Chapter 18: Glossary of Key Symbols and Notation

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Mar 12, 2024
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- Chapter 17: Useful Information
- Back Matter

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

Table $\PageIndex{1}$
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 nth 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

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