Physical Quantities

1. Measurement and Physical Quantities

Measurement is the process of determining the value of an unknown quantity by comparing it with a predefined standard quantity of the same kind.

A physical quantity is any quantity that can be measured, directly or indirectly, and expressed by a number together with a unit. Examples are mass, length and time. Every physical quantity is expressed as:

$\text{Physical quantity} = N \times u$

where $N$ is the numerical value and $u$ is the unit. For a fixed quantity, $N$ and $u$ are inversely related: a larger unit gives a smaller number.

Physical quantities are of two kinds:

• Fundamental quantities: basic quantities taken as standards to measure other quantities, namely length, mass, time, temperature, electric current, amount of substance and luminous intensity.
• Derived quantities: quantities obtained from the fundamental quantities, such as area, volume, speed, force and density.

2. Units and Systems of Units

A unit is the standard quantity in terms of which a given physical quantity is measured (for example kilogram, metre, second, newton).

• Fundamental units: units of the fundamental quantities (kg, m, s, ...).
• Derived units: units of the derived quantities (m s$^{-1}$, m s$^{-2}$, ...).

Systems of units:

• MKS system: length in metre, mass in kilogram, time in second.
• CGS system: length in centimetre, mass in gram, time in second.
• FPS system: length in foot, mass in pound, time in second.
• SI (International System): an extension of MKS covering all physical quantities, based on seven fundamental units and two supplementary units (radian, steradian).

The seven SI base units:

Characteristics of a good (SI) unit: it should be well defined; easily available and reproducible in the laboratory; unchanging with time and place; unaffected by changes in physical conditions; and universally accepted, so that measurements made at different places can be compared.