Glossary of Key Symbols and Notation

In this glossary, key symbols and notation are briefly defined.

Symbol	Definition
$\bar{x}$	an overbar denotes an average (for example, average velocity) or an antiparticle or anticolor, depending on context
$° C$	degree Celsius (unit of temperature)
$° F$	degree Fahrenheit (unit of temperature)
$//$	parallel
$⊥$	perpendicular
$\propto$	proportional to
$\pm$	plus or minus
$x_{0}$	subscript zero denotes an initial, reference, rest, or ground-state value, depending on context
$α$	alpha rays
$α$	angular acceleration
$β$	beta rays
$β$	sound level
$β^{-}$	electron emitted in nuclear beta decay
$β^{+}$	positron decay
$γ$	gamma rays
$γ$	Lorentz factor, which depends on relative speed ( $γ = 1 / \sqrt{1 - v^{2} / c^{2}}$ )
$Δ$	change in whatever quantity follows
$Δ E$	change in energy; for an atomic transition, the difference between the final and initial energy levels
$Δ m$	mass difference; for nuclear reaction energy, total initial rest mass minus total final rest mass
$Δ N$	number of decays that occur
$Δ p$	change in momentum
$Δ p$	momentum spread (standard deviation) for measurements on identically prepared quantum states
$Δ {PE}_{g}$	change in gravitational potential energy
$Δ θ$	rotation angle
$Δ s$	distance traveled along a circular path
$Δ t$	elapsed time interval
$Δ t_{0}$	proper time: the interval measured by a clock present at both events; for an inertial clock, the events occur at the same position in its rest frame
$Δ V$	potential difference (voltage)
$Δ x$	position spread (standard deviation) for measurements on identically prepared quantum states
$ε_{0}$	permittivity of free space
$θ$	angle between the force vector and the displacement vector
$θ$	angle between two lines
$θ$	direction of the resultant
$λ$	decay constant of a nuclide
$λ$	wavelength
$λ_{n}$	wavelength in a medium
$μ_{0}$	permeability of free space
$μ_{k}$	coefficient of kinetic friction
$μ_{s}$	coefficient of static friction
$ν_{e}$	electron neutrino
${\bar{ν}}_{e}$	electron antineutrino
$π^{+}$	positive pion
$π^{-}$	negative pion
$π^{0}$	neutral pion
$ρ$	density
$ρ_{fl}$	fluid density
${\bar{ρ}}_{obj}$	average density of an object
$ρ / ρ_{w}$	specific gravity
$τ$	torque
$Φ$	magnetic flux
$Ω$	ohm (SI unit of electrical resistance)
$ω$	angular velocity
$A$	ampere (SI unit of electric current)
$A$	area
$A$	cross-sectional area
$A$	total number of nucleons
$a$	acceleration
$a_{B}$	Bohr radius
$a_{c}$	centripetal acceleration
$a_{t}$	tangential acceleration
$AC$	alternating current
$AM$	amplitude modulation
$atm$	atmosphere (unit of pressure)
$B$	baryon number
$B$	blue quark color
$\bar{B}$	antiblue antiquark color charge
$b$	quark flavor bottom or beauty
$B$	magnetic field strength
$BE$	binding energy of a nucleus—it is the energy required to completely disassemble it into separate protons and neutrons
$BE / A$	binding energy per nucleon
$Bq$	becquerel (SI unit of activity): one decay per second
$C$	capacitance (amount of charge stored per volt)
$C$	coulomb (SI unit of charge)
$CM$	center of mass
$c$	quark flavor charm
$c$	specific heat
$c$	speed of light
$Cal$	food Calorie (unit of energy): 1 Cal = 1 kcal = 4184 J exactly
$cal$	thermochemical calorie (unit of energy): 1 cal = 4.184 J exactly
${COP}_{hp}$	heat pump’s coefficient of performance
${COP}_{ref}$	coefficient of performance for refrigerators and air conditioners
$cos θ$	cosine
$d$	displacement
$d$	quark flavor down
$dB$	decibel (logarithmic unit of sound level)
$d_{i}$	distance of an image from the center of a lens or the vertex of a mirror
$d_{o}$	distance of an object from the center of a lens or the vertex of a mirror
$DC$	direct current
$D$	absorbed dose (SI unit: gray, Gy)
$E$	electric field strength
$emf$	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
$EC$	electron capture
$Eff$	efficiency—the useful work output divided by the energy input
${Eff}_{C}$	Carnot efficiency
$e$	emissivity of an object
$e$	elementary charge, the positive magnitude of the proton’s charge; the electron has charge −e
$e^{+}$	antielectron or positron
$eV$	electron volt (unit of energy)
$F$	farad (unit of capacitance, a coulomb per volt)
$F$	force
$F$	magnitude of a force
$F$	restoring force
$F_{B}$	buoyant force
$F_{c}$	centripetal force
$F_{net}$	net force
$FM$	frequency modulation
$f$	focal length
$f$	frequency
$f_{0}$	threshold frequency for a particular material (photoelectric effect)
$f_{1}$	fundamental
$f_{2}$	first overtone
$f_{3}$	second overtone
$f_{B}$	beat frequency
$f_{k}$	magnitude of kinetic friction
$f_{s}$	magnitude of static friction
$G$	gravitational constant
$G$	green quark color
$\bar{G}$	antigreen antiquark color charge
$Gy$	gray, the SI unit of absorbed dose: 1 Gy = 1 J/kg = 100 rad
$H$	equivalent dose to an organ or tissue (SI unit: sievert, Sv)
$g$	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
$h_{i}$	height of the image
$h_{o}$	height of the object
$I$	electric current
$I$	intensity
$I$	intensity of a transmitted wave
$I$	moment of inertia (also called rotational inertia)
$J$	joule (SI unit of energy)
$K$	kelvin (SI unit of temperature)
$k_{B}$	Boltzmann constant
$k$	force constant of a spring
$k$	Coulomb constant
$kcal$	kilocalorie (unit of energy): 1 kcal = 1000 cal = 4184 J exactly
$KE$	translational kinetic energy
$KE + PE$	mechanical energy
${KE}_{e}$	kinetic energy of an ejected electron
${KE}_{rel}$	relativistic kinetic energy
${KE}_{rot}$	rotational kinetic energy
$kg$	kilogram (a fundamental SI unit of mass)
$L$	angular momentum
$L$	liter (unit of volume)
$L$	magnitude of angular momentum
$L_{e}$	electron family number
$L_{μ}$	muon family number
$L_{τ}$	tau family number
$L_{f}$	latent heat of fusion
$L_{s}$	latent heat of sublimation
$L_{v}$	latent heat of vaporization
$L_{0}$	proper length: length measured in the rest frame of the object
$m$	indicates metastable state
$m$	magnification
$m$	mass
$m$	mass of an object as measured by a person at rest relative to the object
$m$	meter (a fundamental SI unit of length)
$m$	order of interference
$m_{e}$	mass of the electron
$m_{n}$	mass of a neutron
$mol$	mole (SI unit of amount of substance)
$m_{p}$	mass of a proton
$N$	magnitude of the normal force
$N$	newton (SI unit of force)
$N$	normal force
$N$	number of neutrons
$N$	number of radioactive nuclei remaining in a sample
$n$	index of refraction
$N_{A}$	Avogadro constant (unit: mol⁻¹)
$N \cdot m$	newton-meter (unit of work or energy); equivalent to a joule
$N \cdot m$	newton-meter; SI unit of torque, conventionally not called a joule
$P$	power
$P$	power of a lens
$P$	pressure
$p$	momentum
$p$	momentum magnitude
$p$	relativistic momentum
$p_{tot}$	total momentum
$p_{tot}^{'}$	total momentum some time later
$P_{atm}$	standard atmospheric pressure
$PE$	potential energy
${PE}_{el}$	elastic potential energy
${PE}_{elec}$	electric potential energy
${PE}_{s}$	potential energy of a spring
$Q$	heat transferred during a phase change
$Q$	energy released in a nuclear reaction
$Q$	net heat transferred into a system
$Q$	flow rate—volume per unit time flowing past a point
$+ Q$	positive charge
$- Q$	negative charge
$q_{e}$	electron charge
$q_{p}$	charge of a proton
$q$	test charge
$R$	activity, the rate of decay
$R$	radius of curvature of a spherical mirror
$R$	red quark color
$\bar{R}$	antired antiquark color charge
$R$	resistance
$R$	resultant or total displacement
$R$	Rydberg constant
$R$	universal gas constant
$r$	distance from pivot point to the point where a force is applied
$r_{⊥}$	lever arm: perpendicular distance from the pivot to the force’s line of action
$r$	radius of a nucleus
$r$	radius of curvature
$rem$	rem (unit of equivalent dose and effective dose): 1 rem = 0.01 Sv
$rad$	radian (SI unit of plane angle)
$rad$	rad, an older unit of absorbed dose: 1 rad = 0.01 Gy = 0.01 J/kg
$RBE$	relative biological effectiveness
$w_{R}$	radiation weighting factor
$rms$	root mean square
$r_{n}$	radius of the nth H-atom orbit
$R_{p}$	total resistance of a parallel connection
$R_{s}$	total resistance of a series connection
$S$	entropy
$S$	strangeness quantum number
$Sv$	sievert, the SI unit of equivalent dose and effective dose: 1 Sv = 100 rem
$s$	quark flavor strange
$s$	second (fundamental SI unit of time)
$s$	total displacement
$sin θ$	sine
$T$	period—time to complete one oscillation
$T$	temperature
$T$	tension
$T$	tesla (SI unit of 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
$tan θ$	tangent
$U$	internal energy
$u$	quark flavor up
$u$	unified atomic mass unit (unit of mass)
$u$	velocity of an object relative to an observer
$u^{'}$	velocity relative to another observer
$V$	electric potential
$V$	terminal voltage
$V$	volt (SI unit of electric potential difference)
$V$	volume
$v$	relative velocity between two observers
$v$	speed of light in a material
$v$	velocity
$\bar{v}$	average fluid velocity
$V_{B} - V_{A}$	change in potential
$v_{d}$	drift velocity
$V_{p}$	transformer input voltage
$V_{rms}$	rms voltage
$V_{s}$	transformer output voltage
$v_{w}$	propagation speed of sound or other wave
$v_{w}$	wave velocity
$W$	work
$W$	net work done by a system
$W$	watt (SI unit of power)
$W$	number of microstates corresponding to a macrostate
$w$	weight
$w_{fl}$	weight of the fluid displaced by an object
$W_{c}$	total work done by all conservative forces
$W_{nc}$	total work done by all nonconservative forces
$X$	amplitude
$X$	symbol for an element
${}_{Z}^{A}X_{N}$	notation for a particular nuclide
$x$	deformation or displacement from equilibrium
$x$	displacement of a spring from its undeformed position
$x$	horizontal axis
$y$	vertical axis
$Z$	atomic number (number of protons in a nucleus)