Quantitels
Quantitels are systematic names for coherent units of measure derived directly from the names of the physical quantities they measure, plus the ending -el, which signifies "element", as in the familiar word "pixel" = "picture element". For example, lengthel is the quantitel for a coherent unit of length. When a quantity has multiple synonyms (e.g. "work" and "energy"), it can have multiple synonymous quantitels (e.g. workel and energiel); such synonyms can be used interchangeably.
Quantitels are generic and can be used across potentially many metrologies. When unmarked, a quantitel can be used to speak abstractly about the notion of coherent units. For instance, one may ask the question, "What is the lengthel for SI?" The answer, of course, is the meter. One can say, "The centimeter is an auxiliary unit in SI, but it was the lengthel for CGS." But if a quantitel is marked, or "branded", with some disambiguating adjective or prefix, it can be used to name the coherent unit of a particular metrology.
This metrology is named "Primel" because it is the first (i.e., prime) system to use quantitels for its coherent unit names. "Primel" can be used as its brand-marker (e.g. Primel lengthel). The die-face-1 character (⚀) serves as an abbreviation for this prefix, marking every Primel unit as such (e.g. ⚀lengthel). It may be pronounced "prime" or "Primel" as needed, or optionally left silent in a context where Primel is the only metrology being discussed that uses quantitels.
Table of Quantitels
Mechanics | |||||
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Physical Quantity | Quantitel | Abbr | Derivation/Decomposition | SI Analog | Abbr |
time duration period | timel durationel periodel | tmℓ drnℓ prdℓ | timel | second | s |
frequency inverse time | frequenciel | fqℓ tmℓ\ drnℓ\ prdℓ\ | timel−1 | hertz second−1 | Hz 1/s |
acceleration | accelerel | accℓ | lengthel × timel−2 | meter × second−2 | m/s2 |
velocity speed | velocitel speedel | veℓ spℓ | lengthel × timel−1 accelerel × timel | meter × second−1 | m/s |
length width breadth height depth | lengthel widthel breadthel heightel depthel | lgℓ wdℓ brdℓ hgtℓ dptℓ | lengthel velocitel × timel | meter | m |
inverse length lineic density | lengthelic widthelic breadthelic heightelic depthelic | lgℓ\ wdℓ\ brdℓ\ hgtℓ\ dptℓ\ | lengthel−1 | meter−1 | 1/m |
area | areanel | arℓ | lengthel2 | meter2 | m2 |
inverse area areic density | areanelic | arℓ\ | areanel−1 | meter−2 | 1/m2 |
volume | volumel | voℓ | lengthel3 | meter3 | m3 |
inverse volume volumic density | volumelic | voℓ\ | volumel−1 lengthel−3 | meter−3 | 1/m3 |
density volumic mass | densitel volumelic·massel | dsℓ | massel × volumel−1 massel × lengthel−3 | kilogram × meter−2 | kg/m3 |
mass | massel | msℓ | massel densitel × volumel | kilogram | kg |
inverse mass specific- = massic- | masselic | msℓ\ | massel−1 | kilogram−1 | 1/kg |
momentum | momentumel (or momel) | mmℓ | massel × velocitel massel × lengthel × timel−1 | kilogram × meter × second−1 | kg·m/s |
action | actionel | actℓ | momentumel × lengthel massel × lengthel2 × timel−1 | kilogram × meter2 × second−1 | kg·m2/s |
force weight | forcel weightel | fcℓ wtℓ | massel × accelerel massel × lengthel × timel−2 | newton kilogram × meter × second−2 | N kg·m/s2 |
energy work heat potential | energiel workel heatel potentialel | ngℓ | forcel × lengthel massel × velocitel2 massel × lengthel2 × timel−2 | joule kilogram × meter2 × second−2 | J kg·m2/s2 |
influence | influencel | nfℓ | forcel × areanel massel × lengthel3 × timel−2 | kilogram × meter3 × second−2 | kg·m3/s2 |
power | powerel | pwℓ | energiel × timel−1 massel × lengthel2 × timel−3 | watt kilogram × meter2 × second−3 | W kg·m2/s3 |
tension | tensionel lengthelic·forcel | tsℓ lgℓ\fcℓ | forcel × lengthel−1 massel × timel−2 | newton/meter kilogram × second−2 | N/m kg/s2 |
pressure | pressurel areanelic·forcel | psℓ arℓ\fcℓ | forcel × areanel−1 massel × lengthel−1 × timel−2 | pascal kilogram × meter−1 × second−2 | Pa kg/m·s2 |
intensity | intensitel areanelic·powerel | ntℓ arℓ\pwℓ | powerel × areanel−1 massel × timel−3 | watt/meter2 kilogram × second−3 | W/m2 kg/s3 |
Angular Mechanics | |||||
Physical Quantity | Quantitel | Abbr | Derivation/Decomposition | SI Analog | Abbr |
plane angle | radian | rad | radian lengthel × radiel−1 | radian | rad |
solid angle | steradian | sr | radian2 areanel × steradiel−1 | steradian | sr |
radiality | radialitel (or radiel) radianic·lengthel | rdℓ rad\lgℓ | lengthel × radian−1 | meter × radian−1 | m/rad |
curvature | curvaturel (or curvel) lengthelic·radian | cvℓ lgℓ\rad | radiel−1 radian × lengthel−1 | radian × meter−1 | rad/m |
steradiality | steradialitel (or steradiel) steradianic·areanel | srdℓ sr\arℓ | radiel2 areanel × steradian−1 lengthel2 × radian−2 | meter2 × radian−2 meter2 × steradian−1 | m2/sr |
stercurvature | stercurvaturel (or stercurvel) areanelic·steradian | scvℓ arℓ\sr | steradiel−1 steradian × areanel−1 radian2 × lengthel−2 | meter−2 × radian2 | sr/m2 |
angular displacement | curvel·lengthel angular·lengthel (or anglengthel) radian | cvℓ·lgℓ ∡lgℓ rad | lengthel × curvel radian | radian | rad |
angular velocity | curvel·velocitel angular·velocitel (or angvelocitel) | cvℓ·veℓ ∡veℓ | velocitel × curvel radian × timel−1 | radian × second−1 | rad/s |
angular acceleration | curvel·accelerel angular·accelerel (or angaccelerel) | cvℓ·accℓ ∡accℓ | accelerel × curvel radian × timel−2 | radian × second−2 | rad/s2 |
angular mass moment of inertia | steradiel·massel angular·massel (or angmassel) | srdℓ·msℓ ∡msℓ | massel × steradiel massel × radiel2 massel × areanel × steradian−1 massel × lengthel2 × radian−2 | kilogram × meter2 × radian−2 kilogram × meter2 × steradian−1 | kg·m2/rad2 kg·m2/sr |
angular momentum | radiel·momentumel angular·momentumel (or angmomel) | rdℓ·mmℓ ∡mmℓ | radiel × momentumel actionel × radian−1 massel × lengthel2 × timel−1 × radian−1 | kilogram × meter2 × second−1 × radian−1 | kg·m2/s·rad |
angular force torque | radiel·forcel angular·forcel | rdℓ·fcℓ ∡fcℓ | radiel × forcel workel × radian−1 massel × lengthel2 × timel−2 × radian−1 | kilogram × meter2 × second−2 × radian−1 newton·meter/radian joule/radian | kg·m2/s2·rad N·m/rad J/rad |
Thermodynamics | |||||
Physical Quantity | Quantitel | Abbr | Derivation/Decomposition | SI Analog | Abbr |
temperature | temperaturel | tmpℓ | heatel × heatabilitel−1 | kelvin | K |
heat capacity heatability entropy | heatabilitel entropiel | htbℓ ntpℓ | heatel × temperaturel−1 massel × lengthel2 × timel−2 × temperaturel−1 | joule/kelvin kilogram × meter2 × second−2 × kelvin−1 | J/K |
massic heat capacity massic·heatability massic entropy | masselic·heatabilitel masselic·entropiel | msℓ\htbℓ msℓ\ntpℓ | heatabilitel × massel−1 lengthel2 × timel−2 × temperaturel−1 | joule/kelvin/kilogram meter2 × second−2 × kelvin−1 | J/K/kg m2/s2/K |
temperature gradient lineic·temperature | lengthelic·temperaturel | lgℓ\tmpℓ | temperaturel × lengthel−1 | kelvin × meter−1 | K/m |
Electromagnetism | |||||
Physical Quantity | Quantitel | Abbr | Derivation/Decomposition | SI Analog | Abbr |
quantity of electricity electric charge | electrel | εtℓ | electrel currentel × timel | coulomb | C |
quantity of magnetism magnetic pole strength | magnetel | μtℓ | electrel × velocitel electrel × lengthel × timel−1 currentel × lengthel | coulomb × meter × second−1 ampere × meter | C·m/s A·m |
electric current | currentel | ctℓ | electrel × timel−1 magnetel × lengthel−1 | ampere coulomb × second−1 | A C/s |
inverse electricity | electrelic | εtℓ\ | electrel−1 | coulomb−1 | 1/C |
inverse magnetism | magnetelic | μtℓ\ | magnetel−1 | ampere−1 × meter−1 | 1/A·m |
electrization electric displacement polarization | electrizel areanelic·electrel | εtzℓ arℓ\εtℓ | electrel × areanel−1 electrel × lengthel−2 | coulomb × meter−2 | C/m2 |
magnetization magnetizing field | magnetizel areanelic·magnetel | μtzℓ arℓ\μtℓ | magnetel × areanel−1 | ampere × meter−1 | A/m |
electric density | electrodensitel volumelic·electrel | εdsℓ voℓ\εtℓ | electrel × volumel−1 electrel × lengthel−3 | coulomb × meter−3 | C/m3 |
magnetic density areic current density | magnetodensitel volumelic·magnetel areanelic·currentel | μdsℓ voℓ\μtℓ arℓ\ctℓ | magnetel × volumel−1 currentel × areanel−1 electrel × lengthel−2 × timel−1 | ampere × meter−2 | A/m2 |
electric·force electric field strength | electrelic·forcel | εtℓ\fcℓ | forcel × electrel−1 electric·potentilalel × lengthel−1 massel × lengthel × timel−2 × electrel−1 | newton × coulomb−1 volt × meter−1 | N/C V/m |
magnetic·force magnetic flux density | magnetelic·forcel | μtℓ\fcℓ | forcel × magnetel−1 massel × timel−1 × electrel−1 massel × timel−2 × currentel−1 | tesla | T Wb·m2 |
electric·potential | electrelic·potentialel | εtℓ\ptℓ | potentialel × electrel−1 massel × lengthel2 × timel−2 × electrel−1 | volt | V |
magnetic·potential | magnetelic·potentialel | μtℓ\ptℓ | potential × magnetel−1 massel × lengthel × timel−1 × electrel−1 massel × lengthel × timel−2 × currentel−1 | newton × ampere−1 | N/A Wb·m |
electric·influence electric flux | electrelic·influencel | εtℓ\nfℓ | influencel × electrel−1 massel × lengthel3 × timel−2 × electrel−1 | newton × meter2 × coulomb−1 volt × meter | N·m2/C V·m |
magnetic·influence magnetic flux | magnetelic·influencel | μtℓ\nfℓ | influencel × magnetel−1 massel × lengthel2 × timel−1 × electrel−1 | weber | Wb |
electric·tension | electrelic·tensionel | εtℓ\tsℓ | tensionel × electrel−1 massel × timel−2 × electrel−1 | newton × meter−1 × coulomb−1 volt × meter−2 | N/m/C V/m2 |
magnetic·tension | magnetelic·tensionel | μtℓ\tsℓ | tensionel × electrel−1 massel × lengthel−1 × timel−1 × electrel−1 | tesla × meter−1 | T/m |
electric·pressure | electrelic·pressurel | εtℓ\psℓ | pressurel × electrel−1 massel × lengthel−1 × timel−2 × electrel−1 | pascal × coulomb−1 volt × meter−3 | Pa/C V/m3 |
magnetic·pressure | magnetelic·pressurel | μtℓ\psℓ | pressurel × magnetel−1 massel × lengthel−2 × timel−1 × electrel−1 | tesla × meter−2 | T/m2 |