Operational and Derived Quantaties

Operationally Defined Quantities:

There are only a few fundamental units from which the units of all physical quantities in science can be expressed.
The fundamental units are defined by a measuring process.
The meaning of a fundamental quantity is equivalent to the process one uses to associate a number with the current state of that quantity.
A number/answer without any units has no physical meaning.

Fundamental Units

Quantity Symbol SI Units

Length, Distance m -meters

Time s- seconds

Mass kg - kilograms

Temperature K - degrees Kelvin

Angle rad - radians

Charge C - Coulombs

Derived Quantities:

Derived physical quantities (which are the majority of quantities) are defined by a mathematical expression involving either the fundamental quantities or other derived quantities.

Some Derived Quantities

Quantity Symbol Definition SI Units

Velocity, Speed
m/s

Acceleration
m/s²

Energy:
Kinetic
Potential

J -Joules
J = kg m²/s²

Force N - Newton

Momentum kg m/s

Volume m³

Density
kg/m³

Pressure
Pa -Pascal
Pa = N/m²

Note that the generic units (i.e. units expressed only in terms of the fundamental units) of a derived quantity follows from the mathematical definition of the derived quantity.

Many important derived quantities have been a special name like the energy - Joule. None-the-less, these "brand" names are just pointers to an expression of the fundamental units, Joule = km m²/s².

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