# 1.6 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 n th 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

#### Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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