Physics - Standards

I am very keen to have consistent standards of notation and terminology across this site. Its hard enough to learn these things without being confused by inconsistent standards. It may not be perfect yet so, if you find any inconsistencies across the site please let me know.

The units used are based on the international system of units (SI units) which has 3 primary units as discussed on this page. I have also tried to apply standards to the mathematical notation and terminology (see mathematical standards).

Here are some of the notations for physical quantities:


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l length vector m definition
cm position of centre of mass of object vector m definition
r position of particle relative to object vector m definition
p position of particle in absolute coordinates vector m definition
t time scalar s definition
d … /dt rate of change scalar s-1 definition
Δt time between frame n and frame n+1 scalar s definition
f frequency scalar s-1 definition
ω angular velocity bivector s-1 definition
angle angle in radians scalar none definition


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m rest mass scalar kg definition
mi mass of particle i scalar kg definition
mt total mass scalar kg definition
ρ density   kg m-3  


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F Force vector N=newton=kg*m/s2 definition
P effort vector N=newton=kg*m/s2 definition
W load vector N=newton=kg*m/s2 definition
b static friction vector N=newton=kg*m/s2 definition
moment effort bivector Nm=newton-metre=kg*m2/s2 definition
p pressure   kg m-1 s-2  


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x(t) distance as a function of time vector m definition
xi initial position vector m definition
xf final position vector m definition
v(t) linear velocity as function of time vector m/s definition
vi initial velocity (sometimes denoted by u) vector m definition
vf final velocity vector m definition
c speed of light scalar m/s definition
ω angular velocity vector bivector s-1 definition
a linear acceleration vector m/s2 definition
α angular acceleration bivector s-2 definition


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E energy scalar kg m2/s2 = N m definition
P power scalar kg m2/s3 = N m/s definition
p linear momentum vector kg m/s = N s definition
L angular momentum bivector kg m2/s = N m s definition

inertia tensor (moment of inertia)

Matrix representation:

[I] =
∫(rz²+ry²)dm -∫rx*rydm -∫rx*rzdm
-∫ry*rxdm ∫(rz²+rx²)dm -∫ry*rzdm
-∫rz*rxdm -∫rz*rydm ∫(rx²+ry²)dm
tensor kg m2= N m s2 definition
H the instantaneous angular momentum about PC bivector kg m2/s = N m s definition
F net force vector kg m/s2 = N definition
T torque bivector kg m2/s2 = N m definition
h m * s = mass times distance vector Kg m = N s2 definition
J impulse vector kg m/s= N s definition



I have used the term 'scalar' interchangeably with the term 'real', that is, a continuous value that can be represented by a single number.

Strictly speaking the term 'scalar' should be reserved for a quantity that is used to scale a vector, that is change its magnitude without changing its direction, or in other words a scalar is the ratio of parallel vectors.

For instance I should not really call energy a scalar because there are no vectors involved.

I apologise for my lack of mathematical rigor here, its just that the word scalar seems to better express that it is not a vector and its less likely to cause confusion with the real part of a complex number. Also this (mis?)usage is quite common in the computer world.

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