# OpenMath Content Dictionary: SI_DerivedQuantities1

Canonical URL:
http://www.openmath.org/cd/SI_DerivedQuantities1.ocd
CD File:
SI_DerivedQuantities1.ocd
CD as XML Encoded OpenMath:
SI_DerivedQuantities1.omcd
Defines:
Celsius-temperature, absorbed-dose, angle, area, capacitance, catalytic-activity, charge, concentration, conductance, density, energy, entropy, equivalent-dose, force, frequency, heat, illuminance, inductance, luminous-flux, magnetic-flux, magnetic-flux-density, moment-of-force, momentum, power, pressure, radioactivity, resistance, solid-angle, speed, voltage, volume
Date:
2009-01-10
Version:
1 (Revision 1)
Review Date:
2017-12-31
Status:
experimental


This document is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

The copyright holder grants you permission to redistribute this
document freely as a verbatim copy. Furthermore, the copyright
holder permits you to develop any derived work from this document
provided that the following conditions are met.
a) The derived work acknowledges the fact that it is derived from
this document, and maintains a prominent reference in the
work to the original source.
b) The fact that the derived work is not the original OpenMath
document is stated prominently in the derived work.  Moreover if
both this document and the derived work are Content Dictionaries
then the derived work must include a different CDName element,
chosen so that it cannot be confused with any works adopted by
the OpenMath Society.  In particular, if there is a Content
Dictionary Group whose name is, for example, math' containing
Content Dictionaries named math1', math2' etc., then you should
not name a derived Content Dictionary mathN' where N is an integer.
However you are free to name it private_mathN' or some such.  This
is because the names mathN' may be used by the OpenMath Society
for future extensions.
compilation of derived works, but keep paragraphs a) and b)
intact.  The simplest way to do this is to distribute the derived
work under the OpenMath license, but this is not a requirement.
society at http://www.openmath.org.

Author: Joseph B. Collins (2009), Naval Research Laboratory, Washington, DC.
Copyright Notice:  This is a work of the U.S. Government and is not
may apply.


  Author: J B Collins


## angle

Role:
constant
Description:

This symbol represents the quantity of a geometric planar angle. A variable representing an arbitrary quantity of angle is commonly represented with the italic, lower case greek variable, e.g., "\theta;".

Commented Mathematical property (CMP):
dim(angle) = one
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{angle}\right)=\mathrm{one}$
Signatures:
sts

 [Next: solid-angle] [Last: entropy] [Top]

## solid-angle

Role:
constant
Description:

This symbol represents the quantity of a two dimensional, geometric solid angle. A variable representing an arbitrary quantity of solid angle is commonly represented with the italic, upper case greek variable, "\Omega;".

Commented Mathematical property (CMP):
dim(solid-angle) = one
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{solid-angle}\right)=\mathrm{one}$
Signatures:
sts

 [Next: frequency] [Previous: angle] [Top]

## frequency

Role:
constant
Description:

This symbol represents the physical quantity of frequency. A variable representing an arbitrary quantity of frequency is commonly represented with the italic, lower case greek variable, "\omega;".

Commented Mathematical property (CMP):
dim(frequency) = one/time
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{frequency}\right)=\frac{\mathrm{one}}{\mathrm{time}}$
Signatures:
sts

 [Next: force] [Previous: solid-angle] [Top]

## force

Role:
constant
Description:

This symbol represents the physical quantity of force. A variable representing an arbitrary quantity of force is commonly represented with the italic, upper case letter, "F".

Commented Mathematical property (CMP):
dim(force) = mass*length/(time^2)
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{force}\right)=\frac{\mathrm{mass}×\mathrm{length}}{{\mathrm{time}}^{2}}$
Signatures:
sts

 [Next: pressure] [Previous: frequency] [Top]

## pressure

Role:
constant
Description:

This symbol represents the physical quantity of pressure. A variable representing an arbitrary quantity of pressure is commonly represented with the italic, lower case letter, "p".

Commented Mathematical property (CMP):
dim(pressure) = dim(force)/dim(area) = mass/(length*time*time)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{pressure}\right),\frac{\mathrm{dim}\left(\mathrm{force}\right)}{\mathrm{dim}\left(\mathrm{area}\right)},\frac{\mathrm{mass}}{\mathrm{length}×\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: energy] [Previous: force] [Top]

## energy

Role:
constant
Description:

This symbol represents the physical quantity of energy. A variable representing an arbitrary quantity of energy is commonly represented with the italic, upper case letter, "E".

Commented Mathematical property (CMP):
dim(energy) = dim(force)*length = mass*length^2/(time^2)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{energy}\right),\mathrm{dim}\left(\mathrm{force}\right)\mathrm{length},\frac{\mathrm{mass}×\mathrm{length}×\mathrm{length}}{\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: power] [Previous: pressure] [Top]

## power

Role:
constant
Description:

This symbol represents the physical quantity of power, or energy divided by time. A variable representing an arbitrary quantity of power is commonly represented with the italic, upper case letter, "P".

Commented Mathematical property (CMP):
dim(power) = dim(energy)/time = mass*length^2/(time^3)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{power}\right),\frac{\mathrm{dim}\left(\mathrm{energy}\right)}{\mathrm{time}},\frac{\mathrm{mass}×\mathrm{length}×\mathrm{length}}{\mathrm{time}×\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: charge] [Previous: energy] [Top]

## charge

Role:
constant
Description:

This symbol represents the physical quantity of electric charge. A variable representing an arbitrary quantity of charge is commonly represented with the italic, upper case letter, "Q".

Commented Mathematical property (CMP):
dim(charge) = current*time
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{charge}\right)=\mathrm{current}×\mathrm{time}$
Signatures:
sts

 [Next: voltage] [Previous: power] [Top]

## voltage

Role:
constant
Description:

This symbol represents the physical quantity of voltage or electric tension. A variable representing an arbitrary quantity of voltage is commonly represented with the italic, upper case letter, "V".

Commented Mathematical property (CMP):
dim(voltage) = dim(energy/charge) = mass*length^2/(current*time^3)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{voltage}\right),\mathrm{dim}\left(\frac{\mathrm{energy}}{\mathrm{charge}}\right),\frac{\mathrm{mass}×\mathrm{length}×\mathrm{length}}{\mathrm{current}×\mathrm{time}×\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: capacitance] [Previous: charge] [Top]

## capacitance

Role:
constant
Description:

This symbol represents the physical quantity of electric capacitance. A variable representing an arbitrary quantity of capacitance is commonly represented with the italic, upper case letter, "C".

Commented Mathematical property (CMP):
dim(capacitance) = dim(charge/voltage) = current^2*time^4/(mass*length^2)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{capacitance}\right),\mathrm{dim}\left(\frac{\mathrm{charge}}{\mathrm{voltage}}\right),\frac{\mathrm{current}×\mathrm{current}×\mathrm{time}×\mathrm{time}×\mathrm{time}×\mathrm{time}}{\mathrm{mass}×\mathrm{length}×\mathrm{length}}\right)$
Signatures:
sts

 [Next: resistance] [Previous: voltage] [Top]

## resistance

Role:
constant
Description:

This symbol represents the physical quantity of electrical resistance, the resistance that an electrical circuit has to electrical current. A variable representing an arbitrary quantity of electrical resistance is commonly represented with the italic, upper case letter, "R".

Commented Mathematical property (CMP):
dim(resistance) = dim(voltage/current) = mass*length^2/(current^2*time^3)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{resistance}\right),\mathrm{dim}\left(\frac{\mathrm{voltage}}{\mathrm{current}}\right),\frac{\mathrm{mass}×\mathrm{length}×\mathrm{length}}{\mathrm{current}×\mathrm{current}×\mathrm{time}×\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: conductance] [Previous: capacitance] [Top]

## conductance

Role:
constant
Description:

This symbol represents the physical quantity of electrical conductance, the inverse of resistance. A variable representing an arbitrary quantity of conductance is commonly represented with the italic, upper case letter, "G" or "S".

Commented Mathematical property (CMP):
dim(conductance) = dim(current/voltage) = current^2*time^3/(mass*length^2)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{conductance}\right),\mathrm{dim}\left(\frac{\mathrm{current}}{\mathrm{voltage}}\right),\frac{\mathrm{current}×\mathrm{current}×\mathrm{time}×\mathrm{time}×\mathrm{time}}{\mathrm{mass}×\mathrm{length}×\mathrm{length}}\right)$
Signatures:
sts

 [Next: magnetic-flux] [Previous: resistance] [Top]

## magnetic-flux

Role:
constant
Description:

This symbol represents the physical quantity of magnetic flux. A variable representing an arbitrary quantity of magnetic flux is commonly represented with the italic, upper case greek letter, "\Phi;".

Commented Mathematical property (CMP):
dim(magnetic-flux) = dim(energy/current) = mass*length^2/(current*time^2)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{magnetic-flux}\right),\mathrm{dim}\left(\frac{\mathrm{energy}}{\mathrm{current}}\right),\frac{\mathrm{mass}×\mathrm{length}×\mathrm{length}}{\mathrm{current}×\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: magnetic-flux-density] [Previous: conductance] [Top]

## magnetic-flux-density

Role:
constant
Description:

This symbol represents the physical quantity of magnetic flux density. A variable representing an arbitrary quantity of magnetic flux density is commonly represented with the italic, upper case letter, "B".

Commented Mathematical property (CMP):
dim(magnetic-flux-density) = dim(magnetic-flux)/(length^2) = mass/(current*time^2)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{magnetic-flux-density}\right),\frac{\mathrm{dim}\left(\mathrm{magnetic-flux}\right)}{{\mathrm{length}}^{2}},\frac{\mathrm{mass}}{\mathrm{current}×\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: inductance] [Previous: magnetic-flux] [Top]

## inductance

Role:
constant
Description:

This symbol represents the physical quantity of electrical inductance. A variable representing an arbitrary quantity of inductance is commonly represented with the italic, upper case letter, "L".

Commented Mathematical property (CMP):
dim(inductance) = dim(voltage)*time/current = mass*length^2/(current^2*time^2)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{inductance}\right),\frac{\mathrm{dim}\left(\mathrm{voltage}\right)\mathrm{time}}{\mathrm{current}},\frac{\mathrm{mass}×\mathrm{length}×\mathrm{length}}{\mathrm{current}×\mathrm{current}×\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: Celsius-temperature] [Previous: magnetic-flux-density] [Top]

## Celsius-temperature

Role:
constant
Description:

This symbol represents the physical quantity of Celsius temperature. A variable representing an arbitrary quantity of temperature is commonly represented with the italic, upper case letter, "T".

Commented Mathematical property (CMP):
dim(Celsius-temperature) = temperature
Commented Mathematical property (CMP):
num(Celsius-temperature) + 273.15 = num(temperature)
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{Celsius-temperature}\right)=\mathrm{temperature}$
Formal Mathematical property (FMP):
$\mathrm{num}\left(\mathrm{Celsius-temperature}\right)+273.15$
Signatures:
sts

 [Next: luminous-flux] [Previous: inductance] [Top]

## luminous-flux

Role:
constant
Description:

This symbol represents the physical quantity of luminous flux. A variable representing an arbitrary quantity of luminous flux is commonly represented with the italic, upper case letter, "Φv" (\phi; sub V).

Commented Mathematical property (CMP):
dim(luminous-flux) = (luminous-intensity)*dim(solid-angle) = (luminous-intensity)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{luminous-flux}\right),\mathrm{luminous-intensity}\mathrm{dim}\left(\mathrm{solid-angle}\right)\right)$
Signatures:
sts

 [Next: illuminance] [Previous: Celsius-temperature] [Top]

## illuminance

Role:
constant
Description:

This symbol represents the physical quantity of illuminance. A variable representing an arbitrary quantity of illuminance is commonly represented with the italic, upper case letter, "E".

Commented Mathematical property (CMP):
dim(illuminance) = dim(luminous-flux)/(length^2) = (luminous-intensity)/(length^2)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{illuminance}\right),\frac{\mathrm{dim}\left(\mathrm{luminous-flux}\right)}{\mathrm{length}×\mathrm{length}},\frac{\mathrm{luminous-intensity}}{\mathrm{length}×\mathrm{length}}\right)$
Signatures:
sts

Role:
constant
Description:

This symbol represents the physical quantity of radio nuclide activity, or radioactivity. A variable representing an arbitrary quantity of radioactivity is commonly represented with the italic, upper case letter, "A".

Commented Mathematical property (CMP):
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{radioactivity}\right)=\frac{1}{\mathrm{time}}$
Signatures:
sts

 [Next: absorbed-dose] [Previous: illuminance] [Top]

## absorbed-dose

Role:
constant
Description:

This symbol represents the physical quantity of absorbed dose of ionizing radiation. A variable representing an arbitrary quantity of absorbed dose is commonly represented with the italic, upper case letter, "D".

Commented Mathematical property (CMP):
dim(absorbed-dose) = dim(energy/mass)
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{absorbed-dose}\right)=\mathrm{dim}\left(\frac{\mathrm{energy}}{\mathrm{mass}}\right)$
Signatures:
sts

## equivalent-dose

Role:
constant
Description:

This symbol represents the physical quantity of equivalent dose of ionizing radiation. Equivalent dose is similar to absorbed dose but is weighted to reflect differing biological effects and different radiation types. A variable representing an arbitrary quantity of equivalent dose is commonly represented with the italic, upper case letter, "H".

Commented Mathematical property (CMP):
dim(equivalent-dose) = dim(energy/mass)
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{equivalent-dose}\right)=\mathrm{dim}\left(\frac{\mathrm{energy}}{\mathrm{mass}}\right)$
Signatures:
sts

 [Next: catalytic-activity] [Previous: absorbed-dose] [Top]

## catalytic-activity

Role:
constant
Description:

This symbol represents the physical quantity of catalytic activity, an amount of catalyst that effects a rate of catalytic conversion of an amount of substance.

Commented Mathematical property (CMP):
dim(catalytic-activity) = (amount-of-substance)/time
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{catalytic-activity}\right)=\frac{\mathrm{amount-of-substance}}{\mathrm{time}}$
Signatures:
sts

 [Next: area] [Previous: equivalent-dose] [Top]

## area

Role:
constant
Description:

This symbol represents the physical quantity of area.

Commented Mathematical property (CMP):
dim(area) = length*length
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{area}\right)=\mathrm{length}×\mathrm{length}$
Signatures:
sts

 [Next: volume] [Previous: catalytic-activity] [Top]

## volume

Role:
constant
Description:

This symbol represents the physical quantity of volume. It has the short symbol form, "V".

Commented Mathematical property (CMP):
dim(volume) = length^3
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{volume}\right)={\mathrm{length}}^{3}$
Signatures:
sts

 [Next: speed] [Previous: area] [Top]

## speed

Role:
constant
Description:

This symbol represents the physical quantity of speed. It is the size of the derivative of position with respect to time.

Commented Mathematical property (CMP):
dim(speed) = length/time
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{speed}\right)=\frac{\mathrm{length}}{\mathrm{time}}$
Signatures:
sts

 [Next: momentum] [Previous: volume] [Top]

## momentum

Role:
constant
Description:

This symbol represents the physical quantity of momentum.

Commented Mathematical property (CMP):
dim(momentum) = mass*length/time
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{momentum}\right)=\frac{\mathrm{mass}×\mathrm{length}}{\mathrm{time}}$
Signatures:
sts

 [Next: moment-of-force] [Previous: speed] [Top]

## moment-of-force

Role:
constant
Description:

This symbol represents the physical quantity of force.

Commented Mathematical property (CMP):
dim(moment-of-force) = length*dim(force) = mass*length^2/(time^2)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{moment-of-force}\right),\mathrm{length}\mathrm{dim}\left(\mathrm{force}\right),\frac{\mathrm{mass}×\mathrm{length}×\mathrm{length}}{\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: density] [Previous: momentum] [Top]

## density

Role:
constant
Description:

This symbol represents the physical quantity of volumic mass density.

Commented Mathematical property (CMP):
dim(density) = mass/(length^3)
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{density}\right)=\frac{\mathrm{mass}}{{\mathrm{length}}^{3}}$
Signatures:
sts

 [Next: concentration] [Previous: moment-of-force] [Top]

## concentration

Role:
constant
Description:

This symbol represents the physical quantity of concentration, the amount of a substance in a volume.

Commented Mathematical property (CMP):
dim(concentration) = (amount-of-substance)/length^3
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{concentration}\right)=\frac{\mathrm{amount-of-substance}}{{\mathrm{length}}^{3}}$
Signatures:
sts

 [Next: heat] [Previous: density] [Top]

## heat

Role:
constant
Description:

This symbol represents the physical quantity of energy that is transferred from one object to another due to a difference in temperature.

Commented Mathematical property (CMP):
dim(heat) = dim(energy) = mass*length^2/(time^2)
Formal Mathematical property (FMP):
$\mathrm{eqs}\left(\mathrm{dim}\left(\mathrm{heat}\right),\mathrm{dim}\left(\mathrm{energy}\right),\frac{\mathrm{mass}×\mathrm{length}×\mathrm{length}}{\mathrm{time}×\mathrm{time}}\right)$
Signatures:
sts

 [Next: entropy] [Previous: concentration] [Top]

## entropy

Role:
constant
Description:

This symbol represents the physical quantity of entropy, a measure of the disorder of a system.

Commented Mathematical property (CMP):
dim(entropy) = dim(energy/temperature)
Formal Mathematical property (FMP):
$\mathrm{dim}\left(\mathrm{entropy}\right)=\mathrm{dim}\left(\frac{\mathrm{energy}}{\mathrm{temperature}}\right)$
Signatures:
sts

 [First: angle] [Previous: heat] [Top]