{kg^{-1+2}\,m^{-2+4}\,s^{4-6}\,A^{2-2}}=\mathrm{kg\,m^2\,s^{-2}}=\mathrm J $$ which agrees with $\mathrm{J}=\mathrm{kg\,m^2\,s^{-2}}$ (Table B.3). The fact that the exponent of the current $\mathrm A$ vanishes, $2-2=0$, is how the “transformation” of an electrical quantity into mechanical energy shows up in the units.
Caution: conventions for writing units
- Write unit symbols in upright (roman) type: $\mathrm{m}$, $\mathrm{kg}$. This distinguishes them from the italic $m$ (mass) and $K$ (the bulk modulus, etc.). Put a small space between the number and the unit: $g=9.8\ \mathrm{m/s^2}$.
- For units named after people, the symbol is written with a capital letter ($\mathrm{N},\mathrm{Pa},\mathrm{K}$), but the name is written in lowercase (newton, pascal, kelvin). The symbol for the liter is $\mathrm{L}$ (or $\mathrm l$).
- Do not stack prefixes (not $\mathrm{\mu\mu F}$, but $\mathrm{pF}$). The kilogram is the base unit of mass, but prefixes are attached to “gram,” as in $\mathrm{mg}$ and $\mathrm{Mg}$ (one does not write $\mathrm{\mu kg}$).
- The $\mathrm{m}$ (meter) and the prefix milli, $\mathrm m$, are the same letter, so $\mathrm{mm}$ is read as millimeter, $\mathrm{m^2}$ as square meter, and $\mathrm{ms}$ as millisecond. The last of these is distinguished from $\mathrm{m\,s}$ (meter second) by the space.
- Do not attach “degree” to $\mathrm{K}$ (kelvin) ($300\ \mathrm K$). Celsius temperature is written ${}^\circ\mathrm C$. A temperature difference has the same numerical value whether it is written in $\mathrm{K}$ or in ${}^\circ\mathrm C$.
B.2.3 SI Prefixes
These are the prefixes placed before a unit to indicate a multiple by some power of 10. At the General Conference on Weights and Measures in November 2022, in preparation for the growth in the amount of data, ronna and quetta (on the large side) and ronto and quecto (on the small side) were added, bringing the total to 24, from $10^{30}$ down to $10^{-30}$. The quantities used in science and technology span a very wide range (the size of an atomic nucleus is $10^{-15}\ \mathrm m$, and a galaxy is $10^{21}\ \mathrm m$), so different prefixes are used as appropriate.
| Multiple | Name (English) | Reading | Symbol | Example |
|---|---|---|---|---|
| $10^{30}$ | quetta | KET-uh | $\mathrm Q$ | added in 2022 |
| $10^{27}$ | ronna | RON-uh | $\mathrm R$ | added in 2022. The mass of the Earth is about $6\ \mathrm{Rg}$ |
| $10^{24}$ | yotta | YOT-uh | $\mathrm Y$ | |
| $10^{21}$ | zetta | ZET-uh | $\mathrm Z$ | |
| $10^{18}$ | exa | EX-uh | $\mathrm E$ | |
| $10^{15}$ | peta | PET-uh | $\mathrm P$ | |
| $10^{12}$ | tera | TER-uh | $\mathrm T$ | $1\ \mathrm{THz}=10^{12}\ \mathrm{Hz}$ (terahertz waves) |
| $10^{9}$ | giga | GIG-uh | $\mathrm G$ | $1\ \mathrm{GPa}=10^9\ \mathrm{Pa}$ (Young's modulus) |
| $10^{6}$ | mega | MEG-uh | $\mathrm M$ | $1\ \mathrm{MPa}=10^6\ \mathrm{Pa}$ (stress), $1\ \mathrm{MeV}$ |
| $10^{3}$ | kilo | KIL-oh | $\mathrm k$ | $1\ \mathrm{km}=10^3\ \mathrm m$ |
| $10^{2}$ | hecto | HEK-toh | $\mathrm h$ | $1\ \mathrm{hPa}=100\ \mathrm{Pa}$ (atmospheric pressure) |
| $10^{1}$ | deca | DEK-uh | $\mathrm{da}$ | rarely used |
| Multiple | Name (English) | Reading | Symbol | Example |
|---|---|---|---|---|
| $10^{-1}$ | deci | DES-ih | $\mathrm d$ | $1\ \mathrm{dL}=0.1\ \mathrm L$ |
| $10^{-2}$ | centi | SEN-tee | $\mathrm c$ | $1\ \mathrm{cm}=10^{-2}\ \mathrm m$ |
| $10^{-3}$ | milli | MIL-ee | $\mathrm m$ | $1\ \mathrm{mm}=10^{-3}\ \mathrm m$ |
| $10^{-6}$ | micro | MY-kroh | $\mu$ | $1\ \mu\mathrm m=10^{-6}\ \mathrm m$ |
| $10^{-9}$ | nano | NAN-oh | $\mathrm n$ | $1\ \mathrm{nm}=10^{-9}\ \mathrm m$ (wavelength of light) |
| $10^{-12}$ | pico | PEE-koh | $\mathrm p$ | $1\ \mathrm{pF}=10^{-12}\ \mathrm F$ |
| $10^{-15}$ | femto | FEM-toh | $\mathrm f$ | $1\ \mathrm{fm}=10^{-15}\ \mathrm m$ (size of an atomic nucleus) |
| $10^{-18}$ | atto | AT-oh | $\mathrm a$ | |
| $10^{-21}$ | zepto | ZEP-toh | $\mathrm z$ | |
| $10^{-24}$ | yocto | YOK-toh | $\mathrm y$ | |
| $10^{-27}$ | ronto | RON-toh | $\mathrm r$ | added in 2022 |
| $10^{-30}$ | quecto | KEK-toh | $\mathrm q$ | added in 2022 |
The first explanation of the prefixes in this book is in Section 1.3 (Table 1.1).
B.2.4 Commonly Used Conversions
This section collects the formulas for converting non-SI units, and units commonly used in the world of atoms and elementary particles, into SI. Those marked “exact (defined) value” are exact equalities; those accompanied by $\approx$ or $\ldots$ are approximate values.
| Quantity | Conversion | Note and where it is used in this book |
|---|---|---|
| Energy (electronvolt) | $1\ \mathrm{eV}=1.602\,176\,634\times10^{-19}\ \mathrm J$ (exact (defined) value) $1\ \mathrm{MeV}=10^6\ \mathrm{eV}=1.602\,176\,634\times10^{-13}\ \mathrm J$ | Used, for example, when expressing $k_{\mathrm B}T$ in eV (Section 24.3). |
| Energy (calorie) | $1\ \mathrm{cal}=4.184\ \mathrm J$ (thermochemical calorie; exact (defined) value) $1\ \mathrm{kcal}=4184\ \mathrm J$ | In this book, $1\ \mathrm{cal}\approx4.2\ \mathrm J$ is sometimes used as a rounded value (Section 23.2). In engineering, the International Steam Table calorie $1\ \mathrm{cal}_{\mathrm{IT}}=4.1868\ \mathrm J$ is also used. |
| Energy (electric energy) | $1\ \mathrm{kWh}=3.6\times10^6\ \mathrm J$ | $1\ \mathrm{kW}\times3600\ \mathrm s$ (Section 37.4). |
| Energy ↔ temperature | $1\ \mathrm{eV}\leftrightarrow e/k_{\mathrm B}=11\,604.518\,12\ldots\ \mathrm K$ $k_{\mathrm B}=8.617\,333\,262\ldots\times10^{-5}\ \mathrm{eV/K}$ At $T=300\ \mathrm K$, $k_{\mathrm B}T=0.025\,85\ \mathrm{eV}$ | The thermal energy at room temperature is about $\tfrac1{40}\ \mathrm{eV}$ (Section 24.3, Section 49.8). |
| Energy ↔ energy per amount of substance | Expressed per 1 mol, $1\ \mathrm{eV}$ becomes $eN_{\mathrm A}=F=96\,485.332\ldots\ \mathrm{J/mol}\approx96.5\ \mathrm{kJ/mol}$ | When estimating the energies of chemical reactions in eV (Section 30.5). |
| Energy ↔ wavelength | $hc=1239.841\,984\ldots\ \mathrm{eV\,nm}$, that is, $E\ [\mathrm{eV}]=1239.84/\lambda\ [\mathrm{nm}]$ | The energy of a single photon. For visible light ($\lambda=500\ \mathrm{nm}$), about $2.5\ \mathrm{eV}$ (Section 57.9). |
| $\hbar c$ (elementary particles and nuclei) | $\hbar c=197.326\,980\,4\ldots\ \mathrm{MeV\,fm}$ (in this book, $197.327\ \mathrm{MeV\,fm}$) | Connects length and energy in natural units (Section 58.1). $1\ \mathrm{fm}^{-1}\leftrightarrow197.327\ \mathrm{MeV}$. |
| Mass (expressed as energy) | $1\ \mathrm{MeV}/c^2=1.782\,661\,92\ldots\times10^{-30}\ \mathrm{kg}$ $1\ \mathrm u\,c^2=931.494\,102\,42\ \mathrm{MeV}$ | The masses of particles are expressed in $\mathrm{MeV}/c^2$ (Section 57.5). |
| Pressure | $1\ \mathrm{atm}=101\,325\ \mathrm{Pa}=1.013\,25\ \mathrm{bar}$ (exact (defined) value) $1\ \mathrm{bar}=10^5\ \mathrm{Pa}$ $1\ \mathrm{Torr}=\dfrac{101\,325}{760}\ \mathrm{Pa}=133.322\ldots\ \mathrm{Pa}$ (the $\mathrm{mmHg}$ used for blood pressure is almost the same as this) | The units $\mathrm{atm},\mathrm{bar}$ are used in experiments with gases (Section 23.5). |
| Pressure, stress (materials) | $1\ \mathrm{MPa}=10^6\ \mathrm{Pa}=1\ \mathrm{N/mm^2}$ $1\ \mathrm{GPa}=10^9\ \mathrm{Pa}$ | Units for the strength of materials ($\mathrm{MPa}$) and Young's modulus ($\mathrm{GPa}$) (Section 18.3). |
| Force | $1\ \mathrm{kgf}=9.806\,65\ \mathrm N$ (exact (defined) value) | An engineering unit of weight: “the magnitude of the gravitational force acting on a body of $1\ \mathrm{kg}$” (Section 21.5). |
| Volume | $1\ \mathrm L=10^{-3}\ \mathrm{m^3}=1\ \mathrm{dm^3}$ | The volume of a gas (Section 23.5). |
| Length | $1\ \text{Å}=10^{-10}\ \mathrm m=0.1\ \mathrm{nm}$ (ångström) $1\ \mathrm{fm}=10^{-15}\ \mathrm m$ | Spacings between atoms ($\text{Å}$) and the size of an atomic nucleus ($\mathrm{fm}$). |
| Angle | $180^\circ=\pi\ \mathrm{rad}$, $1\ \mathrm{rad}=57.2957\ldots{}^\circ$ | In the formulas of calculus, angles are measured in radians (Section 3.1). |
| Magnetism (old units) | $1\ \mathrm T=10^4\ \mathrm G$ (gauss) $1\ \mathrm{Oe}=\dfrac{1000}{4\pi}\ \mathrm{A/m}=79.577\ldots\ \mathrm{A/m}$ (oersted) | Used in old literature and in magnet catalogs (Section 38.1). |
| Time | $1\ \text{day}=86\,400\ \mathrm s$, $1\ \text{year (Julian year)}=365.25\ \text{days}=3.155\,76\times10^7\ \mathrm s$ | Time scales of astronomical objects and of the universe (Section 53.6). |
B.3 Table of Greek Letters
Greek letters are used very often in physics. Lowercase letters are used for variables, constants, and angles, while capital letters are often used for quantities that represent a “whole” (the sum $\Sigma$, a change $\Delta$, a flux $\Phi$, and so on). The readings follow Japanese usage and are shown here as English letter names; for letters that have two readings in Japanese, both are listed (romanized). Of the capital letters, those that have the same form as a Latin letter ($A,B,E,Z,H,I,K,M,N,O,P,T,X$) are regarded as Latin capitals when used as symbols, so they are not used in their Greek-letter sense. In the “Main uses in this book” column, we have attached links to the sections where each use actually occurs. Because the same letter often has different meanings in different parts of the book, please also see the “Caution” in B.4 (Table B.17).
| Capital | Lowercase | Reading | Main uses in this book |
|---|---|---|---|
| $A$ (same form as the Latin letter A) | $\alpha$ | alpha | Coefficient of linear expansion (Section 23.9), coefficient of volume expansion (Section 27.4), $\alpha=-n/(2m)$ for damped oscillation (Section 7.3), fine-structure constant (Section 58.1). The capital $A$ has the same form as the Latin letter and is used for amplitude, cross-sectional area, and so on. |
| $B$ (same form as the Latin letter B) | $\beta$ | beta | $\beta=v/c$ (Section 54.3), inverse temperature $\beta=1/(k_{\mathrm B}T)$ (Section 50.2), coefficient of volume expansion (Section 23.9). |
| $\Gamma$ | $\gamma$ | gamma | Shear strain (Section 18.5), surface energy $\gamma_{\mathrm s}$ (Section 21.1), heat capacity ratio $C_p/C_V$ (Section 23.8), Lorentz factor (Section 54.5). The capital $\Gamma$ denotes the gamma function (Section 47.1) and the path around the crack tip (Section 21.6). |
| $\Delta$ | $\delta$ | delta | Capital $\Delta$: amount of change, difference (Section 1.2), invariant interval $\Delta s^2$ (Section 56.4). Lowercase $\delta$: phase difference of waves (Section 11.6), virtual displacement and variation (Section 43.6). |
| $E$ (same form as the Latin letter E) | $\varepsilon$ | epsilon | Eccentricity (Section 6.3), longitudinal strain (Section 18.4), vacuum permittivity $\varepsilon_0$ (Section 35.1), energy of a single particle (Section 52.4). The lowercase letter has two glyph forms, $\varepsilon$ (ε) and $\epsilon$; this book uses the former. |
| $Z$ (same form as the Latin letter Z) | $\zeta$ | zeta | Riemann zeta function $\zeta(s)$ (Section 47.4), complex coordinate for the Earth's rotation $\zeta=x+iy$ (Section 9.4). |
| $H$ (same form as the Latin letter H) | $\eta$ | eta (Japanese: iita / eeta) | Thermal efficiency (Section 28.3), viscosity (Section 5.2). |
| $\Theta$ | $\theta$ | theta (Japanese: shiita / teeta) | Angle and argument (Section 3.1), angle of incidence and angle of refraction (Section 11.8), Einstein temperature $\theta_{\mathrm E}$ (Section 51.2), Debye temperature $\theta_{\mathrm D}$ (Section 53.8). Capital $\Theta$: function of time only (Section 33.3). |
| $I$ (same form as the Latin letter I) | $\iota$ | iota | Not used in this book (the capital $I$ has the same form as the Latin letter and is used for moment of inertia, electric current, and so on). |
| $K$ (same form as the Latin letter K) | $\kappa$ | kappa | Spring constant (Section 11.1), isothermal compressibility $\kappa_T$ (Section 27.4), thermal diffusivity $\kappa^2$ (Section 33.1). |
| $\Lambda$ | $\lambda$ | lambda | Wavelength (Section 11.3), thermal conductivity (Section 33.1), Lagrange multiplier (Section 44.7), thermal de Broglie wavelength $\lambda_{\mathrm T}$ (Section 49.6). Capital $\Lambda$: matrix of the Lorentz transformation (Section 54.7). |
| $M$ (same form as the Latin letter M) | $\mu$ | mu | Coefficient of kinetic friction (Section 4.3), Joule–Thomson coefficient (Section 27.6), permeability (Section 38.1), chemical potential (Section 52.3), index of a four-vector (Section 57.1), the prefix micro, $10^{-6}$ (Section 1.3). |
| $N$ (same form as the Latin letter N) | $\nu$ | nu | Poisson's ratio (Section 18.4), frequency of light $\nu$ (Section 53.1), index of a four-vector (Section 57.1). |
| $\Xi$ | $\xi$ | xi (Japanese: guzai / kusai) | Lowercase $\xi$: independent variable of the wave equation (Section 11.2), variable of the equipartition theorem (Section 50.7). Capital $\Xi$: grand partition function (Section 52.2). |
| $O$ (same form as the Latin letter O) | $o$ | omicron | Not used in this book (easily confused with the Latin letters O and o). |
| $\Pi$ | $\pi$ | pi | The ratio of the circumference of a circle to its diameter, $\pi=3.141\,59\ldots$ (throughout this book). Internal pressure $\pi_T$ (Section 27.4). The capital $\Pi$ is not used in this book. |
| $P$ (same form as the Latin letter P) | $\rho$ | rho | Density (Section 10.1), linear density (Section 11.2), radius of curvature (Section 3.4), charge density (Section 35.2), resistivity (Section 37.3), distribution function in phase space (Section 46.5). |
| $\Sigma$ | $\sigma$ | sigma | Normal stress (Section 18.3), electrical conductivity (Section 37.2), surface charge density (Section 35.6), Stefan–Boltzmann constant (Section 53.5). The symbol $\sum$, which has the form of the capital $\Sigma$, denotes a sum (Section 2.4). |
| $T$ (same form as the Latin letter T) | $\tau$ | tau | Shear stress (Section 18.3), time constant (Section 37.7, Section 40.8), proper time (Section 55.2). |
| $\Upsilon$ | $\upsilon$ | upsilon | Not used in this book (easily confused with $\nu$). |
| $\Phi$ | $\varphi$ | phi | Lowercase: electric potential $\varphi$ (Section 36.1), latitude (Section 9.4). The glyph $\phi$ is used for the phase (Section 11.1) and the rapidity (Section 56.7). Capital $\Phi$: flux of the electric field and magnetic flux (Section 35.3, Section 38.2). |
| $X$ (same form as the Latin letter X) | $\chi$ | chi | Electric susceptibility and magnetic susceptibility $\chi_{\mathrm e},\chi_{\mathrm m}$ (Section 41.1). |
| $\Psi$ | $\psi$ | psi (Japanese: pusai / pushii) | Lowercase: wave function of a wave packet (Section 17.5), angle of rotation of a rotating frame (Section 9.2). Capital $\Psi$: auxiliary function (Section 52.9). |
| $\Omega$ | $\omega$ | omega | Lowercase: angular velocity and angular frequency (Section 3.4, Section 7.1). Capital $\Omega$: number of states $\Omega(E)$ (Section 48.4), angular velocity of a rotating wire (Section 45.3), the ohm $\Omega$, the unit of electrical resistance (Section 37.3). |
B.4 List of Symbols (by Part)
This section lists the symbols of the main physical quantities used in this book, part by part, in order of appearance. “Reading” is the name by which the symbol is read aloud, “Unit” is the SI unit, and “First appears in” is a link to the section of the main text where the symbol first appears (or is defined) with that meaning. Because the meaning of each symbol is fixed within a part, reading the notation conventions of the part first makes the table easier to follow. Symbols for which the same letter is used with different meanings in different parts are collected in the last table, Table B.17.
Mathematical Symbols Common to All Parts
Notation conventions
Boldface letters ($\bm F$, $\bm r$) denote vectors; lightface letters ($F$, $r$) denote their magnitudes or quantities that are not vectors. These are the same as $\vec F$, which is written with an arrow in high-school textbooks. The d of differentiation is the upright $\dd$ (to distinguish it from the variable $d$).
| Symbol | Reading | Meaning | Unit | First appears in |
|---|---|---|---|---|
| $\approx$, $\fallingdotseq$ | nearly equal | Approximately equal (both symbols are used with the same meaning) | — | Section 1.1 |
| $\ll$, $\gg$ | much less than; much greater than | For example, $x\ll1$ means “$x$ is much smaller than 1” | — | Section 1.1 |
| $\Delta$ | capital delta | Change or difference. As in $\Delta t=t_2-t_1$, it is “the later value − the earlier value” | Same as the original quantity | Section 1.2 |
| $\dd x$, $\diff{x}{t}$ | dee ex (upright d); dee ex dee tee | An infinitesimal quantity. The upright d is the d of differentiation (not the d of a variable) | — | Section 1.2 |
| $\dot{x}$, $\ddot{x}$ | ex dot; ex double dot | The first and second derivatives with respect to time, $\dd x/\dd t$ and $\dd^2x/\dd t^2$ | Original quantity ÷ s, ÷ s² | Section 1.2 |
| $\bm{F}$, $\bm{r}$ | boldface eff; boldface ar | Boldface letters are vectors (quantities having both magnitude and direction). The same as $\vec{F}$, which is written with an arrow in high school | — | Section 1.2 |
| $\equiv$ | “is defined as” (not “congruent”) | An equals sign meaning that the left-hand side is defined by the right-hand side | — | Section 1.2 |
| $\bm{a}\times\bm{b}$ | vector product (cross product) | The vector perpendicular to both $\bm a$ and $\bm b$, with magnitude $\abs{\bm a}\abs{\bm b}\sin\theta$. It is used for torque (moment of force), angular momentum, and the Lorentz force | — | Section 1.7 |
| $\bm{a}\cdot\bm{b}$ | scalar product (inner product, dot product) | $\abs{\bm a}\abs{\bm b}\cos\theta$. Used for work and flux | — | Section 1.7 |
| $\sum$ | sigma | Summation. $\sum_i m_i=m_1+m_2+\cdots$ | — | Section 2.4 |
| $\therefore$ | therefore | The symbol for “thus” | — | Section 2.4 |
| $\partial$ | partial (round d) | Partial derivative. Differentiate with respect to only one variable, holding the other variables fixed ($\pdiff{f}{x}$) | — | Section 4.4 |
| $\nabla$ | nabla (del) | $\nabla=(\partial_x,\partial_y,\partial_z)$. The operator that produces the gradient, divergence, and curl | — | Section 4.4 |
| $\operatorname{rot}$ | curl | The curl of a vector field (the strength of the swirl). $\operatorname{rot}\bm F=\bm 0$ is the condition for a conservative force | — | Section 4.4 |
| $\oint$ | circuit integral (an integral that goes once all the way around) | A line integral once around a closed path (used to test whether a force is conservative) | — | Section 4.4 |
| $\propto$ | proportional to | $y\propto x$ means “$y$ is proportional to $x$” | — | Section 5.3 |
| $i$ | eye | Imaginary unit $i^2=-1$ ($j$ is used for the current density) | — | Section 7.1 |
| $\langle\cdots\rangle$ | angle brackets (average) | Average value. For example, $\langle E\rangle$ is the average of $E$ | — | Section 13.2 |
| $\operatorname{div}$ | divergence | The divergence of a vector field (the strength of the sources) | — | Section 35.3 |
| $\iint_S$, $\iiint_V$ | surface integral; volume integral | Integral over the surface $S$ (flux of the electric field or magnetic flux density); integral over the region $V$ | — | Section 35.3 |
Part I Mechanics
Notation conventions for this part
The unit vectors of polar coordinates are $\bm e_r,\bm e_\theta$, and the unit tangent and principal normal vectors of a curve are $\bm e_t,\bm e_n$. Angular momentum is $\bm L=\bm r\times\bm p$, and torque is $\bm N=\bm r\times\bm F$. Kinetic energy is $K$ and potential energy is $U$ (in Part VI, kinetic energy is written $T$).
| Symbol | Reading | Meaning | Unit | First appears in |
|---|---|---|---|---|
| $t$ | tee | Time | $\mathrm{s}$ | Section 1.2 |
| $x$, $y$, $z$ | ex, wye, zee | Rectangular (Cartesian) coordinates (components of position) | $\mathrm{m}$ | Section 1.2 |
| $\bm{r}$ | boldface ar | Position vector | $\mathrm{m}$ | Section 1.2 |
| $\Delta\bm{r}$ | delta ar | Displacement vector (change in position) | $\mathrm{m}$ | Section 1.2 |
| $\bm{v}$, $v$ | boldface vee; vee | Velocity vector; speed ($v=\abs{\bm v}$) | $\mathrm{m/s}$ | Section 1.2 |
| $\bm{a}$ | boldface ay | Acceleration vector | $\mathrm{m/s^2}$ | Section 1.2 |
| $\bm{e}_x$, $\bm{e}_y$, $\bm{e}_z$ | ee sub ex, ee sub wye, ee sub zee | Basis vectors of rectangular coordinates (unit vectors of length 1) | Dimensionless | Section 1.2 |
| $g$ | gee | Gravitational acceleration ($9.8\ \mathrm{m/s^2}$ in this book) | $\mathrm{m/s^2}$ | Section 1.4 |
| $m$ | em | Mass | $\mathrm{kg}$ | Section 2.2 |
| $\bm{F}$ | boldface eff | Force | $\mathrm{N}$ | Section 2.2 |
| $\bm{p}$ | boldface pee | Momentum $\bm p=m\bm v$ | $\mathrm{kg\,m/s}$ | Section 2.2 |
| $\bm{I}$ | boldface eye | Impulse $\bm I=\int\bm F\,\dd t$ | $\mathrm{N\,s}$ | Section 2.2 |
| $\bm{N}$ | boldface en | Torque $\bm N=\bm r\times\bm F$ | $\mathrm{N\,m}$ | Section 2.5 |
| $\bm{L}$ | boldface el | Angular momentum $\bm L=\bm r\times\bm p$ | $\mathrm{kg\,m^2/s}$ | Section 2.5 |
| $e$ | ee | Coefficient of restitution (rebound coefficient) | Dimensionless | Section 2.6 |
| $r$ | ar | Radial coordinate in plane polar coordinates (distance from the origin) | $\mathrm{m}$ | Section 3.1 |
| $\theta$ | theta | Polar angle in plane polar coordinates (the angle measured counterclockwise from the initial line) | $\mathrm{rad}$ | Section 3.1 |
| $\bm{e}_r$, $\bm{e}_\theta$ | ee sub ar, ee sub theta | Unit vectors of polar coordinates (radial direction and angular direction) | Dimensionless | Section 3.2 |
| $\bm{e}_t$, $\bm{e}_n$ | ee sub tee, ee sub en | Unit tangent vector and unit principal normal vector of a curve | Dimensionless | Section 3.3 |
| $\rho$ | rho | Radius of curvature of a curve | $\mathrm{m}$ | Section 3.4 |
| $\omega$ | lowercase omega | Angular velocity (the angle turned per second) | $\mathrm{rad/s}$ | Section 3.4 |
| $W$ | double-u | Work | $\mathrm{J}$ | Section 4.1 |
| $K$ | kay | Kinetic energy $K=\tfrac12mv^2$ | $\mathrm{J}$ | Section 4.2 |
| $\mu$ | mu | Coefficient of kinetic friction (also used in an example in Chapter 43) | Dimensionless | Section 4.3 |
| $U$ | you | Potential energy | $\mathrm{J}$ | Section 4.4 |
| $k$ | kay | Spring constant (in Chapters 6 and 8, $k$ is used for the semi-latus rectum of the orbit) | $\mathrm{N/m}$ | Section 4.5 |
| $E$ | ee | Mechanical energy $E=K+U$ | $\mathrm{J}$ | Section 4.5 |
| $P$ | pee | Power ($P=\dd W/\dd t$) | $\mathrm{W}$ | Section 4.6 |
| $B$ | bee | Proportionality constant of the drag force, which is proportional to velocity ($\bm F_{\text{drag}}=-B\bm v$) | $\mathrm{kg/s}$ | Section 5.2 |
| $b$ | lowercase bee | Drag coefficient $b=B/m$ | $\mathrm{s^{-1}}$ | Section 5.2 |
| $v_{\mathrm{t}}$ | vee sub tee | Terminal velocity $v_{\mathrm t}=g/b$ | $\mathrm{m/s}$ | Section 5.2 |
| $\varepsilon$ | epsilon | (In Chapters 6 and 8) the eccentricity of a conic section | Dimensionless | Section 6.3 |
| $T$ | tee | Period (the time taken for one round trip) | $\mathrm{s}$ | Section 7.1 |
| $f$ | eff | Frequency (the number of round trips per second) $f=1/T$ | $\mathrm{Hz}$ | Section 7.1 |
| $A$ | ay | Amplitude of simple harmonic motion | $\mathrm{m}$ | Section 7.1 |
| $\omega_0$ | omega sub zero | Natural angular frequency (the angular frequency when there is neither drag nor an external force). It is $\sqrt{k/m}$ for a spring pendulum and $\sqrt{g/\ell}$ for a simple pendulum | $\mathrm{rad/s}$ | Section 7.2 |
| $n$ | en | Drag coefficient of damped oscillation (equation of motion $m\ddot x+n\dot x+kx=0$) | $\mathrm{kg/s}$ | Section 7.3 |
| $Q$ | cue | Quality factor $Q$ (sharpness), $Q=m\omega_0/n$ | Dimensionless | Section 7.4 |
| $G$ | gee | Gravitational constant | $\mathrm{N\,m^2/kg^2}$ | Section 8.1 |
| $M$ | em | Mass of a celestial body; total mass of a system of particles | $\mathrm{kg}$ | Section 8.1 |
| $v_{\mathrm{esc}}$ | vee sub escape | Escape velocity $\sqrt{2GM/R}$ | $\mathrm{m/s}$ | Section 8.4 |
| $\bm\omega$ | boldface omega | Angular velocity vector (directed along the axis of rotation, with magnitude $\omega$) | $\mathrm{rad/s}$ | Section 9.3 |
| $\bm{r}_{\mathrm{cm}}$ | ar sub cee em | Position of the center of mass of a system of particles (cm stands for center of mass) | $\mathrm{m}$ | Section 10.1 |
| $\rho$ | rho | Mass density (volume density) | $\mathrm{kg/m^3}$ | Section 10.1 |
| $I$ | eye | Moment of inertia $I=\sum m_ir_i^2$ | $\mathrm{kg\,m^2}$ | Section 10.3 |
Part II Waves
Notation conventions for this part
A sinusoidal wave is $y=A\sin(\omega t-kx+\phi)$ (a wave traveling in the $+x$ direction). $k=2\pi/\lambda$ (wavenumber), $\omega=2\pi f=2\pi/T$, and the phase velocity is $v=\omega/k=f\lambda$. When the complex form $e^{i(kx-\omega t)}$ is used, the relation to the real and imaginary parts and the difference in the sign of the phase are explicitly noted. The speed of light in vacuum is written $c_0$ in this part.
| Symbol | Reading | Meaning | Unit | First appears in |
|---|---|---|---|---|
| $\kappa$ | kappa | (In Chapter 11) spring constant. $\kappa$ is used to distinguish it from the wavenumber $k$ | $\mathrm{N/m}$ | Section 11.1 |
| $\phi$ | phi | Initial phase (phase constant) | $\mathrm{rad}$ | Section 11.1 |
| $y(x,t)$ | wye of ex and tee | Displacement of the wave (position $x$, time $t$) | $\mathrm{m}$ | Section 11.2 |
| $S$ | ess | Tension of the string | $\mathrm{N}$ | Section 11.2 |
| $\rho$ | rho | Linear density of the string (mass per unit length) | $\mathrm{kg/m}$ | Section 11.2 |
| $k$ | kay | Wavenumber $k=2\pi/\lambda$ | $\mathrm{rad/m}$ | Section 11.3 |
| $\lambda$ | lambda | Wavelength | $\mathrm{m}$ | Section 11.3 |
| $v$ | vee | Phase velocity of the wave $v=\omega/k=f\lambda$ | $\mathrm{m/s}$ | Section 11.4 |
| $I$ | eye | Intensity of the wave (the time average of the energy passing through unit area per second) | $\mathrm{W/m^2}$ | Section 11.5 |
| $\delta$ | lowercase delta | Phase difference between two waves $\delta=k(\ell_2-\ell_1)$ | $\mathrm{rad}$ | Section 11.6 |
| $\theta_{\mathrm i}$, $\theta_{\mathrm r}$ | theta sub eye, theta sub ar | Angle of incidence; angle of reflection | $\mathrm{rad}$ | Section 11.8 |
| $c_0$, $c$ | cee sub zero; cee | Speed of light in vacuum. In Part II, some chapters write $c_0$ and others write $c$ (the same quantity) | $\mathrm{m/s}$ | Section 11.8 |
| $V$ | vee | Speed of sound (Chapter 12) $V=331.5+0.6\,t$ | $\mathrm{m/s}$ | Section 12.1 |
| $v_s$ | vee sub ess | Speed of the sound source | $\mathrm{m/s}$ | Section 12.2 |
| $M$ | em | Mach number $M=v_s/V$ | Dimensionless | Section 12.2 |
| $n$ | en | Absolute refractive index $n=c_0/v$ | Dimensionless | Section 13.3 |
| $\theta_{\mathrm c}$ | theta sub cee | Critical angle $\sin\theta_c=n_2/n_1$ | $\mathrm{rad}$ | Section 14.7 |
| $f$ | eff | Focal length of a lens (positive for a convex lens, negative for a concave lens) | $\mathrm{m}$ | Section 15.1 |
| $a$ | ay | Object distance of a lens | $\mathrm{m}$ | Section 15.1 |
| $b$ | bee | Image distance of a lens | $\mathrm{m}$ | Section 15.1 |
| $m$ | em | Magnification of a lens $m=h_B/h_A=-b/a$ | Dimensionless | Section 15.1 |
| $D_0$ | dee sub zero | Distance of distinct vision ($25\ \mathrm{cm}$ in this book) | $\mathrm{m}$ | Section 15.5 |
| $n\ell$ | en el | Optical path length (optical distance) | $\mathrm{m}$ | Section 16.1 |
| $d$ | dee | Slit spacing, grating spacing | $\mathrm{m}$ | Section 16.3 |
| $\omega_n$, $k_n$ | omega sub en, kay sub en | Angular frequency and wavenumber of the $n$th normal mode | $\mathrm{rad/s},\ \mathrm{rad/m}$ | Section 17.3 |
| $v_{\mathrm p}$, $v_{\mathrm g}$ | vee sub pee; vee sub gee | Phase velocity $\omega/k$; group velocity $\dd\omega/\dd k$ | $\mathrm{m/s}$ | Section 17.5 |
Part III Mechanics of Materials and Fracture Mechanics
Notation conventions for this part
Normal stress is $\sigma$, shear stress is $\tau$, longitudinal strain is $\varepsilon$, transverse strain is $\varepsilon'$, and shear strain is $\gamma$. Poisson's ratio is $\nu=\abs{\varepsilon'/\varepsilon}$, and Poisson's number is $m=1/\nu$. Because the chapters on fracture mechanics write the Weibull modulus as $m$, Poisson's number is not used there; only $\nu$ is used. An unsubscripted $K$ is the bulk modulus, and the stress intensity factor is always given a subscript, as in $K_{\mathrm I}$. The energy release rate is the script $\mathcal G$ (to distinguish it from the Gibbs energy $G$, also called the Gibbs free energy, and the shear modulus $G$).
| Symbol | Reading | Meaning | Unit | First appears in |
|---|---|---|---|---|
| $P$ | pee | Load (axial force) | $\mathrm{N}$ | Section 18.3 |
| $A$ | ay | Cross-sectional area | $\mathrm{m^2}$ | Section 18.3 |
| $\sigma$ | lowercase sigma | Normal stress $\sigma=P/A$ | $\mathrm{Pa}$ | Section 18.3 |
| $\tau$ | tau | Shear stress | $\mathrm{Pa}$ | Section 18.3 |
| $\varepsilon$, $\varepsilon'$ | epsilon; epsilon prime | Longitudinal strain; transverse strain (the ratio of the deformation to the original length) | Dimensionless | Section 18.4 |
| $\nu$ | nu | Poisson's ratio $\nu=\abs{\varepsilon'/\varepsilon}$ | Dimensionless | Section 18.4 |
| $m$ | em | Poisson's number $m=1/\nu$ (used only up to partway through the chapters on mechanics of materials; because it conflicts with the Weibull modulus, only $\nu$ is used from Chapter 22 on) | Dimensionless | Section 18.4 |
| $\gamma$ | gamma | Shear strain | Dimensionless | Section 18.5 |
| $\varepsilon_V$ | epsilon-V | Volumetric strain $\Delta V/V$ | Dimensionless | Section 18.5 |
| $E$ | ee | Young's modulus (modulus of longitudinal elasticity) | $\mathrm{Pa}$ | Section 19.2 |
| $G$ | gee | Shear modulus (modulus of rigidity) | $\mathrm{Pa}$ | Section 19.2 |
| $K$ | kay | Bulk modulus | $\mathrm{Pa}$ | Section 19.2 |
| $\sigma_{\mathrm p}$, $\sigma_{\mathrm e}$ | sigma-p, sigma-e | Proportional limit and elastic limit | $\mathrm{Pa}$ | Section 19.4 |
| $\sigma_{\mathrm{UTS}}$ | sigma-U-T-S | Tensile strength (ultimate strength) | $\mathrm{Pa}$ | Section 19.5 |
| $\bm\sigma$ | boldface sigma | Stress tensor (a 3×3 matrix in which the normal stresses $\sigma_x$ and the shear stresses $\tau_{xy}$ are arranged) | $\mathrm{Pa}$ | Section 20.1 |
| $\sigma_1,\sigma_2,\sigma_3$ | sigma-one, two, three | Principal stresses (the normal stresses on the planes on which the shear stress is 0) | $\mathrm{Pa}$ | Section 20.2 |
| $\tau_{\max}$ | tau-max | Maximum shear stress | $\mathrm{Pa}$ | Section 20.2 |
| $I$ | eye | Second moment of area $I=\int y^2\,\dd A$ | $\mathrm{m^4}$ | Section 20.5 |
| $M$ | em | Bending moment | $\mathrm{N\,m}$ | Section 20.5 |
| $V$ | vee | Shear force (internal force in a beam) | $\mathrm{N}$ | Section 20.5 |
| $w$ | double-u | Distributed load on a beam (per unit length) | $\mathrm{N/m}$ | Section 20.6 |
| $J$ | jay | Polar second moment of area $J=\int r^2\,\dd A$ | $\mathrm{m^4}$ | Section 20.7 |
| $T$ | tee | Torsional moment (torque) | $\mathrm{N\,m}$ | Section 20.7 |
| $a$ | ay | Crack length (half-length for a central crack) | $\mathrm{m}$ | Section 21.1 |
| $\gamma_{\mathrm s}$ | gamma-s | Surface energy (per unit area) | $\mathrm{J/m^2}$ | Section 21.1 |
| $\sigma_{\mathrm{th}}$ | sigma-T-H | Theoretical strength | $\mathrm{Pa}$ | Section 21.1 |
| $K_{\mathrm I}$ | kay-I | Mode I stress intensity factor $K_{\mathrm I}=Y\sigma\sqrt{\pi a}$ | $\mathrm{Pa\sqrt m}$ | Section 21.3 |
| $Y$ | wye | Geometry factor (a dimensionless number determined by the shapes of the crack and the plate) | Dimensionless | Section 21.3 |
| $\mathcal{G}$ | script gee | Energy release rate (the energy released when the crack advances by a unit area) | $\mathrm{J/m^2}$ | Section 21.4 |
| $K_{\mathrm{IC}}$ | kay-I-C | Fracture toughness (the value of $K_{\mathrm I}$ at which the crack begins to advance unstably) | $\mathrm{Pa\sqrt m}$ | Section 21.5 |
| $J$ | jay | J-integral (a path integral around the crack tip) | $\mathrm{J/m^2}$ | Section 21.6 |
| $R$ | ar | Crack growth resistance (R-curve) | $\mathrm{J/m^2}$ | Section 21.7 |
| $\sigma_{\mathrm a}$, $\sigma_{\mathrm m}$ | sigma-a, sigma-m | Stress amplitude; mean stress | $\mathrm{Pa}$ | Section 22.1 |
| $\sigma_{\mathrm w}$ | sigma-w | Fatigue limit | $\mathrm{Pa}$ | Section 22.1 |
| $N_{\mathrm f}$ | en-f | Number of cycles to fracture (fatigue life) | Dimensionless | Section 22.1 |
| $C$ | cee | Coefficient of the Paris law $\dd a/\dd N=C(\Delta K)^n$ | — | Section 22.3 |
| $n$ | en | Exponent of the Paris law (written $n$ to distinguish it from the Weibull modulus $m$) | Dimensionless | Section 22.3 |
| $D$ | dee | Damage index (Miner's rule $D=\sum n_i/N_i$) | Dimensionless | Section 22.4 |
| $m$ | em | Weibull modulus (an exponent expressing how small the scatter in strength is) | Dimensionless | Section 22.6 |
| $P_{\mathrm f}$ | pee-f | Failure probability | Dimensionless | Section 22.6 |
| $V_{\mathrm{eff}}$ | vee-E-F-F | Effective volume | $\mathrm{m^3}$ | Section 22.7 |
Part IV Thermodynamics
Notation conventions for this part
For work, we write $W$ for the work done on the system by its surroundings and $W'$ for the work done by the system on its surroundings ($W'=-W$), so the first law reads $\Delta U=Q+W=Q-W'$. Inexact differentials are written $\dd'Q$ and $\dd'W$. Pressure is $p$ (external pressure is $p_{\mathrm{ex}}$). The Helmholtz free energy is $A$ (physics textbooks often write it as $F$). The efficiency of a heat engine is $\eta=W'/Q_{\text{absorbed}}$.
| Symbol | Reading | Meaning | Unit | First appears in |
|---|---|---|---|---|
| $t$ | tee | Celsius temperature (in Section 12.1 and in Chapter 23 it has this meaning, not time) | ${}^\circ\mathrm{C}$ | Section 23.1 |
| $T$ | tee | Absolute temperature (thermodynamic temperature) $T=t+273.15$ | $\mathrm{K}$ | Section 23.1 |
| $Q$ | cue | Quantity of heat (heat flowing into the system) | $\mathrm{J}$ | Section 23.2 |
| $c$ | cee | Specific heat (in Chapter 33, the $c$ in the heat conduction equation has the same meaning) | $\mathrm{J/(g\,K)}$ | Section 23.2 |
| $C$ | capital cee | Heat capacity $C=mc$ | $\mathrm{J/K}$ | Section 23.2 |
| $U$ | you | Internal energy | $\mathrm{J}$ | Section 23.3 |
| $W$, $W'$ | double-u; double-u prime | Work done on the system by its surroundings; work done by the system on its surroundings ($W'=-W$) | $\mathrm{J}$ | Section 23.4 |
| $p_{\mathrm{ex}}$ | pee-E-X | External pressure (pressure applied from outside the system) | $\mathrm{Pa}$ | Section 23.4 |
| $p$ | lowercase pee | Pressure | $\mathrm{Pa}$ | Section 23.5 |
| $V$ | vee | Volume | $\mathrm{m^3}$ | Section 23.5 |
| $n$ | en | Amount of substance | $\mathrm{mol}$ | Section 23.6 |
| $R$ | ar | Gas constant $R=N_{\mathrm A}k_{\mathrm B}$ | $\mathrm{J/(mol\,K)}$ | Section 23.6 |
| $N_{\mathrm A}$ | en-A | Avogadro constant | $\mathrm{mol^{-1}}$ | Section 23.6 |
| $C_{V,\mathrm m}$, $C_{p,\mathrm m}$ | cee-V-m, cee-p-m | Molar heat capacities at constant volume and at constant pressure (per 1 mol) | $\mathrm{J/(mol\,K)}$ | Section 23.7 |
| $\gamma$ | gamma | Heat capacity ratio $\gamma=C_p/C_V$ | Dimensionless | Section 23.8 |
| $\alpha$ | alpha | Coefficient of linear expansion (Chapter 23) | $\mathrm{K^{-1}}$ | Section 23.9 |
| $\beta$ | beta | Coefficient of volume expansion (Chapter 23) | $\mathrm{K^{-1}}$ | Section 23.9 |
| $N$ | en | Number of molecules (particles) | Dimensionless | Section 24.2 |
| $k_{\mathrm B}$ | kay-B | Boltzmann constant | $\mathrm{J/K}$ | Section 24.3 |
| $a$ | ay | Van der Waals constant (correction for the intermolecular attraction) | $\mathrm{Pa\,m^6/mol^2}$ | Section 24.4 |
| $b$ | bee | Van der Waals constant (correction for the size of the molecules themselves) | $\mathrm{m^3/mol}$ | Section 24.4 |
| $T_{\mathrm c}$ | tee-c | Critical temperature ($p_{\mathrm c},V_{\mathrm c}$ are the critical pressure and the critical volume) | $\mathrm{K}$ | Section 24.4 |
| $Z$ | zee | Compression factor $Z=pV_{\mathrm m}/(RT)$ | Dimensionless | Section 25.2 |
| $B(T)$ | bee-T | Second virial coefficient (expresses the deviation of a real gas from ideal behavior) | $\mathrm{m^3/mol}$ | Section 25.3 |
| $f$ | eff | Degrees of freedom of molecular motion | Dimensionless | Section 26.5 |
| $\dd'Q$, $\dd'W$ | d-prime-Q | Inexact differentials (infinitesimal amounts of heat and work, which are not state quantities) | $\mathrm{J}$ | Section 26.6 |
| $C_V$, $C_p$ | cee-V, cee-p | Heat capacities at constant volume and at constant pressure | $\mathrm{J/K}$ | Section 27.2 |
| $H$ | aitch | Enthalpy $H=U+pV$ | $\mathrm{J}$ | Section 27.2 |
| $\pi_T$ | pi-T | Internal pressure $\left(\partial U/\partial V\right)_T$ | $\mathrm{Pa}$ | Section 27.4 |
| $\alpha$ | alpha | Coefficient of volume expansion (Chapter 27; the same quantity as $\beta$ in Chapter 23) | $\mathrm{K^{-1}}$ | Section 27.4 |
| $\kappa_T$ | kappa-T | Isothermal compressibility | $\mathrm{Pa^{-1}}$ | Section 27.4 |
| $\mu$ | mu | Joule–Thomson coefficient $(\partial T/\partial p)_H$ | $\mathrm{K/Pa}$ | Section 27.6 |
| $\eta$ | eta | Thermal efficiency of a heat engine $\eta=W'/Q$ | Dimensionless | Section 28.3 |
| $\mathrm{COP}$ | COP (pronounced “cop”) | Coefficient of performance (refrigerators and heat pumps) | Dimensionless | Section 28.8 |
| $S$ | ess | Entropy $\dd S=\dd'Q_{\mathrm{rev}}/T$ | $\mathrm{J/K}$ | Section 29.1 |
| $\Delta_{\mathrm{fus}}$, $\Delta_{\mathrm{vap}}$ | delta-F-U-S, delta-V-A-P | Changes accompanying fusion (fus) and vaporization (vap). $\Delta_{\mathrm{fus}}H$ is the heat of fusion, and $\Delta_{\mathrm{vap}}S$ is the entropy change of vaporization | $H$ in $\mathrm{J/mol}$, $S$ in $\mathrm{J/(K\,mol)}$ | Section 30.2 |
| $A$ | ay | Helmholtz free energy $A=U-TS$ (the same symbol is used in Part VII) | $\mathrm{J}$ | Section 30.4 |
| $G$ | gee | Gibbs energy $G=H-TS$ | $\mathrm{J}$ | Section 30.4 |
| $F$ | eff | Faraday constant $F=N_{\mathrm A}e$ | $\mathrm{C/mol}$ | Section 30.5 |
| $\lambda$ | lambda | Thermal conductivity | $\mathrm{W/(m\,K)}$ | Section 33.1 |
| $\kappa^2$ | kappa squared | Thermal diffusivity $\kappa^2=\lambda/(c\rho)$ | $\mathrm{m^2/s}$ | Section 33.1 |
| $f(v_x,v_y,v_z)$ | eff | Distribution function of molecular velocities | — | Section 34.2 |
| $v_{\mathrm{rms}}$ | vee-R-M-S | Root-mean-square speed | $\mathrm{m/s}$ | Section 34.5 |
Part V Electromagnetism
Notation conventions for this part
SI units. The current density is written $\bm j$ to distinguish it from the imaginary unit $i$. In this part the exponential function is also written $\exp(\cdot)$, so that it is not confused with the elementary charge $e$. The charge density $\rho$ and the resistivity $\rho$ are the same letter, so where they appear together the distinction is made explicit. $c=1/\sqrt{\varepsilon_0\mu_0}$.
| Symbol | Reading | Meaning | Unit | First appears in |
|---|---|---|---|---|
| $q$, $Q$ | cue | Electric charge | $\mathrm{C}$ | Section 35.1 |
| $\varepsilon_0$ | epsilon zero | Vacuum permittivity | $\mathrm{F/m}$ | Section 35.1 |
| $\bm{E}$ | boldface ee | Electric field (also called electric field strength) | $\mathrm{N/C}=\mathrm{V/m}$ | Section 35.2 |
| $\rho$ | rho | Charge density (charge per unit volume) | $\mathrm{C/m^3}$ | Section 35.2 |
| $\Phi$ | capital phi | Flux of the electric field (corresponds to the number of electric field lines). Also used for magnetic flux in Chapter 38 | $\mathrm{N\,m^2/C}$ | Section 35.3 |
| $\bm{D}$ | boldface dee | Electric displacement (electric flux density) $\bm D=\varepsilon_0\bm E$ (in matter, $\varepsilon_0\bm E+\bm P$) | $\mathrm{C/m^2}$ | Section 35.4 |
| $\sigma$ | sigma | Surface charge density (charge per unit area) | $\mathrm{C/m^2}$ | Section 35.6 |
| $\varphi$ | lowercase phi | Electric potential ($\bm E=-\nabla\varphi$) | $\mathrm{V}$ | Section 36.1 |
| $V$ | vee | Potential difference (voltage) | $\mathrm{V}$ | Section 36.1 |
| $C$ | cee | Capacitance (the capacity of a capacitor) $C=Q/V$ | $\mathrm{F}$ | Section 36.6 |
| $u$ | you | Energy density (the electric-field part $\tfrac12\varepsilon_0E^2$, the magnetic-field part $\tfrac{1}{2\mu_0}B^2$) | $\mathrm{J/m^3}$ | Section 36.6 |
| $\bm{p}$ | boldface pee | Electric dipole moment $\bm p=q\bm d$ (in Chapter 41, its sum per unit volume gives the polarization $\bm P$) | $\mathrm{C\,m}$ | Section 36.8 |
| $I$ | eye | Electric current | $\mathrm{A}$ | Section 37.1 |
| $\bm{j}$ | boldface jay | Current density $\bm j=\rho\bm v$ (the letter $j$ is used to distinguish it from the imaginary unit $i$) | $\mathrm{A/m^2}$ | Section 37.2 |
| $\sigma$ | sigma | Electrical conductivity ($\bm j=\sigma\bm E$) | $\mathrm{S/m}$ | Section 37.2 |
| $R$ | ar | Electrical resistance | $\Omega$ | Section 37.3 |
| $\rho$ | rho | Resistivity | $\Omega\,\mathrm{m}$ | Section 37.3 |
| $\mathcal{E}$ | script ee | Electromotive force (emf; the energy a battery gives to 1 C of charge) | $\mathrm{V}$ | Section 37.6 |
| $\tau_{\mathrm{RC}}$ | tau ar cee | Time constant $RC$ of an RC circuit | $\mathrm{s}$ | Section 37.7 |
| $\bm{H}$ | boldface aitch | Magnetic field strength (also called the magnetic field) | $\mathrm{A/m}$ | Section 38.1 |
| $\bm{B}$ | boldface bee | Magnetic flux density | $\mathrm{T}$ | Section 38.1 |
| $\mu$ | mu | Permeability ($\bm B=\mu\bm H$) | $\mathrm{H/m}$ | Section 38.1 |
| $\Phi$ | capital phi | Magnetic flux ($\Phi=\iint\bm B\cdot\bm n\,\dd S$; the same symbol as for the flux of the electric field) | $\mathrm{Wb}$ | Section 38.2 |
| $\mu_0$ | mu zero | Vacuum permeability | $\mathrm{N/A^2}$ | Section 38.3 |
| $n$ | en | Number of turns per unit length of a solenoid | $\mathrm{m^{-1}}$ | Section 38.4 |
| $N$ | en | Number of turns of a coil | Dimensionless | Section 38.4 |
| $\bm{m}$ | boldface em | Magnetic dipole moment $\bm m=I\bm S$ | $\mathrm{A\,m^2}$ | Section 38.6 |
| $\omega_{\mathrm c}$ | omega cee | Cyclotron angular frequency $qB/m$ | $\mathrm{rad/s}$ | Section 39.6 |
| $V_{\mathrm H}$ | vee aitch | Hall voltage | $\mathrm{V}$ | Section 39.8 |
| $L$ | el | Self-inductance $N\Phi=LI$ | $\mathrm{H}$ | Section 40.5 |
| $M$ | em | Mutual inductance | $\mathrm{H}$ | Section 40.6 |
| $\tau$ | tau | Time constant $\tau=L/R$ of an RL circuit | $\mathrm{s}$ | Section 40.8 |
| $\bm{P}$ | boldface pee | Polarization vector (electric dipole moment per unit volume) | $\mathrm{C/m^2}$ | Section 41.1 |
| $\varepsilon_{\mathrm r}$, $\mu_{\mathrm r}$ | epsilon ar, mu ar | Relative permittivity; relative permeability | Dimensionless | Section 41.1 |
| $\chi_{\mathrm e}$, $\chi_{\mathrm m}$ | chi ee, chi em | Electric susceptibility; magnetic susceptibility | Dimensionless | Section 41.1 |
| $\rho_{\mathrm b}$, $\sigma_{\mathrm b}$ | rho bee, sigma bee | Volume density and surface density of bound charge | $\mathrm{C/m^3},\ \mathrm{C/m^2}$ | Section 41.1 |
| $\bm{M}$ | boldface em | Magnetization vector (magnetic dipole moment per unit volume) | $\mathrm{A/m}$ | Section 41.2 |
| $\bm{K}_{\mathrm b}$ | kay bee | Bound (magnetization) surface current density $\bm M\times\bm n$ | $\mathrm{A/m}$ | Section 41.2 |
| $\bm{k}$ | boldface kay | Wave vector (points in the direction of propagation) | $\mathrm{rad/m}$ | Section 42.4 |
| $\bm{S}$ | boldface ess | Poynting vector $\bm E\times\bm H$ (flow of energy) | $\mathrm{W/m^2}$ | Section 42.5 |
Part VI Analytical Mechanics
Notation conventions for this part
The Lagrangian is $L=T-U$ (kinetic energy $T$ minus potential energy $U$). The generalized coordinates are $q_i$, the generalized momenta $p_i$, the generalized forces $Q_i$, and the Hamiltonian $H$.
| Symbol | Reading | Meaning | Unit | First appears in |
|---|---|---|---|---|
| $q_i$ | cue eye | Generalized coordinate | — | Section 43.1 |
| $\dot{q}_i$ | cue eye dot | Generalized velocity | — | Section 43.2 |
| $p_i$ | pee eye | Generalized momentum $p_i=\partial T/\partial\dot q_i$ | — | Section 43.2 |
| $T$ | tee | Kinetic energy (written $T$ in Part VI; the same quantity as $K$ in Chapter 4) | $\mathrm{J}$ | Section 43.2 |
| $Q_i$ | cue eye | Generalized force | — | Section 43.3 |
| $L$ | el | Lagrangian $L=T-U$ | $\mathrm{J}$ | Section 43.4 |
| $\delta x_j$, $\delta S$ | delta ex jay | Virtual displacement; variation (a change that is infinitesimally small but not actually carried out) | — | Section 43.6 |
| $S[q]$ | ess cue | Action $S=\int L\,\dd t$ | $\mathrm{J\,s}$ | Section 44.4 |
| $\lambda$ | lambda | Lagrange multiplier | — | Section 44.7 |
| $H$ | aitch | Hamiltonian $H=\sum p_i\dot q_i-L$ | $\mathrm{J}$ | Section 45.1 |
| $h$ | lowercase aitch | Energy function (a conserved quantity built from the Lagrangian) | $\mathrm{J}$ | Section 46.1 |
| $\{A,B\}$ | Poisson bracket | $\sum\left(\partial_qA\,\partial_pB-\partial_pA\,\partial_qB\right)$ | — | Section 46.3 |
| $(Q,P)$ | cue, pee | Coordinates and momenta after a canonical transformation | — | Section 46.4 |
| $\rho(q,p,t)$ | rho | Distribution function in phase space (density of points) | — | Section 46.5 |
Part VII Statistical Mechanics
Notation conventions for this part
We use $\beta=1/(k_{\mathrm B}T)$, the partition function $Z$, the number of microstates $W$, Boltzmann's principle $S=k_{\mathrm B}\ln W$, the Helmholtz free energy $A=-k_{\mathrm B}T\ln Z$ (the same symbol as in Part IV), and the chemical potential $\mu$. Energy levels are given in the form “it is known from quantum mechanics that …”, and we do not derive them from quantum mechanics.
| Symbol | Reading | Meaning | Unit | First appears in |
|---|---|---|---|---|
| $V_n(R)$ | vee en ar | Volume of the $n$-dimensional ball (radius $R$) | — | Section 47.1 |
| $\Gamma(x)$ | gamma ex | Gamma function (the extension of the factorial to real numbers) | — | Section 47.1 |
| $\zeta(s)$ | zeta ess | Riemann zeta function $\sum_k k^{-s}$ | — | Section 47.4 |
| $\Omega(E)$ | capital omega ee | Number of microstates with energy at most $E$ | Dimensionless | Section 48.4 |
| $W$ | double-u | Number of microstates with energy in $[E,E+\Delta E]$. The thermodynamic weight $W(E)=\dd\Omega/\dd E$ uses the same symbol (distinct from the work $W$ of Part IV) | Dimensionless ($\mathrm{J^{-1}}$ for $W(E)=\dd\Omega/\dd E$) | Section 48.4 |
| $\lambda_{\mathrm T}$ | lambda tee | Thermal de Broglie wavelength $h/\sqrt{2\pi mk_{\mathrm B}T}$ | $\mathrm{m}$ | Section 49.6 |
| $Z$ | zee | Partition function $Z=\sum g_je^{-E_j/(k_{\mathrm B}T)}$ | Dimensionless | Section 50.1 |
| $E_j$ | ee jay | Energy level | $\mathrm{J}$ | Section 50.1 |
| $g_j$ | gee jay | Degeneracy (the number of states with the same energy $E_j$) | Dimensionless | Section 50.1 |
| $P_j$ | pee jay | Probability of a state of energy $E_j$ | Dimensionless | Section 50.1 |
| $\beta$ | beta | Inverse temperature $\beta=1/(k_{\mathrm B}T)$ | $\mathrm{J^{-1}}$ | Section 50.2 |
| $\theta_{\mathrm E}$, $\theta_{\mathrm D}$ | theta ee, theta dee | Einstein temperature; Debye temperature (in the form $\hbar\omega/k_{\mathrm B}$) | $\mathrm{K}$ | Section 51.2 |
| $\theta_{\mathrm{rot}}$, $\theta_{\mathrm{vib}}$ | theta rot, theta vib | Rotational temperature; vibrational temperature | $\mathrm{K}$ | Section 51.5 |
| $\Xi$ | capital xi | Grand partition function | Dimensionless | Section 52.2 |
| $J$ | jay | Grand potential $J=-k_{\mathrm B}T\ln\Xi$ | $\mathrm{J}$ | Section 52.2 |
| $z$ | zee | Fugacity $z=e^{\beta\mu}$ (activity) | Dimensionless | Section 52.2 |
| $\mu$ | mu | Chemical potential (the change in energy when one particle is added) | $\mathrm{J}$ | Section 52.3 |
| $\varepsilon_i$ | epsilon eye | Energy of single-particle state $i$ | $\mathrm{J}$ | Section 52.4 |
| $n_i$ | en eye | Occupation number of single-particle state $i$ (the number of particles in that state) | Dimensionless | Section 52.4 |
| $g_s$ | gee ess | Number of internal states (spin states) of a particle (2 for an electron) | Dimensionless | Section 52.7 |
| $g(\varepsilon)$ | gee epsilon | Density of states (the number of single-particle states in $\varepsilon\sim\varepsilon+\dd\varepsilon$) | $\mathrm{J^{-1}}$ | Section 52.8 |
| $\nu$ | nu | Frequency of light ($\omega=2\pi\nu$) | $\mathrm{Hz}$ | Section 53.1 |
| $b$ | bee | Wien constant $\lambda_{\max}T=b$ | $\mathrm{m\,K}$ | Section 53.4 |
| $\sigma$ | sigma | Stefan–Boltzmann constant (written $\sigma$ in this book), $j=\sigma T^4$ | $\mathrm{W\,m^{-2}K^{-4}}$ | Section 53.5 |
| $c_s$ | cee ess | Speed of sound in a solid (speed of the waves of lattice vibration) | $\mathrm{m/s}$ | Section 53.7 |
| $\omega_{\mathrm D}$ | omega dee | Debye frequency (upper limit of the angular frequency of lattice vibrations) | $\mathrm{rad/s}$ | Section 53.8 |
Part VIII Special Relativity
Notation conventions for this part
We use an inertial frame S and a frame S′ that moves with speed $v$ in the positive direction of the $x$ axis relative to S. We also use $\beta=v/c$, $\gamma=1/\sqrt{1-\beta^2}$, $x^0=ct$, and the metric $(+,-,-,-)$ (the opposite sign convention also exists). The superscript and subscript indices of four-vectors run over $\mu=0,1,2,3$.
| Symbol | Reading | Meaning | Unit | First appears in |
|---|---|---|---|---|
| $\mathrm{S},\ \mathrm{S}'$ | ess, ess prime | An inertial frame S, and the inertial frame S′ that moves with speed $v$ in the positive direction of the $x$ axis relative to S | — | Section 54.1 |
| $\beta$ | beta | $\beta=v/c$ (the ratio of the speed to the speed of light) | Dimensionless | Section 54.3 |
| $\gamma$ | gamma | Lorentz factor $\gamma=1/\sqrt{1-\beta^2}$ | Dimensionless | Section 54.5 |
| $x^\mu$ | ex mu | Four-position $(ct,x,y,z)$. The index $\mu=0,1,2,3$ | $\mathrm{m}$ | Section 54.5 |
| $\Lambda^\mu{}_\nu$ | lambda | Matrix of the Lorentz transformation ($x'^\mu=\Lambda^\mu{}_\nu x^\nu$) | — | Section 54.7 |
| $\tau$ | tau | Proper time (the time ticked off by a moving clock) | $\mathrm{s}$ | Section 55.2 |
| $\Delta s^2$ | delta ess squared | Invariant interval $c^2\Delta t^2-\Delta x^2-\Delta y^2-\Delta z^2$ | $\mathrm{m^2}$ | Section 56.4 |
| $\phi$ | phi | Rapidity $\tanh\phi=\beta$ | Dimensionless | Section 56.7 |
| $g_{\mu\nu}$ | gee mu nu | Metric ($\mathrm{diag}(1,-1,-1,-1)$) | — | Section 57.2 |
| $u^\mu$ | you mu | Four-velocity $\dd x^\mu/\dd\tau$ | $\mathrm{m/s}$ | Section 57.4 |
| $p^\mu$ | pee mu | Four-momentum $(E/c,\bm p)$ | $\mathrm{kg\,m/s}$ | Section 57.5 |
| $E_0=mc^2$ | ee zero | Rest energy | $\mathrm{J}$ | Section 57.6 |
| $M_{\mathrm{inv}}$ | em invariant | Invariant mass | $\mathrm{kg}$ | Section 57.8 |
| $\hbar$ | h-bar | Reduced Planck constant $h/2\pi$. In natural units, $\hbar=c=1$ | $\mathrm{J\,s}$ | Section 58.1 |
| $\partial_\mu$ | partial mu | Four-gradient $\partial/\partial x^\mu$ | — | Section 58.2 |
| $\Box$ | box (d'Alembertian) | D'Alembertian $\Box=\partial_\mu\partial^\mu$ | — | Section 58.2 |
| $j^\mu$, $A^\mu$ | jay mu; ay mu | Four-current; four-potential | — | Section 58.3 |
| $F^{\mu\nu}$ | eff mu nu | Field-strength tensor (combining the electric field and the magnetic flux density) | — | Section 58.5 |
Symbols with Different Meanings (Caution)
Physical symbols number only about 100, even counting the Latin alphabet and the Greek letters together, whereas there are several hundred physical quantities. As a result, the same letter may denote different quantities depending on the part, and sometimes even within the same part. For example, $m$ is mass, but it is also Poisson's number in mechanics of materials and the Weibull modulus in fracture mechanics, and $\rho$ can be any of density, charge density, resistivity, and radius of curvature. Which meaning is intended is determined by the part and chapter in which the letter is used, and by the unit. The table below lists the letters that this book uses with different meanings, together with the section in which each meaning first appears. (The symbols in this table are collected from the tables of the parts above; the rightmost item of each entry is the section of first appearance.)
Caution: how to tell apart different quantities written with the same letter
- Look at the unit: $\rho\ [\mathrm{kg/m^3}]$ is the density, $\rho\ [\mathrm{C/m^3}]$ is the charge density, and $\rho\ [\Omega\,\mathrm{m}]$ is the resistivity. If the unit is written along with the symbol, there is no confusion.
- Look at the subscripts: By convention, some letters are distinguished by subscripts or typeface, such as $K$ (bulk modulus) and $K_{\mathrm I}$ (stress intensity factor), or $G$ (shear modulus), $G$ (Gibbs energy), and $\mathcal G$ (energy release rate).
- Look at the note at the beginning of the chapter: In some places, such as Chapters 21 and 22, where the meaning of $m$ changes, the text states explicitly “In this chapter we write …”.
| Symbol | Meaning in this book (part, unit, section of first appearance) |
|---|---|
| $A$ (five meanings) |
|
| $a$ (four meanings) |
|
| $B$ (three meanings) |
|
| $b$ (four meanings) |
|
| $C$ (four meanings) |
|
| $c$ (two meanings) |
|
| $D$ (three meanings) |
|
| $E$ (four meanings) |
|
| $e$ (three meanings) |
|
| $F$ (three meanings) |
|
| $f$ (four meanings) |
|
| $G$ (four meanings) |
|
| $g$ (two meanings) |
|
| $H$ (three meanings) |
|
| $h$ (two meanings) |
|
| $I$ (five meanings) |
|
| $J$ (three meanings) |
|
| $K$ (four meanings) |
|
| $k$ (four meanings) |
|
| $L$ (three meanings) |
|
| $M$ (five meanings) |
|
| $m$ (six meanings) |
|
| $N$ (three meanings) |
|
| $n$ (five meanings) |
|
| $P$ (four meanings) |
|
| $p$ (three meanings) |
|
| $Q$ (three meanings) |
|
| $R$ (three meanings) |
|
| $S$ (five meanings) |
|
| $T$ (four meanings) |
|
| $t$ (two meanings) |
|
| $U$ (two meanings) |
|
| $u$ (two meanings) |
|
| $V$ (four meanings) |
|
| $W$ (three meanings) |
|
| $Z$ (two meanings) |
|
| $\alpha$ (four meanings) |
|
| $\beta$ (three meanings) |
|
| $\gamma$ (three meanings) |
|
| $\varepsilon$ (three meanings) |
|
| $\kappa$ (three meanings) |
|
| $\lambda$ (five meanings) |
|
| $\mu$ (five meanings) |
|
| $\nu$ (four meanings) |
|
| $\rho$ (six meanings) |
|
| $\sigma$ (four meanings) |
|
| $\tau$ (three meanings) |
|
| $\Phi$ (two meanings) |
|
| $\phi$ (four meanings) |
|
| $\Omega$ (three meanings) |
|
B.5 Index of Terms (Alphabetical Order)
This index lists the principal terms that the main text of this book has gathered into boxes (definition boxes and law boxes) as definitions, laws, or theorems, together with closely related terms. In this English edition the terms are arranged in alphabetical order of their English names (the Japanese original lists them in the order of their Japanese readings, together with the English names given in the main text). Each link leads to the chapter and section in which the term is defined; where there are several, the first is the main definition. The index contains 571 terms in all.
A
| Term | Defined in |
|---|---|
| absolute entropy | Section 32.2 |
| absolute refractive index (refractive index) | Section 13.3 |
| absolute temperature | Section 23.1 |
| absolute zero | Section 23.1 |
| acceleration vector | Section 1.2 |
| action | Section 44.4 |
| additivity of entropy | Section 49.3 |
| adiabatic process | Section 23.8 |
| air wedge | Section 16.5 |
| Ampère force | Section 39.1 |
| Ampère's law | Section 38.5 |
| Ampère–Maxwell law | Section 42.1 |
| angle of twist | Section 20.7 |
| angular frequency | Section 7.1 |
| angular magnification | Section 15.5 |
| angular momentum | Section 2.5 |
| areal velocity | Section 8.1 |
| average speed | Section 34.5 |
B
| Term | Defined in |
|---|---|
| basis vectors of polar coordinates | Section 3.2 |
| Basquin's law | Section 22.2 |
| beats | Section 12.3, Section 17.4 |
| Beltrami identity | Section 44.6 |
| bending stress | Section 20.5 |
| Biot–Savart law | Section 38.2 |
| blueshift | Section 55.4 |
| Boltzmann constant | Section 24.3 |
| Boltzmann factor | Section 50.1 |
| Boltzmann's principle | Section 49.2 |
| Bose-type integral | Section 47.5 |
| Bose–Einstein condensation | Section 52.10 |
| Bose–Einstein distribution | Section 52.6 |
| boson | Section 52.4 |
| bound charge | Section 41.1 |
| boundary condition | Section 41.3 |
| Boyle temperature | Section 25.4 |
| Boyle's law | Section 23.5 |
| Boyle–Charles law | Section 23.5 |
| brachistochrone | Section 44.6 |
| Bragg condition | Section 16.7 |
| bulk modulus | Section 19.2 |
C
| Term | Defined in |
|---|---|
| calculus of variations | Section 44.5 |
| canonical distribution | Section 50.1 |
| canonical ensemble | Section 50.1 |
| canonical transformation | Section 46.4 |
| capacitance | Section 36.6 |
| capacitor | Section 36.6 |
| Carnot cycle | Section 28.2 |
| Carnot's theorem | Section 28.4 |
| causality | Section 56.4 |
| cavity radiation (black-body radiation) | Section 53.1 |
| cavity resonator | Section 42.7 |
| Celsius temperature | Section 23.1 |
| center of curvature | Section 3.4 |
| center of mass | Section 10.1 |
| central force | Section 8.1, Section 4.4 |
| centrifugal force | Section 9.3 |
| centripetal acceleration | Section 5.4 |
| centripetal force | Section 5.4 |
| charge density | Section 37.2 |
| Charles's law | Section 23.5 |
| Charpy impact test | Section 22.5 |
| chemical potential | Section 52.3, Section 49.5 |
| classical limit | Section 52.7 |
| Clausius inequality | Section 29.7 |
| Clausius statement | Section 28.1 |
| Clausius–Clapeyron equation | Section 32.5 |
| closed system | Section 26.1 |
| coefficient of linear expansion | Section 23.9 |
| coefficient of performance (COP) | Section 28.8 |
| coefficient of restitution | Section 2.6 |
| coefficient of thermal expansion | Section 27.4 |
| coefficient of volume expansion | Section 23.9 |
| compression factor | Section 25.2 |
| Compton scattering | Section 57.9 |
| conic section | Section 6.3 |
| conservation of angular momentum | Section 10.8 |
| conservation of charge (continuity equation) | Section 37.2 |
| conservation of heat | Section 23.2 |
| conservation of mechanical energy | Section 4.5 |
| conservation of momentum | Section 2.4 |
| conservative force | Section 4.4 |
| constant-acceleration formulas (the three) | Section 1.4 |
| constraint | Section 43.1 |
| contravariant components | Section 57.2 |
| Coriolis force | Section 9.3 |
| cosmic microwave background | Section 53.6 |
| Coulomb's law | Section 35.1 |
| covariant components | Section 57.2 |
| covariant Lorentz force | Section 58.8 |
| critical angle | Section 14.7 |
| critical damping | Section 7.3 |
| critical point | Section 24.4 |
| critical temperature, critical pressure, critical volume | Section 24.4 |
| Curie's law | Section 51.4 |
| current density | Section 37.2 |
| cyclic coordinate | Section 45.6, Section 46.1 |
| cyclotron angular frequency | Section 39.6 |
| cyclotron motion | Section 39.6 |
D
| Term | Defined in |
|---|---|
| d'Alembert's principle | Section 43.6 |
| d'Alembert's solution | Section 11.2 |
| d'Alembertian | Section 58.2 |
| damped oscillation | Section 7.3 |
| Debye frequency | Section 53.8 |
| Debye model | Section 53.8 |
| Debye temperature | Section 53.8 |
| Debye's T³ law | Section 53.9 |
| deflection | Section 20.6 |
| degeneracy | Section 50.1 |
| degenerate Fermi gas | Section 52.9 |
| degrees of freedom (of a mechanical system) | Section 43.1 |
| degrees of freedom (of molecular motion) | Section 26.5 |
| delayed fracture | Section 22.9 |
| dense region (compression) | Section 11.3 |
| density of states | Section 52.8, Section 53.2 |
| diamagnetism | Section 41.2 |
| dielectric | Section 41.1 |
| Diesel cycle | Section 28.7 |
| diffraction | Section 11.9 |
| diffraction grating | Section 16.3 |
| dimension | Section 1.3 |
| dimensional analysis | Section 1.3 |
| dimensional homogeneity | Section 1.3 |
| dispersion | Section 14.6 |
| dispersion relation | Section 17.5 |
| displacement current | Section 42.1 |
| displacement vector | Section 1.2 |
| distance of distinct vision | Section 15.5 |
| distribution function | Section 34.2 |
| Doppler effect | Section 12.1, Section 12.3 |
| ductile-to-brittle transition | Section 22.5 |
| Dugdale strip-yield model | Section 21.6 |
| Dulong–Petit law | Section 51.2 |
E
| Term | Defined in |
|---|---|
| eccentricity | Section 6.3 |
| effective potential | Section 8.4 |
| effective value (of alternating current) | Section 40.10 |
| effective volume | Section 22.7 |
| Einstein model | Section 51.2 |
| Einstein solid | Section 48.5 |
| Einstein summation convention | Section 57.2 |
| Einstein temperature | Section 51.2 |
| elastic limit | Section 19.5 |
| elasticity | Section 18.1 |
| electric current | Section 37.1 |
| electric dipole | Section 36.8 |
| electric displacement (electric flux density) | Section 35.4 |
| electric field | Section 35.2 |
| electric field line | Section 35.2 |
| electric potential | Section 36.1 |
| electrical resistance | Section 37.3 |
| electromagnetic induction | Section 40.1 |
| electromagnetic spectrum | Section 42.6 |
| electromagnetic wave | Section 14.6 |
| electromotive force | Section 37.6 |
| electrostatic energy | Section 36.6 |
| electrostatic equilibrium (charge distribution of a conductor) | Section 35.6 |
| electrostatic induction | Section 36.3 |
| elongation | Section 19.5 |
| energy density of the electric field | Section 36.6 |
| energy density of the electromagnetic field | Section 42.5 |
| energy density of the magnetic field | Section 40.7 |
| energy fluctuation | Section 50.5 |
| energy function | Section 46.1 |
| energy release rate | Section 21.4 |
| enthalpy | Section 27.2 |
| entropy | Section 29.1 |
| entropy of mixing | Section 49.7 |
| equation of motion | Section 2.2 |
| equation of state of an ideal gas (ideal gas law) | Section 23.6 |
| equilibrium point (stable and unstable) | Section 4.6 |
| equipartition theorem | Section 50.7 |
| equivalent resistance | Section 37.5 |
| ergodic hypothesis | Section 48.3 |
| escape velocity | Section 8.4 |
| Euler–Lagrange equation | Section 44.5 |
| exact differential | Section 26.6 |
| extensive variable | Section 23.2 |
| external force | Section 2.3 |
F
| Term | Defined in |
|---|---|
| Faraday's law of induction | Section 40.2 |
| fatigue | Section 22.1 |
| fatigue limit | Section 22.1 |
| Fermat's principle | Section 14.5 |
| Fermi energy | Section 52.8 |
| Fermi-type integral | Section 47.5 |
| fermion | Section 52.4 |
| Fermi–Dirac distribution | Section 52.5 |
| ferromagnetism | Section 41.2 |
| fictitious force | Section 9.1 |
| field-strength tensor (electromagnetic field tensor) | Section 58.5 |
| first law of thermodynamics | Section 23.4, Section 26.6 |
| Fizeau's experiment | Section 13.6 |
| flux of the electric field | Section 35.3 |
| focal point, focal length | Section 15.1 |
| forced oscillation | Section 7.4 |
| four-current | Section 58.3 |
| four-gradient | Section 58.2 |
| four-momentum | Section 57.5 |
| four-position | Section 57.1 |
| four-potential | Section 58.4 |
| four-vector | Section 57.3 |
| four-velocity | Section 57.4 |
| Fourier series | Section 17.2 |
| Fourier transform | Section 17.6 |
| Fourier's law of heat conduction | Section 33.1 |
| fracture | Section 19.5 |
| fracture toughness | Section 21.5 |
| free fall | Section 1.5 |
| frequency | Section 7.1 |
| functional | Section 44.4 |
G
| Term | Defined in |
|---|---|
| Galilean relativity | Section 54.1 |
| Galilean transformation | Section 54.1 |
| gas constant | Section 23.6 |
| Gauss's law | Section 35.3, Section 35.4 |
| Gaussian integral | Section 47.2 |
| generalized coordinates | Section 43.1 |
| generalized force | Section 43.3 |
| generalized Hooke's law | Section 20.4 |
| generalized momentum | Section 43.2 |
| generator | Section 40.10 |
| Gibbs energy (Gibbs free energy) | Section 30.4 |
| Gibbs paradox | Section 49.7 |
| Gibbs–Helmholtz equation | Section 30.6 |
| grand canonical distribution | Section 52.1 |
| grand partition function | Section 52.2 |
| grand potential | Section 52.2 |
| grating equation | Section 16.3 |
| gravitational potential energy | Section 8.4 |
| Griffith's criterion | Section 21.2 |
| group velocity | Section 17.5 |
H
| Term | Defined in |
|---|---|
| Hall coefficient | Section 39.8 |
| Hall effect | Section 39.8 |
| Hall voltage | Section 39.8 |
| Hamilton's canonical equations | Section 45.2 |
| Hamilton's principle (principle of least action) | Section 44.4 |
| Hamiltonian | Section 45.1 |
| Hamilton–Jacobi equation | Section 46.5 |
| harmonic oscillator | Section 51.2 |
| heat | Section 26.2 |
| heat bath | Section 50.2 |
| heat capacity | Section 23.2, Section 27.2 |
| heat capacity at constant pressure | Section 27.2 |
| heat capacity at constant volume | Section 27.2 |
| heat conduction equation (heat equation) | Section 33.1 |
| heat pump | Section 28.8 |
| Helmholtz free energy | Section 30.4 |
| Hollomon's equation | Section 19.5 |
| holonomic constraint | Section 43.1 |
| homogeneous body | Section 18.1 |
| Hooke's law | Section 19.1 |
| Huygens's principle | Section 11.8 |
| hysteresis curve | Section 41.2 |
I
| Term | Defined in |
|---|---|
| impulse | Section 2.2 |
| impulse–momentum theorem | Section 2.2 |
| inertial frame | Section 2.1 |
| inexact differential | Section 26.6 |
| Inglis's formula | Section 21.1 |
| intensity of a wave | Section 11.5 |
| intensive variable | Section 23.2 |
| interference | Section 11.6 |
| internal energy | Section 23.3 |
| internal force | Section 2.3, Section 18.1 |
| internal pressure | Section 27.4 |
| invariant interval (spacetime interval) | Section 56.4 |
| invariant mass | Section 57.8 |
| inversion temperature | Section 27.7 |
| irreversible process | Section 26.4 |
| isolated system | Section 26.1 |
| isothermal compressibility | Section 27.4 |
| isothermal process | Section 23.8 |
| isotropic body | Section 18.1 |
J
| Term | Defined in |
|---|---|
| J-integral | Section 21.6 |
| Joule heating | Section 37.4 |
| Joule's law | Section 37.4 |
| Joule–Thomson coefficient | Section 27.6 |
| Joule–Thomson effect | Section 27.6 |
K
| Term | Defined in |
|---|---|
| Kelvin–Planck statement (Thomson's or Kelvin's principle) | Section 28.1 |
| Kepler's first law | Section 8.2 |
| Kepler's second law | Section 8.1 |
| Kepler's third law | Section 8.3 |
| kinetic energy | Section 4.2 |
| kinetic theory of gases | Section 24.2 |
| Kirchhoff's laws | Section 37.6 |
L
| Term | Defined in |
|---|---|
| Lagrange's equations of motion | Section 43.4 |
| Lagrangian | Section 43.4 |
| latent heat (heat of fusion, heat of vaporization) | Section 23.2 |
| law of action and reaction | Section 2.3 |
| law of entropy increase | Section 29.7 |
| law of equipartition of energy | Section 24.3, Section 50.7 |
| law of inertia | Section 2.1 |
| law of reflection | Section 11.8, Section 14.4 |
| law of refraction | Section 11.8, Section 14.4 |
| LC circuit | Section 40.9 |
| Legendre transformation | Section 31.5, Section 45.1 |
| lens | Section 15.1 |
| lens equation (imaging formula) | Section 15.2 |
| lenses in contact | Section 15.4 |
| Lenz's law | Section 40.1 |
| light cone | Section 56.3 |
| lightlike interval | Section 56.4 |
| linearly polarized light | Section 13.1 |
| Liouville's theorem | Section 46.5 |
| load | Section 18.2 |
| longitudinal strain | Section 18.4 |
| longitudinal wave | Section 11.3 |
| Lorentz contraction | Section 55.1 |
| Lorentz factor | Section 54.6 |
| Lorentz force | Section 39.4 |
| Lorentz transformation | Section 54.5 |
| Lorentz velocity transformation | Section 55.6, Section 56.1 |
| Lorenz condition (Lorenz gauge) | Section 58.6 |
| lower shelf | Section 22.5 |
| lower yield point | Section 19.5 |
M
| Term | Defined in |
|---|---|
| Mach cone | Section 12.2 |
| Mach number | Section 12.2 |
| macrostate | Section 48.1 |
| magnetic dipole moment | Section 38.6 |
| magnetic field | Section 38.1 |
| magnetic flux | Section 38.2 |
| magnetic flux density | Section 38.1 |
| magnetic force | Section 38.1 |
| magnetization | Section 41.2 |
| magnetization vector | Section 41.2 |
| magnification | Section 15.1 |
| Malus's law | Section 13.2 |
| mass-shell condition | Section 57.5 |
| mass–energy equivalence | Section 57.6 |
| material testing | Section 19.4 |
| maximum non-expansion work | Section 30.5 |
| maximum work | Section 30.5 |
| Maxwell relations | Section 31.1 |
| Maxwell's equal-area rule | Section 25.1 |
| Maxwell's equations | Section 42.2, Section 35.3 |
| Maxwell's hypothesis of independence | Section 34.2 |
| Maxwell's velocity distribution law | Section 34.4 |
| Mayer's relation | Section 27.5 |
| mean stress | Section 22.1 |
| mechanical stability | Section 31.8 |
| median rank method | Section 22.7 |
| method of Lagrange multipliers | Section 44.7 |
| metric (metric tensor) | Section 57.2 |
| Michelson–Morley experiment | Section 54.3 |
| microcanonical distribution | Section 48.4 |
| microstate | Section 48.1 |
| Miner's rule | Section 22.4 |
| Minkowski spacetime | Section 56.4 |
| modulus of rigidity | Section 19.2 |
| Mohr's circle | Section 20.3 |
| molar heat capacity at constant pressure | Section 23.7 |
| molar heat capacity at constant volume | Section 23.7 |
| moment | Section 2.5 |
| moment of inertia | Section 10.3 |
| momentum | Section 2.2 |
| most probable speed | Section 34.5 |
| mutual inductance | Section 40.6 |
N
| Term | Defined in |
|---|---|
| n-dimensional ball | Section 47.1 |
| natural frequency | Section 12.4 |
| natural units | Section 58.1 |
| natural variables | Section 31.5 |
| negative temperature | Section 51.3 |
| Nernst's theorem | Section 32.1 |
| Newton's first law | Section 2.1 |
| Newton's law of universal gravitation | Section 8.1 |
| Newton's rings | Section 16.6 |
| Newton's second law (equation of motion) | Section 2.2 |
| Newton's third law (law of action and reaction) | Section 2.3 |
| Noether's theorem | Section 46.2 |
| non-inertial frame | Section 9.1 |
| normal mode (eigenmode) | Section 17.3 |
| normal stress | Section 18.3 |
| number of states | Section 48.1 |
O
| Term | Defined in |
|---|---|
| occupation number | Section 52.4 |
| Ohm's law | Section 37.3 |
| open system | Section 26.1 |
| optical axis | Section 15.1 |
| optical path length (optical distance) | Section 16.1 |
| Otto cycle | Section 28.6 |
| overdamping | Section 7.3 |
P
| Term | Defined in |
|---|---|
| parallel connection | Section 37.5 |
| parallel-axis theorem (Steiner's theorem) | Section 10.7 |
| paramagnetism | Section 41.2 |
| Paris law | Section 22.3 |
| particle (point mass) | Section 1.1 |
| partition function | Section 50.1 |
| path function | Section 26.3 |
| perfectly elastic collision | Section 24.1 |
| period | Section 7.1 |
| perpendicular-axis theorem | Section 10.7 |
| phase space | Section 45.5, Section 48.2 |
| phase trajectory | Section 45.5 |
| phase transition | Section 30.2 |
| phase velocity | Section 11.4, Section 17.5 |
| phonon | Section 53.7 |
| photon | Section 53.1 |
| physical pendulum | Section 10.10 |
| Planck's radiation law | Section 53.3 |
| plane electromagnetic wave | Section 42.4 |
| plane polar coordinates | Section 3.1 |
| plane-section assumption | Section 20.5 |
| plastic zone | Section 21.6 |
| plasticity | Section 18.1 |
| Poisson bracket | Section 46.3 |
| Poisson's equation | Section 36.7 |
| Poisson's formula | Section 27.3 |
| Poisson's number | Section 18.4 |
| Poisson's ratio | Section 18.4 |
| polar coordinates | Section 3.1 |
| polar second moment of area | Section 20.7 |
| polarization | Section 41.1 |
| polarization (of light) | Section 13.1 |
| polarization vector | Section 41.1 |
| position vector | Section 1.2 |
| potential difference (voltage) | Section 36.1 |
| potential energy | Section 4.4 |
| power | Section 4.6 |
| Poynting vector | Section 42.5 |
| Poynting's theorem | Section 42.5 |
| principal stress | Section 20.2 |
| principle of corresponding states | Section 25.1 |
| principle of equal a priori probability | Section 48.4 |
| principle of maximum work | Section 29.7 |
| principle of relativity | Section 54.4 |
| principle of superposition | Section 17.1, Section 18.1 |
| principle of superposition of electric fields | Section 35.2 |
| principle of the constancy of the speed of light | Section 54.4 |
| principle of virtual work | Section 43.6 |
| projectile motion | Section 5.1 |
| proof stress (0.2% offset method) | Section 19.5 |
| proper length | Section 55.1 |
| proper time | Section 55.2, Section 56.5, Section 57.4 |
| proportional limit | Section 19.4 |
Q
| Term | Defined in |
|---|---|
| quality factor Q (sharpness) | Section 7.4 |
| quasi-static process | Section 26.4 |
R
| Term | Defined in |
|---|---|
| R-curve (crack growth resistance curve) | Section 21.7 |
| radius of curvature | Section 3.4 |
| rapidity | Section 56.7 |
| RC circuit | Section 37.7 |
| real image | Section 15.1 |
| redshift | Section 55.4 |
| reduced variables | Section 25.1 |
| reduction of area | Section 19.5 |
| reflection at a fixed end | Section 14.1 |
| reflection at a free end | Section 14.1 |
| refrigerator | Section 28.8 |
| relative permittivity | Section 41.1 |
| relativistic Doppler effect | Section 55.4 |
| relativity of simultaneity | Section 56.2 |
| resistivity | Section 37.3 |
| resonance | Section 7.4, Section 12.4 |
| resonance of a string | Section 12.6 |
| rest energy | Section 57.6 |
| reversible process | Section 26.4 |
| Richards's rule | Section 32.4 |
| rigid body | Section 10.2 |
| RL circuit | Section 40.8 |
| root-mean-square speed | Section 34.5 |
| rotating frame | Section 9.2 |
| rotating-mirror method (Foucault) | Section 13.7 |
| rotational equation of motion | Section 2.5 |
| rotational kinetic energy | Section 10.8 |
| rotational temperature | Section 51.5 |
S
| Term | Defined in |
|---|---|
| Sackur–Tetrode equation | Section 49.6 |
| Saint-Venant's principle | Section 18.1 |
| Schottky heat capacity | Section 51.3 |
| second law of thermodynamics | Section 23.4, Section 28.1 |
| second moment of area | Section 20.5 |
| self-inductance | Section 40.5 |
| semi-latus rectum | Section 6.3 |
| separation of variables | Section 33.3 |
| sequential-imaging method | Section 15.4 |
| series connection | Section 37.5 |
| shear modulus (modulus of rigidity) | Section 19.2 |
| shear strain | Section 18.5 |
| shear stress | Section 18.3 |
| shell theorem (Newton's shell theorem) | Section 8.5 |
| shock wave | Section 12.2 |
| SI base units | Section 1.3 |
| simple harmonic motion | Section 7.1 |
| simple pendulum | Section 7.2 |
| sinusoidal wave | Section 11.3 |
| size effect (volume effect) | Section 22.7 |
| Snell's law | Section 14.4 |
| solenoid | Section 38.4 |
| spacelike interval | Section 56.4 |
| spacetime diagram | Section 56.3 |
| sparse region (rarefaction) | Section 11.3 |
| specific heat | Section 23.2 |
| speed of sound | Section 12.1 |
| standing wave | Section 11.7 |
| state function (state quantity) | Section 26.3 |
| statistical definition of temperature | Section 49.4 |
| Stefan–Boltzmann law | Section 53.5 |
| Stirling's formula | Section 47.3 |
| Stokes's drag law | Section 5.2 |
| strain energy density | Section 20.4 |
| stress | Section 18.3 |
| stress amplitude | Section 22.1 |
| stress concentration | Section 21.1 |
| stress corrosion cracking | Section 22.9 |
| stress intensity factor | Section 21.3 |
| stress ratio | Section 22.1 |
| stress tensor | Section 20.1 |
| system and surroundings | Section 26.1 |
| S–N curve | Section 22.1 |
T
| Term | Defined in |
|---|---|
| tangential and normal components of acceleration | Section 3.4 |
| tensile strength (ultimate strength) | Section 19.5 |
| terminal velocity | Section 5.2 |
| theoretical strength | Section 21.1 |
| thermal conductivity | Section 33.1 |
| thermal de Broglie wavelength | Section 49.6, Section 51.1 |
| thermal diffusivity | Section 33.1 |
| thermal efficiency | Section 28.3 |
| thermal equilibrium state | Section 26.4 |
| thermal shock resistance | Section 22.8 |
| thermal stability | Section 31.8 |
| thermal stress | Section 20.4 |
| thermodynamic equation of state | Section 31.6 |
| thermodynamic square | Section 31.4 |
| thermodynamic weight | Section 49.1 |
| thin-film interference | Section 16.4 |
| third law of thermodynamics | Section 32.2, Section 30.3 |
| threshold energy | Section 57.8 |
| time constant | Section 37.7, Section 40.8 |
| time dilation | Section 55.2 |
| timelike interval | Section 56.4 |
| torque | Section 2.5 |
| torque (moment of force) | Section 2.5 |
| torsional stress | Section 20.7 |
| total internal reflection | Section 14.7 |
| transformer | Section 40.10 |
| transverse strain | Section 18.4 |
| transverse wave | Section 11.3 |
| triple point of water | Section 29.6 |
| Trouton's rule | Section 32.4 |
| true strain | Section 19.5 |
| true stress | Section 19.5 |
| turning point | Section 4.6 |
| twin paradox | Section 56.6 |
| two-body decay | Section 57.7 |
| two-level system | Section 48.5 |
U
| Term | Defined in |
|---|---|
| uniform circular motion | Section 5.4 |
| unit principal normal vector | Section 3.3 |
| unit tangent vector | Section 3.3 |
| upper shelf | Section 22.5 |
| upper yield point | Section 19.5 |
V
| Term | Defined in |
|---|---|
| van der Waals equation of state | Section 24.4 |
| vector potential | Section 58.4 |
| velocity vector | Section 1.2 |
| vibrational temperature | Section 51.5 |
| virial coefficient | Section 25.4 |
| virial equation of state | Section 25.3 |
| virtual displacement | Section 43.6 |
| virtual image | Section 15.1 |
| voltage drop | Section 37.6 |
| volumetric strain | Section 18.5 |
W
| Term | Defined in |
|---|---|
| wave | Section 11.3 |
| wave equation | Section 11.2 |
| wave equation for electromagnetic waves | Section 42.3 |
| wave packet | Section 17.4 |
| waveguide | Section 42.7 |
| weakest-link model | Section 22.6 |
| Weibull distribution | Section 22.6 |
| Wien's displacement law | Section 53.4 |
| work | Section 4.1 |
| work hardening | Section 19.5 |
| work–energy theorem | Section 4.2 |
| world line | Section 56.3 |
X
| Term | Defined in |
|---|---|
| x–t graph and v–t graph | Section 1.6 |
Y
| Term | Defined in |
|---|---|
| Young's double-slit experiment | Section 16.2 |
| Young's modulus | Section 19.2 |
| Young's modulus (modulus of longitudinal elasticity) | Section 19.2 |
Z
| Term | Defined in |
|---|---|
| zeroth law of thermodynamics | Section 24.1 |
| zeta function | Section 47.4 |
B.6 References and Sources
- This appendix supplements material not in the notes. Related notes: Yasuhide Mochizuki, Physics Notes (handwritten lecture notes, in Japanese), eight volumes in all (Mechanics, Waves, Mechanics of Materials, Thermodynamics, Electromagnetism, Analytical Mechanics, Statistical Mechanics, and Special Relativity). The symbols have been unified in this book.
- E. Tiesinga, P. J. Mohr, D. B. Newell, B. N. Taylor, “CODATA recommended values of the fundamental physical constants: 2018”, Reviews of Modern Physics 93, 025010 (2021). (Source of the physical constants in B.1.)
- Bureau International des Poids et Mesures (BIPM), The International System of Units (SI), 9th edition (2019). (Source of the SI units and prefixes in B.2. The prefixes added in 2022 are based on a resolution of the General Conference on Weights and Measures (27th meeting).)