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Reference

Style sheet

These are the conventions used in this book.

Vector quantities (F,g,v) are written in a bold, serif font — including vector quantities written with Greek symbols (α,τ,ω).
Scalar quantities (m,K,t) and the magnitudes of vector quantities (F,g,v) are written in an italic, serif font — except for Greek symbols (α,τ,ω), which use a roman serif font.
Mathematical symbols use a roman, serif font (½,+,√,cos) — except when they are applied to calculations with units.
Units are written with a roman, sans-serif font (m,N,℃) as are mathematical operations with numbers and units (7 kg × 10 m/s ÷ 3 s = 23.3 N).

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	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
a_c,a_c	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
F_g,W,W	force of gravity, weight	N	newton
F_n,N,N	normal force, normal	N	newton
F_f,f_s,f_k	force of friction (static, kinetic)	N	newton
μ_s, μ_k	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,K_t,K_r	kinetic energy (translational, rotational)	J	joule
U,U_g,U_s	potential energy (gravitational, spring)	J	joule
V_g	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
F_B,B,B	buoyancy, buoyant force	N	newton
q_m	mass flow rate	kg/s	kilogram per second
q_V	volume flow rate	m³/s	cubic meter per second
F_D,R,R	drag, aerodynamic drag, air resistance	N	newton
C,C_D	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
F_E, F_E	electric force, electrostatic force	N	newton
E,E	electric field	N/C, V/m	newton per coulomb, volt per meter
Φ_E	electric flux	N m²/C, V m	newton meter squared per coulomb, volt meter
U,U_E	potential energy, electric potential energy	J	joule
V, V_E	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
F_B, F_B	magnetic force	N	newton
B,B	magnetic field	T	tesla
Φ_B	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
T_½	half life	s	second
D	dose, absorbed dose	Gy	gray
H	equivalent dose	Sv	sievert
E	effective dose	Sv	sievert
w_R	radiation weighting factor		unitless
w_T	tissue weighting factor		unitless

Miscellaneous symbols

Mathematical symbols and notation
symbol	description
+	plus, add, sum, positive
−	minus, subtract, difference, negative
±	uncertainty, error, plus-minus
·	multiply, dot, dot product, scalar product
×	multiply, cross, cross product, vector product
÷,/	divide
x²	square
x³	cube
√	square root, root, radical
∛	cube root
¹_x,x⁻¹	invert, reciprocal
=	equal to, equality
≈	approximately equal to
∝	proportional to
≠	not equal to, inequality
~	on the order of
<	less than
>	greater than
≤	less than or equal to
≥	greater than or equal to
≪	much less than
≫	much greater than
⇒, ⇐	logical implication
⇔	logical equivalence
→	approaches
…	and so on
∴	therefore
f(x)	function
sin	sine
cos	cosine
tan	tangent
sinh	hyperbolic sine
cosh	hyperbolic cosine
tanh	hyperbolic tangent
x̂	unit vector, x hat
∥	parallel
⟂	perpendicular
x	mean, average, antiparticle, x bar
x̃	median, supersymetric particle, x tilde
⟨⟩	time average, ensemble average, bracket
p(x)	probability distribution, probability density function
∆	increment, change, delta
d	differential, d
∂	partial differential, d partial, del
ẋ	time rate of change, first derivative with respect to time, 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
∑	summation, sigma
∫	integral
∬	double integral
∭	triple integral
∮	contour integral
∯	surface integral
∰	volume integral
∞	infinity
ℵ₀	transfinite number, aleph null

Greek alphabet (with variants)
letter	Englishname	letter	Englishname
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	celestialbody	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