Glossary of Key Symbols and Notation

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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., $\overline{v}$ 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

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