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:
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.
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metadata block
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| see also: |
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| Correspondence about this page |
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Book Shop - Further reading.
Where I can, I have put links to Amazon for books that are relevant to
the subject, click on the appropriate country flag to get more details
of the book or to buy it from them.
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Feynman lectures on Physics 3 volume set.
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Commercial Software Shop
Where I can, I have put links to Amazon for commercial software, not
directly related to the software project, but related to the subject being
discussed, click on the appropriate country flag to get more details of
the software or to buy it from them.
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SuSE Linux 11.0. Operating system with a wide range of applications
including Open Office. A good distribution for developers as it contains KDevelop.
Java, Mono, etc. Can install itself as a dual-boot system with an existing Windows OS if required.
For information about installing it see this
page.
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Can you help?
Please send me any improvements to
here. I would appreciate ideas to make the pages more useful including
error correction, ideas for new pages, improvements to wording. It helps
if you quote the full URL of the page.
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progam
I am working on a project which uses these principles, if you would like
to help me with this you are welcome to join in, here:
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http://sourceforge.net/projects/mjbworld/
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This site may have errors. Don't use for critical systems.
