Chapter 18: Glossary of Key Symbols and Notation
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., \(\bar{v}\) is average velocity) |
|
\({ }^{\circ} \mathrm{C}\) |
Celsius degree |
|
\({ }^{\circ} \mathrm{F}\) |
Fahrenheit degree |
| \(\text { // }\) | parallel |
| \(\perp\) | perpendicular |
|
\(\propto\) |
proportional to |
|
\(\pm\) |
plus or minus |
|
\(0\) |
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 |
|
\(\Delta E\) |
change in energy between the initial and final orbits of an electron in an atom |
|
\(\Delta E\) |
uncertainty in energy |
|
\(\Delta m\) |
difference in mass between initial and final products |
|
\(\Delta N\) |
number of decays that occur |
|
\(\Delta p\) |
change in momentum |
|
\(\Delta p\) |
uncertainty in momentum |
|
\(\Delta \mathrm{PE}_{\mathrm{g}}\) |
change in gravitational potential energy |
|
\(\Delta \theta\) |
rotation angle |
|
\(\Delta s\) |
distance traveled along a circular path |
|
\(\Delta t\) |
uncertainty in time |
|
\(\Delta t_{0}\) |
proper time as measured by an observer at rest relative to the process |
|
\(\Delta V\) |
potential difference |
|
\(\Delta x\) |
uncertainty in position |
|
\(\varepsilon_{0}\) |
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 |
|
\(\mu_{\mathrm{k}}\) |
coefficient of kinetic friction |
|
\(\mu_{\mathrm{s}}\) |
coefficient of static friction |
|
\(v_{e}\) |
electron neutrino |
|
\(\pi^{+}\) |
positive pion |
|
\(\pi^{-}\) |
negative pion |
|
\(\pi^{0}\) |
neutral pion |
|
\(\rho\) |
density |
|
\(\rho_{\mathrm{c}}\) |
critical density, the density needed to just halt universal expansion |
|
\(\rho_{\mathrm{fl}}\) |
fluid density |
|
\(\bar{\rho}_{\text {obj }}\) |
average density of an object |
|
\(\rho / \rho_{\mathrm{w}}\) |
specific gravity |
|
\(\tau\) |
characteristic time constant for a resistance and inductance \((R L)\) or resistance and capacitance \((R C)\) circuit |
|
\(\tau\) |
characteristic time for a resistor and capacitor \((R C)\) circuit |
|
\(\tau\) |
torque |
|
\(\Upsilon\) |
upsilon meson |
|
\(\Phi\) |
magnetic flux |
|
\(\phi\) |
phase angle |
|
\(\Omega\) |
ohm (unit) |
|
\(\omega\) |
angular velocity |
|
\(\text { A }\) |
ampere (current unit) |
|
\(A\) |
area |
| \(A\) | cross-sectional area |
| \(A\) | total number of nucleons |
|
\(a\) |
acceleration |
|
\(a_{\mathrm{B}}\) |
Bohr radius |
|
\(a_{\mathrm{c}}\) |
centripetal acceleration |
|
\(a_{\mathrm{t}}\) |
tangential acceleration |
|
\(\mathrm{AC}\) |
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 |
|
\(B_{\text {int }}\) |
electron’s intrinsic magnetic field |
|
\(\mathrm{B}_{\mathrm{orb}}\) |
orbital magnetic field |
|
\(\text { BE }\) |
binding energy of a nucleus—it is the energy required to completely disassemble it into separate protons and neutrons |
|
\(\mathrm{BE} / A\) |
binding energy per nucleon |
|
\(\mathrm{Bq}\) |
becquerel—one decay per second |
|
\(C\) |
capacitance (amount of charge stored per volt) |
|
\(C\) |
coulomb (a fundamental SI unit of charge) |
|
\(C_{\mathrm{p}}\) |
total capacitance in parallel |
|
\(C_{\mathrm{s}}\) |
total capacitance in series |
|
\(\mathrm{CG}\) |
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 |
|
\(C O P_{\mathrm{hp}}\) |
heat pump’s coefficient of performance |
|
\(C O P_{\text {ref }}\) |
coefficient of performance for refrigerators and air conditioners |
|
\(\cos \theta\) |
cosine |
|
\(\cot \theta\) |
cotangent |
|
\(\csc \theta\) |
cosecant |
|
\(D\) |
diffusion constant |
|
\(d\) |
displacement |
| \(d\) | quark flavor down |
|
\(\mathrm{dB}\) |
decibel |
|
\(d_{\mathrm{i}}\) |
distance of an image from the center of a lens |
|
\(d_{\mathrm{o}}\) |
distance of an object from the center of a lens |
|
\(\text { DC }\) |
direct current |
|
\(E\) |
electric field strength |
|
\(\varepsilon\) |
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 |
|
\(\mathrm{EC}\) |
electron capture |
|
\(E_{\text {cap }}\) |
energy stored in a capacitor |
|
\(E f f\) |
efficiency—the useful work output divided by the energy input |
|
\(E f f_{C}\) |
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 |
|
\(\mathrm{eV}\) |
electron volt |
|
\(\mathrm{F}\) |
farad (unit of capacitance, a coulomb per volt) |
|
\(\mathrm{F}\) |
focal point of a lens |
|
\(\mathbf{F}\) |
force |
|
\(F\) |
magnitude of a force |
|
\(F\) |
restoring force |
|
\(F_{\mathrm{B}}\) |
buoyant force |
|
\(F_{\mathrm{c}}\) |
centripetal force |
|
\(F_{\mathrm{i}}\) |
force input |
|
\(\mathbf{F}_{\text {net }}\) |
net force |
|
\(F_{\circ}\) |
force output |
|
\(\text { FM }\) |
frequency modulation |
|
\(f\) |
focal length |
|
\(f\) |
frequency |
|
\(f_{0}\) |
resonant frequency of a resistance, inductance, and capacitance \((R L C)\) series circuit |
|
\(f_{0}\) |
threshold frequency for a particular material (photoelectric effect) |
|
\(f_{1}\) |
fundamental |
|
\(f_{2}\) |
first overtone |
|
\(f_{3}\) |
second overtone |
|
\(f_{\mathrm{B}}\) |
beat frequency |
|
\(f_{\mathrm{k}}\) |
magnitude of kinetic friction |
|
\(f_{\mathrm{s}}\) |
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 |
|
\(h f\) |
photon energy |
|
\(h_{\mathrm{i}}\) |
height of the image |
|
\(h_{\mathrm{o}}\) |
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 |
|
\(\mathrm{J}\) |
joule |
|
\(J / \Psi\) |
Joules/psi meson |
|
\(\mathrm{K}\) |
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 |
|
\(\mathrm{KE}+\mathrm{PE}\) |
mechanical energy |
|
\(\mathrm{KE}_{e}\) |
kinetic energy of an ejected electron |
|
\(\mathrm{KE}_{\mathrm{rel}}\) |
relativistic kinetic energy |
|
\(\mathrm{KE}_{\mathrm{rot}}\) |
rotational kinetic energy |
|
\(\overline{\mathrm{KE}}\) |
thermal energy |
|
\(\mathrm{kg}\) |
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 |
|
\(L_{\mathrm{f}}\) |
heat of fusion |
|
\(L_{\mathrm{f}} \text { and } L_{\mathrm{v}}\) |
latent heat coefficients |
|
\(\mathrm{L}_{\text {orb }}\) |
orbital angular momentum |
|
\(L_{\mathrm{s}}\) |
heat of sublimation |
|
\(L_{\mathrm{v}}\) |
heat of vaporization |
|
\(L_{z}\) |
z - component of the angular momentum |
|
\(M\) |
angular magnification |
|
\(M\) |
mutual inductance |
|
\(\mathrm{m}\) |
indicates metastable state |
|
\(m\) |
magnification |
|
\(m\) |
mass |
|
\(m\) |
mass of an object as measured by a person at rest relative to the object |
|
\(\mathrm{m}\) |
meter (a fundamental SI unit of length) |
|
\(m\) |
order of interference |
|
\(m\) |
overall magnification (product of the individual magnifications) |
|
\(m\left({ }^{A} \mathrm{X}\right)\) |
atomic mass of a nuclide |
|
\(\text { MA }\) |
mechanical advantage |
|
\(m_{\mathrm{e}}\) |
magnification of the eyepiece |
|
\(m_{\mathrm{e}}\) |
mass of the electron |
|
\(m_{\ell}\) |
angular momentum projection quantum number |
|
\(m_{n}\) |
mass of a neutron |
|
\(m_{\mathrm{o}}\) |
magnification of the objective lens |
|
\(\mathrm{mol}\) |
mole |
|
\(m_{p}\) |
mass of a proton |
|
\(m_{\mathrm{s}}\) |
spin projection quantum number |
|
\(N\) |
magnitude of the normal force |
|
\(\mathrm{N}\) |
newton |
|
\(\mathbf{N}\) |
normal force |
|
\(N\) |
number of neutrons |
|
\(n\) |
index of refraction |
| \(n\) | number of free charges per unit volume |
|
\(N_{\mathrm{A}}\) |
Avogadro's number |
|
\(N_{\mathrm{r}}\) |
Reynolds number |
|
\(\mathrm{N} \cdot \mathrm{m}\) |
newton-meter (work-energy unit) |
|
\(\mathrm{N} \cdot \mathrm{m}\) |
newtons times meters (SI unit of torque) |
|
\(\text { OE }\) |
other energy |
|
\(P\) |
power |
| \(P\) | power of a lens |
| \(P\) | pressure |
|
\(\mathbf{p}\) |
momentum |
|
\(p\) |
momentum magnitude |
|
\(p\) |
relativistic momentum |
|
\(\mathbf{p}_{\text {tot }}\) |
total momentum |
|
\(\mathbf{p}_{\text {tot }}^{\prime}\) |
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 |
|
\(\mathrm{PE}_{\mathrm{el}}\) |
elastic potential energy |
|
\(\mathrm{PE}_{\text {elec }}\) |
electric potential energy |
|
\(\mathrm{PE}_{\mathrm{s}}\) |
potential energy of a spring |
|
\(P_{\mathrm{g}}\) |
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 |
|
\(\mathrm{R}\) |
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 |
|
\(\mathrm{rad}\) |
radian |
|
\(\text { RBE }\) |
relative biological effectiveness |
|
\(R C\) |
resistor and capacitor circuit |
|
\(\text { rms }\) |
root mean square |
|
\(r_{n}\) |
radius of the n th H-atom orbit |
|
\(R_{\mathrm{p}}\) |
total resistance of a parallel connection |
|
\(R_{\mathrm{s}}\) |
total resistance of a series connection |
|
\(R_{\mathrm{s}}\) |
Schwarzschild radius |
|
\(S\) |
entropy |
|
\(\mathbf{S}\) |
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 |
|
\(s\) |
second (fundamental SI unit of time) |
|
\(s\) |
spin quantum number |
|
\(s\) |
total displacement |
|
\(\sec \theta\) |
secant |
|
\(\sin \theta\) |
sine |
|
\(s_{z}\) |
z -component of spin angular momentum |
|
\(T\) |
period—time to complete one oscillation |
|
\(T\) |
temperature |
|
\(T_{\mathrm{c}}\) |
critical temperature—temperature below which a material becomes a superconductor |
|
\(T\) |
tension |
|
\(T\) |
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 |
|
\(\tan \theta\) |
tangent |
|
\(U\) |
internal energy |
|
\(u\) |
quark flavor up |
|
\(\mathrm{u}\) |
unified atomic mass unit |
|
\(\mathbf{u}\) |
velocity of an object relative to an observer |
|
\(\mathbf{u}^{\prime}\) |
velocity relative to another observer |
|
\(V\) |
electric potential |
|
\(V\) |
terminal voltage |
|
\(\mathrm{V}\) |
volt (unit) |
|
\(V\) |
volume |
|
\(\mathbf{v}\) |
relative velocity between two observers |
|
\(v\) |
speed of light in a material |
|
\(\mathbf{v}\) |
velocity |
|
\(\overline{\mathbf{v}}\) |
average fluid velocity |
|
\(V_{\mathrm{B}}-V_{\mathrm{A}}\) |
change in potential |
|
\(\mathbf{v}_{\mathrm{d}}\) |
drift velocity |
|
\(V_{\mathrm{p}}\) |
transformer input voltage |
|
\(V_{\text {rms }}\) |
rms voltage |
|
\(V_{\mathrm{s}}\) |
transformer output voltage |
|
\(\mathbf{v}_{\text {tot }}\) |
total velocity |
|
\(v_{\mathrm{w}}\) |
propagation speed of sound or other wave |
|
\(\mathbf{v}_{\mathrm{w}}\) |
wave velocity |
|
\(W\) |
work |
| \(W\) | net work done by a system |
|
\(\text { W }\) |
watt |
|
\(w\) |
weight |
|
\(w_{\mathrm{fl}}\) |
weight of the fluid displaced by an object |
|
\(W_{\mathrm{c}}\) |
total work done by all conservative forces |
|
\(W_{\mathrm{nc}}\) |
total work done by all nonconservative forces |
|
\(W_{\text {out }}\) |
useful work output |
|
\(X\) |
amplitude |
|
\(\mathrm{X}\) |
symbol for an element |
|
\({ }_{A}^{Z} X_{N}\) |
notation for a particular nuclide |
|
\(x\) |
deformation or displacement from equilibrium |
|
\(x\) |
displacement of a spring from its undeformed position |
|
\(x\) |
horizontal axis |
|
\(X_{\mathrm{C}}\) |
capacitive reactance |
|
\(X_{\mathrm{L}}\) |
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 |