Physics - Standards

Dimensions

symbol	description	type	units	web page
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

Matter

symbol	description	type	units	web page
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

Forces

symbol	description	type	units	web page
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

Kinematics

symbol	description	type	units	web page
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

Dynamics

symbol	description	type	units	web page
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
[I]	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

Terminology

Scalar

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.