Glossary of Key Symbols and Notation
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In this glossary, key symbols and notation are briefly defined.
| Symbol | Definition |
|---|---|
| \(\overline{\text{any symbol}}\) | average (indicated by a bar over a symbol—e.g., \(\overline{v}\) is average velocity) |
| \(°\text{C}\) | Celsius degree |
| \(°\text{F}\) | Fahrenheit degree |
| \(\text{//}\) | parallel |
| \(\perp \) | perpendicular |
| \(\propto \) | proportional to |
| \(±\) | plus or minus |
| \({\phantom{\rule{0.25em}{0ex}}}_{0}\) | zero as a subscript denotes an initial value |
| \(\alpha \) | alpha rays |
| \(\alpha \) | angular acceleration |
| \(\alpha \) | temperature coefficient(s) of resistivity |
| \(\beta \) | beta rays |
| \(\beta \) | sound level |
| \(\beta \) | volume coefficient of expansion |
| \({\beta }^{-}\) | electron emitted in nuclear beta decay |
| \({\beta }^{+}\) | positron decay |
| \(\gamma \) | gamma rays |
| \(\gamma \) | surface tension |
| \(\gamma =1/\sqrt{1-{v}^{2}/{c}^{2}}\) | a constant used in relativity |
| \(\Delta \) | change in whatever quantity follows |
| \(\delta \) | uncertainty in whatever quantity follows |
| \(\mathrm{\Delta E}\) | change in energy between the initial and final orbits of an electron in an atom |
| \(\mathrm{\Delta E}\) | uncertainty in energy |
| \(\mathrm{\Delta m}\) | difference in mass between initial and final products |
| \(\mathrm{\Delta N}\) | number of decays that occur |
| \(\mathrm{\Delta p}\) | change in momentum |
| \(\mathrm{\Delta p}\) | uncertainty in momentum |
| \(\Delta {\text{PE}}_{\text{g}}\) | change in gravitational potential energy |
| \(\mathrm{\Delta \theta }\) | rotation angle |
| \(\mathrm{\Delta s}\) | distance traveled along a circular path |
| \(\mathrm{\Delta t}\) | uncertainty in time |
| \({\mathrm{\Delta t}}_{0}\) | proper time as measured by an observer at rest relative to the process |
| \(\mathrm{\Delta V}\) | potential difference |
| \(\mathrm{\Delta x}\) | uncertainty in position |
| \({\epsilon }_{0}\) | permittivity of free space |
| \(\eta \) | viscosity |
| \(\theta \) | angle between the force vector and the displacement vector |
| \(\theta \) | angle between two lines |
| \(\theta \) | contact angle |
| \(\theta \) | direction of the resultant |
| \({\theta }_{b}\) | Brewster’s angle |
| \({\theta }_{c}\) | critical angle |
| \(\kappa \) | dielectric constant |
| \(\lambda \) | decay constant of a nuclide |
| \(\lambda \) | wavelength |
| \({\lambda }_{n}\) | wavelength in a medium |
| \({\mu }_{0}\) | permeability of free space |
| \({\mu }_{\text{k}}\) | coefficient of kinetic friction |
| \({\mu }_{\text{s}}\) | coefficient of static friction |
| \({v}_{e}\) | electron neutrino |
| \({\pi }^{+}\) | positive pion |
| \({\pi }^{-}\) | negative pion |
| \({\pi }^{0}\) | neutral pion |
| \(\rho \) | density |
| \({\rho }_{\text{c}}\) | critical density, the density needed to just halt universal expansion |
| \({\rho }_{\text{fl}}\) | fluid density |
| \({\overline{\rho }}_{\text{obj}}\) | average density of an object |
| \(\rho /{\rho }_{\text{w}}\) | specific gravity |
| \(\tau \) | characteristic time constant for a resistance and inductance \(\left(\text{RL}\right)\) or resistance and capacitance \(\left(\text{RC}\right)\) circuit |
| \(\tau \) | characteristic time for a resistor and capacitor \(\left(\text{RC}\right)\) circuit |
| \(\tau \) | torque |
| \(Υ\) | upsilon meson |
| \(\Phi \) | magnetic flux |
| \(\varphi \) | phase angle |
| \(\Omega \) | ohm (unit) |
| \(\omega \) | angular velocity |
| \(A\) | ampere (current unit) |
| \(A\) | area |
| \(A\) | cross-sectional area |
| \(A\) | total number of nucleons |
| \(a\) | acceleration |
| \({a}_{\text{B}}\) | Bohr radius |
| \({a}_{\text{c}}\) | centripetal acceleration |
| \({a}_{\text{t}}\) | tangential acceleration |
| \(\text{AC}\) | alternating current |
| \(\text{AM}\) | amplitude modulation |
| \(\text{atm}\) | atmosphere |
| \(B\) | baryon number |
| \(B\) | blue quark color |
| \(\overline{B}\) | antiblue (yellow) antiquark color |
| \(b\) | quark flavor bottom or beauty |
| \(B\) | bulk modulus |
| \(B\) | magnetic field strength |
| \({\text{B}}_{\text{int}}\) | electron’s intrinsic magnetic field |
| \({\text{B}}_{\text{orb}}\) | orbital magnetic field |
| \(\text{BE}\) | binding energy of a nucleus—it is the energy required to completely disassemble it into separate protons and neutrons |
| \(\text{BE}/A\) | binding energy per nucleon |
| \(\text{Bq}\) | becquerel—one decay per second |
| \(C\) | capacitance (amount of charge stored per volt) |
| \(C\) | coulomb (a fundamental SI unit of charge) |
| \({C}_{\text{p}}\) | total capacitance in parallel |
| \({C}_{\text{s}}\) | total capacitance in series |
| \(\text{CG}\) | center of gravity |
| \(\text{CM}\) | center of mass |
| \(c\) | quark flavor charm |
| \(c\) | specific heat |
| \(c\) | speed of light |
| \(\text{Cal}\) | kilocalorie |
| \(\text{cal}\) | calorie |
| \({\text{COP}}_{\text{hp}}\) | heat pump’s coefficient of performance |
| \({\text{COP}}_{\text{ref}}\) | coefficient of performance for refrigerators and air conditioners |
| \(\text{cos}\phantom{\rule{0.20em}{0ex}}\theta \) | cosine |
| \(\text{cot}\phantom{\rule{0.20em}{0ex}}\theta \) | cotangent |
| \(\text{csc}\phantom{\rule{0.20em}{0ex}}\theta \) | cosecant |
| \(D\) | diffusion constant |
| \(d\) | displacement |
| \(d\) | quark flavor down |
| \(\text{dB}\) | decibel |
| \({d}_{\text{i}}\) | distance of an image from the center of a lens |
| \({d}_{\text{o}}\) | distance of an object from the center of a lens |
| \(\text{DC}\) | direct current |
| \(E\) | electric field strength |
| \(\epsilon \) | emf (voltage) or Hall electromotive force |
| \(\text{emf}\) | electromotive force |
| \(E\) | energy of a single photon |
| \(E\) | nuclear reaction energy |
| \(E\) | relativistic total energy |
| \(E\) | total energy |
| \({E}_{0}\) | ground state energy for hydrogen |
| \({E}_{0}\) | rest energy |
| \(\text{EC}\) | electron capture |
| \({E}_{\text{cap}}\) | energy stored in a capacitor |
| \(\text{Eff}\) | efficiency—the useful work output divided by the energy input |
| \({\text{Eff}}_{\text{C}}\) | Carnot efficiency |
| \({E}_{\text{in}}\) | energy consumed (food digested in humans) |
| \({E}_{\text{ind}}\) | energy stored in an inductor |
| \({E}_{\text{out}}\) | energy output |
| \(e\) | emissivity of an object |
| \({e}^{+}\) | antielectron or positron |
| \(\text{eV}\) | electron volt |
| \(\text{F}\) | farad (unit of capacitance, a coulomb per volt) |
| \(\text{F}\) | focal point of a lens |
| \(\mathbf{\text{F}}\) | force |
| \(F\) | magnitude of a force |
| \(F\) | restoring force |
| \({F}_{\text{B}}\) | buoyant force |
| \({F}_{\text{c}}\) | centripetal force |
| \({F}_{\text{i}}\) | force input |
| \({\mathbf{\text{F}}}_{\text{net}}\) | net force |
| \({F}_{\text{o}}\) | force output |
| \(\text{FM}\) | frequency modulation |
| \(f\) | focal length |
| \(f\) | frequency |
| \({f}_{0}\) | resonant frequency of a resistance, inductance, and capacitance \(\left(\text{RLC}\right)\) series circuit |
| \({f}_{0}\) | threshold frequency for a particular material (photoelectric effect) |
| \({f}_{1}\) | fundamental |
| \({f}_{2}\) | first overtone |
| \({f}_{3}\) | second overtone |
| \({f}_{\text{B}}\) | beat frequency |
| \({f}_{\text{k}}\) | magnitude of kinetic friction |
| \({f}_{\text{s}}\) | magnitude of static friction |
| \(G\) | gravitational constant |
| \(G\) | green quark color |
| \(\overline{G}\) | antigreen (magenta) antiquark color |
| \(g\) | acceleration due to gravity |
| \(g\) | gluons (carrier particles for strong nuclear force) |
| \(h\) | change in vertical position |
| \(h\) | height above some reference point |
| \(h\) | maximum height of a projectile |
| \(h\) | Planck’s constant |
| \(\text{hf}\) | photon energy |
| \({h}_{\text{i}}\) | height of the image |
| \({h}_{\text{o}}\) | height of the object |
| \(I\) | electric current |
| \(I\) | intensity |
| \(I\) | intensity of a transmitted wave |
| \(I\) | moment of inertia (also called rotational inertia) |
| \({I}_{0}\) | intensity of a polarized wave before passing through a filter |
| \({I}_{\text{ave}}\) | average intensity for a continuous sinusoidal electromagnetic wave |
| \({I}_{\text{rms}}\) | average current |
| \(\text{J}\) | joule |
| \(J/\text{Ψ}\) | Joules/psi meson |
| \(\text{K}\) | kelvin |
| \(k\) | Boltzmann constant |
| \(k\) | force constant of a spring |
| \({K}_{\alpha }\) | x rays created when an electron falls into an \(n=1\) shell vacancy from the \(n=3\) shell |
| \({K}_{\beta }\) | x rays created when an electron falls into an \(n=2\) shell vacancy from the \(n=3\) shell |
| \(\text{kcal}\) | kilocalorie |
| \(\text{KE}\) | translational kinetic energy |
| \(\text{KE}+\text{PE}\) | mechanical energy |
| \({\text{KE}}_{e}\) | kinetic energy of an ejected electron |
| \({\text{KE}}_{\text{rel}}\) | relativistic kinetic energy |
| \({\text{KE}}_{\text{rot}}\) | rotational kinetic energy |
| \(\overline{\text{KE}}\) | thermal energy |
| \(\text{kg}\) | kilogram (a fundamental SI unit of mass) |
| \(L\) | angular momentum |
| \(\text{L}\) | liter |
| \(L\) | magnitude of angular momentum |
| \(L\) | self-inductance |
| \(\ell \) | angular momentum quantum number |
| \({L}_{\alpha }\) | x rays created when an electron falls into an \(n=2\) shell from the \(n=3\) shell |
| \({L}_{e}\) | electron total family number |
| \({L}_{\mu }\) | muon family total number |
| \({L}_{\tau }\) | tau family total number |
| \({L}_{\text{f}}\) | heat of fusion |
| \({L}_{\text{f}}\phantom{\rule{0.20em}{0ex}}\text{and}\phantom{\rule{0.20em}{0ex}}{L}_{\text{v}}\) | latent heat coefficients |
| \({\text{L}}_{\text{orb}}\) | orbital angular momentum |
| \({L}_{\text{s}}\) | heat of sublimation |
| \({L}_{\text{v}}\) | heat of vaporization |
| \({L}_{z}\) | z – component of the angular momentum |
| \(M\) | angular magnification |
| \(M\) | mutual inductance |
| \(\text{m}\) | indicates metastable state |
| \(m\) | magnification |
| \(m\) | mass |
| \(m\) | mass of an object as measured by a person at rest relative to the object |
| \(\text{m}\) | meter (a fundamental SI unit of length) |
| \(m\) | order of interference |
| \(m\) | overall magnification (product of the individual magnifications) |
| \(m\left({\text{}}^{A}\text{X}\right)\) | atomic mass of a nuclide |
| \(\text{MA}\) | mechanical advantage |
| \({m}_{\text{e}}\) | magnification of the eyepiece |
| \({m}_{e}\) | mass of the electron |
| \({m}_{\ell }\) | angular momentum projection quantum number |
| \({m}_{n}\) | mass of a neutron |
| \({m}_{\text{o}}\) | magnification of the objective lens |
| \(\text{mol}\) | mole |
| \({m}_{p}\) | mass of a proton |
| \({m}_{\text{s}}\) | spin projection quantum number |
| \(N\) | magnitude of the normal force |
| \(\text{N}\) | newton |
| \(\mathbf{\text{N}}\) | normal force |
| \(N\) | number of neutrons |
| \(n\) | index of refraction |
| \(n\) | number of free charges per unit volume |
| \({N}_{\text{A}}\) | Avogadro’s number |
| \({N}_{\text{r}}\) | Reynolds number |
| \(\text{N}\cdot \text{m}\) | newton-meter (work-energy unit) |
| \(\text{N}\cdot \text{m}\) | newtons times meters (SI unit of torque) |
| \(\text{OE}\) | other energy |
| \(P\) | power |
| \(P\) | power of a lens |
| \(P\) | pressure |
| \(\mathbf{\text{p}}\) | momentum |
| \(p\) | momentum magnitude |
| \(p\) | relativistic momentum |
| \({\mathbf{\text{p}}}_{\text{tot}}\) | total momentum |
| \({\mathbf{\text{p}}}_{\text{tot}}^{\text{‘}}\) | total momentum some time later |
| \({P}_{\text{abs}}\) | absolute pressure |
| \({P}_{\text{atm}}\) | atmospheric pressure |
| \({P}_{\text{atm}}\) | standard atmospheric pressure |
| \(\text{PE}\) | potential energy |
| \({\text{PE}}_{\text{el}}\) | elastic potential energy |
| \({\text{PE}}_{\text{elec}}\) | electric potential energy |
| \({\text{PE}}_{\text{s}}\) | potential energy of a spring |
| \({P}_{\text{g}}\) | gauge pressure |
| \({P}_{\text{in}}\) | power consumption or input |
| \({P}_{\text{out}}\) | useful power output going into useful work or a desired, form of energy |
| \(Q\) | latent heat |
| \(Q\) | net heat transferred into a system |
| \(Q\) | flow rate—volume per unit time flowing past a point |
| \(+Q\) | positive charge |
| \(-Q\) | negative charge |
| \(q\) | electron charge |
| \({q}_{p}\) | charge of a proton |
| \(q\) | test charge |
| \(\text{QF}\) | quality factor |
| \(R\) | activity, the rate of decay |
| \(R\) | radius of curvature of a spherical mirror |
| \(R\) | red quark color |
| \(\overline{R}\) | antired (cyan) quark color |
| \(R\) | resistance |
| \(\text{R}\) | resultant or total displacement |
| \(R\) | Rydberg constant |
| \(R\) | universal gas constant |
| \(r\) | distance from pivot point to the point where a force is applied |
| \(r\) | internal resistance |
| \({r}_{\perp }\) | perpendicular lever arm |
| \(r\) | radius of a nucleus |
| \(r\) | radius of curvature |
| \(r\) | resistivity |
| \(\text{r or rad}\) | radiation dose unit |
| \(\text{rem}\) | roentgen equivalent man |
| \(\text{rad}\) | radian |
| \(\text{RBE}\) | relative biological effectiveness |
| \(\text{RC}\) | resistor and capacitor circuit |
| \(\text{rms}\) | root mean square |
| \({r}_{n}\) | radius of the nth H-atom orbit |
| \({R}_{\text{p}}\) | total resistance of a parallel connection |
| \({R}_{\text{s}}\) | total resistance of a series connection |
| \({R}_{\text{s}}\) | Schwarzschild radius |
| \(S\) | entropy |
| \(\mathbf{\text{S}}\) | intrinsic spin (intrinsic angular momentum) |
| \(S\) | magnitude of the intrinsic (internal) spin angular momentum |
| \(S\) | shear modulus |
| \(S\) | strangeness quantum number |
| \(s\) | quark flavor strange |
| \(\text{s}\) | second (fundamental SI unit of time) |
| \(s\) | spin quantum number |
| \(\mathbf{\text{s}}\) | total displacement |
| \(\text{sec}\phantom{\rule{0.20em}{0ex}}\theta \) | secant |
| \(\text{sin}\phantom{\rule{0.20em}{0ex}}\theta \) | sine |
| \({s}_{z}\) | z-component of spin angular momentum |
| \(T\) | period—time to complete one oscillation |
| \(T\) | temperature |
| \({T}_{\text{c}}\) | critical temperature—temperature below which a material becomes a superconductor |
| \(T\) | tension |
| \(\text{T}\) | tesla (magnetic field strength B) |
| \(t\) | quark flavor top or truth |
| \(t\) | time |
| \({t}_{1/2}\) | half-life—the time in which half of the original nuclei decay |
| \(\text{tan}\phantom{\rule{0.20em}{0ex}}\theta \) | tangent |
| \(U\) | internal energy |
| \(u\) | quark flavor up |
| \(\text{u}\) | unified atomic mass unit |
| \(\mathbf{\text{u}}\) | velocity of an object relative to an observer |
| \({\mathbf{\text{u}}}^{\mathbf{\text{‘}}}\) | velocity relative to another observer |
| \(V\) | electric potential |
| \(V\) | terminal voltage |
| \(\text{V}\) | volt (unit) |
| \(V\) | volume |
| \(\mathbf{\text{v}}\) | relative velocity between two observers |
| \(v\) | speed of light in a material |
| \(\mathbf{\text{v}}\) | velocity |
| \(\overline{\mathbf{\text{v}}}\) | average fluid velocity |
| \({V}_{\text{B}}-{V}_{\text{A}}\) | change in potential |
| \({\mathbf{\text{v}}}_{\text{d}}\) | drift velocity |
| \({V}_{\text{p}}\) | transformer input voltage |
| \({V}_{\text{rms}}\) | rms voltage |
| \({V}_{\text{s}}\) | transformer output voltage |
| \({\mathbf{\text{v}}}_{\text{tot}}\) | total velocity |
| \({v}_{\text{w}}\) | propagation speed of sound or other wave |
| \({\mathbf{\text{v}}}_{\text{w}}\) | wave velocity |
| \(W\) | work |
| \(W\) | net work done by a system |
| \(\text{W}\) | watt |
| \(w\) | weight |
| \({w}_{\text{fl}}\) | weight of the fluid displaced by an object |
| \({W}_{\text{c}}\) | total work done by all conservative forces |
| \({W}_{\text{nc}}\) | total work done by all nonconservative forces |
| \({W}_{\text{out}}\) | useful work output |
| \(X\) | amplitude |
| \(\text{X}\) | symbol for an element |
| \({\text{}}^{Z}{X}_{N}\) | notation for a particular nuclide |
| \(x\) | deformation or displacement from equilibrium |
| \(x\) | displacement of a spring from its undeformed position |
| \(x\) | horizontal axis |
| \({X}_{\text{C}}\) | capacitive reactance |
| \({X}_{\text{L}}\) | inductive reactance |
| \({x}_{\text{rms}}\) | root mean square diffusion distance |
| \(y\) | vertical axis |
| \(Y\) | elastic modulus or Young’s modulus |
| \(Z\) | atomic number (number of protons in a nucleus) |
| \(Z\) | impedance |
