# 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.