The Physics
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Opus in profectus

Special Symbols

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Reference

Style sheet

These are the conventions used in this book.

Symbols for physical quantities and their international units

Space & Time
symbol quantity symbol SI unit
r, r position, separation, radius, radius of curvature m meter
s, s displacement, distance m meter
θ, φ, θ, φ angle, angular displacement, angular separation, rotation angle rad radian
x, y, z cartesian coordinates m meter
î, ĵ, k̂ cartesian unit vectors unitless
r, θ, φ spherical coordinates m, rad meter, radian
r̂, θ̂, φ̂ spherical unit vectors unitless
ρ, φ, z cylindrical coordinates m, rad meter, radian
ρ̂, φ̂, ẑ cylindrical unit vectors unitless
n̂ normal unit vector unitless
t̂ tangential unit vector unitless
h height, depth m meter
ℓ, L length m meter
d distance, separation, thickness m meter
t thickness m meter
D diameter m meter
C circumference m meter
A, A area, cross-sectional area, projected area, surface area m2 square meter
V volume m3 cubic meter
t time, duration s second
T period, periodic time s second
τ time constant, characteristic time s second
f frequency Hz hertz
ω angular frequency rad/s radian per second
Mechanics
symbol quantity symbol SI unit
v, v velocity, speed m/s meter per second
a, a acceleration m/s2 meter per second squared
ac, ac centripetal acceleration, centrifugal acceleration m/s2 meter per second squared
g, g gravitational field, acceleration due to gravity m/s2 meter per second squared
m mass kg kilogram
F, F force N newton
Fg, W, W force of gravity, weight N newton
Fn, N, N normal force, normal N newton
Ff, fs, fk force of friction (static, kinetic) N newton
μs, μk coefficient of friction (static, kinetic) unitless
p, p momentum kg m/s kilogram meter per second
J, J impulse N s newton second
W work J joule
E energy, total energy J joule
K, Kt, Kr kinetic energy (translational, rotational) J joule
U, Ug, Us potential energy (gravitational, spring) J joule
Vg gravitational potential J/kg joule per kilogram
η efficiency   unitless
P power W watt
ω, ω rotational velocity, rotational speed rad/s radian per second
α, α rotational acceleration rad/s2 radian per second squared
τ, τ torque N m newton meter
I moment of inertia kg m2 kilogram meter squared
L, L angular momentum kg m2/s kilogram meter squared per second
H, H angular impulse N m s newton meter second
k spring constant N/m newton per meter
P pressure Pa pascal
σ normal stress Pa pascal
τ shear stress Pa pascal
ρ density, volume mass density kg/m3 kilogram per cubic meter
σ area mass density, superficial mass density kg/m2 kilogram per square meter
λ linear mass density kg/m kilogram per meter
FB, B, B buoyancy, buoyant force N newton
qm mass flow rate kg/s kilogram per second
qV volume flow rate m3/s cubic meter per second
FD, R, R drag, aerodynamic drag, air resistance N newton
C, CD drag coefficient, coefficient of drag   unitless
η viscosity, dynamic viscosity Pa s pascal second
ν kinematic viscosity m2/s square meter per second
Ma mach number   unitless
Re reynolds number   unitless
Fr froude number   unitless
E young's modulus, modulus of elasticity Pa pascal
G shear modulus, modulus of rigidity Pa pascal
K bulk modulus, modulus of compression Pa pascal
ε linear strain   unitless
γ shear strain   unitless
θ volume strain   unitless
γ surface tension N/m newton per meter
Thermal Physics
symbol quantity symbol SI unit
T temperature K kelvin
α linear expansivity, coefficient of linear thermal expansion K−1 inverse kelvin
β volume expansivity, coefficient of volume thermal expansion K−1 inverse kelvin
Q heat J joule
c specific heat, specific heat capacity J/kg K joule per kilogram kelvin
L latent heat, specific latent heat J/kg joule per kilogram
n amount of substance mole
N number of particles unitless
P heat flow rate W watt
k thermal conductivity W/m K watt per meter kelvin
ε emissivity unitless
U internal energy J joule
S entropy J/K joule per kelvin
w ways, number of identical microstates unitless
COP coefficient of performance unitless
Waves & Optics
symbol quantity symbol SI unit
λ wavelength m meter
v, c wave speed m/s meter per second
I intensity W/m2 watt per square meter
L level dB, dNp decibel, decineper
n index of refraction, absolute index of refraction unitless
f focal length m meter
M magnification unitless
Electricity & Magnetism
symbol quantity symbol SI unit
q, Q charge, electric charge C coulomb
ρ charge density, volume charge density C/m3 coulomb per cubic meter
σ area charge density, superficial charge density C/m2 coulomb per square meter
λ linear charge density C/m coulomb per meter
FE, FE electric force, electrostatic force N newton
E, E electric field N/C, V/m newton per coulomb, volt per meter
ΦE electric flux N m2/C, V m newton meter squared per coulomb, volt meter
U, UE potential energy, electric potential energy J joule
V, VE voltage, potential, electric potential V volt
ℰ electromotive force, emf V volt
C capacitance F farad
κ dielectric constant unitless
I current, electric current A ampère
R, r resistance, electrical resistance, internal resistance Ω ohm
ρ resistivity Ω m ohm meter
G conductance S siemens
σ conductivity S/m siemens per meter
FB, FB magnetic force N newton
B, B magnetic field T tesla
ΦB magnetic flux Wb weber
N number of turns   unitless
n turns per unit length, turns density m−1 inverse meter
η energy density J/m3 joule per cubic meter
S, S poynting vector, intensity W/m2 watt per square meter
Modern Physics
symbol quantity symbol SI unit
γ lorentz factor, lorentz gamma unitless
φ work function J joule
ψ(r,t), ψ(r)φ(t) wave function   unitless
T½ half life s second
D dose, absorbed dose Gy gray
H equivalent dose Sv sievert
E effective dose Sv sievert
wR radiation weighting factor   unitless
wT tissue weighting factor   unitless

Miscellaneous symbols

Mathematical symbols and notation
symbol description
+ plus, add, addition, sum, positive
− minus, subtract, subtraction, difference, negative
± plus or minus, uncertainty, error
∓ minus or plus
· multiply, times, dot, dot product, scalar product
× multiply, cross, cross product, vector product
/, ÷ divide
x2 square
x3 cube
√, x½ square root, root, radical
∛, x⅓ cube root
1x, x−1 invert, reciprocal
= equals, equal to, equality
≠ not equal to, inequality
≈ approximately equal to
~ on the order of
∝ proportional to
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to
≪ much less than, significantly less than
≫ much greater than, significantly greater than
( ) parentheses
[ ] square brackets, brackets
{ } curly brackets, braces
⟨ ⟩ angle brackets
⇒, ⇐ logical implication
⇔ logical equivalence
→ approaches, goes to, tends to
… and so on, ellipsis
∴ therefore
∥ parallel
⟂ perpendicular
x̂ unit vector, x hat
x mean, arithmetic mean, average, antiparticle, x bar
x̃ median, supersymetric particle, x tilde
xrms root mean square, quadratic mean, x rms
⟨x⟩ time average, ensemble average, brackets x
f(x) function, f of x
p(x) probability distribution, probability density function, p of x
∆x change, increment, delta x
dx differential, infinitessimal increment, d x
∂x partial differential, d partial, del x
ẋ first derivative with respect to time, time rate of change, x dot
ẍ second derivative with respect to time, x double dot
x⃛ third derivative with respect to time, x triple dot
∇ gradient, grad, del, nabla
∇ · divergence, div, del dot
∇ × curl, del cross
∇2 laplacian, del squared
∑ sum, summation, sigma
∫ integral
∬ double integral
∭ triple integral
∮ closed line integral, closed path integral, contour integral
∯ closed surface integral
∰ closed volume integral
π, π pi, ratio of circumference to diameter for a circle
e e, base of natural logarithm
ex, exp(x) e to the power x
log logarithm, log base 10
ln natural logarithm, log base e
sin sine
cos cosine
tan tangent
sinh hyperbolic sine
cosh hyperbolic cosine
tanh hyperbolic tangent
lim limit
∞ infinity
ℵ0 first transfinite cardinal number, aleph null
Greek alphabet (with variants)
letter English name letter English name
Α, α alpha Ν, ν nu
Β, β, ϐ beta Ξ, ξ xi
Γ, γ gamma Ο, ο omicron
Δ, ∆, δ delta Π, ∏, π, ϖ pi
Ε, ε, ϵ epsilon Ρ, ρ, ϱ rho
Ζ, ζ zeta Σ, ∑, σ, ς sigma
Η, η eta Τ, τ tau
Θ, ϴ, θ, ϑ theta Υ, υ upsilon
Ι, ι iota Φ, φ, ϕ phi
Κ, κ, ϰ kappa Χ, χ chi
Λ, λ lambda Ψ, ψ psi
Μ, μ, µ mu Ω, Ω, ω omega
Astronomical symbols
symbol celestial body symbol constellation
☉ Sun ♈ Aries
☿ Mercury ♉ Taurus
♀ Venus ♊ Gemini
♁ Earth ♋ Cancer
☽, ☾ Moon ♌ Leo
♂ Mars ♍ Virgo
♃ Jupiter ♎ Libra
♄ Saturn ♏ Scorpius
♅, ⛢ Uranus ♐ Sagittarius
♆ Neptune ♑ Capricorn
♇, ⯓ Pluto ♒ Aquarius
⚳ Ceres ♓ Pisces
Musical symbols
symbol name
♭ flat, semitone lower
♮ natural, no semitone adjustment
♯ sharp, semitone higher