Physical Quantities

Physical quantities are measurable values, each composed of a numerical value and a unit of measurement.

Every physical law is a relationship between scalar quantities.

The scientific community has established specific physical quantities to measure every type of physical phenomenon.

Example: To measure length, a one-meter tape (1 m) is used, representing the unit of measurement (standard unit) for the physical quantity of length. Therefore, any length is measured as a multiple or submultiple of the meter.

Of course, the selection of physical quantities is somewhat arbitrary. As a result, various systems of measurement units are still in use today.

The International System of Units (SI) is the most widely used system worldwide.

Other measurement systems include the CGS (centimeter-gram-second) system and the British Imperial system.

Fundamental and Derived Quantities

Quantities are categorized into two types:

• Fundamental Quantities
  These are quantities that are not derived from other quantities. The fundamental quantities are as follows:
  • Length (l)
  • Mass (m)
  • Time (t)
  • Electric current (i)
  • Temperature (T)
  • Amount of substance (n)
  • Luminous intensity (i_v)
  The choice of fundamental quantities is still arbitrary; it is a convention agreed upon by the scientific community.
• Derived Quantities
  These are quantities derived from fundamental ones.

  Example: A derived quantity is volume, measured in cubic meters (m³). Another example is density, measured in kilograms per cubic meter (kg/m³). Force is measured in newtons (N), but a newton is a derived quantity because N = kg·m/s². Velocity is the ratio of length to time, so it is measured in meters per second (m/s), and so on.

Units of Measurement for Quantities

Each quantity is measured using a reference unit, which is consistent and standardized.

To avoid confusion from using different units of measurement, the scientific community has standardized certain units with the adoption of the International System of Units (SI).

Units of Measurement for Fundamental Quantities

Fundamental quantities have their own units of measurement, while derived quantities have units that depend on the fundamental ones.

Fundamental Quantity	Quantity Symbol	Unit of Measurement	Unit Symbol
Length	l	Meter	m
Mass	m	Kilogram	kg
Time	t	Second	s
Electric current	i	Ampere	A
Temperature	T	Kelvin	K
Amount of substance	n	Mole	mol
Luminous intensity	iv	Candela	cd

The definitions and standards of measurement units have evolved over time as measurement techniques have advanced.

For instance, since the 1980s, the meter (m) has been defined as the distance light travels in a vacuum in 2.99792458 × 10^-8 seconds.

Units of Measurement for Derived Quantities

The unit of measurement for a derived quantity depends on the fundamental quantities that define it.

Here are some practical examples of units of measurement for derived quantities:

Quantity	Unit of Measurement	Symbol	Derivation
Area	Square meter	m2
Volume	Cubic meter	m3
Density	Kilogram per cubic meter	kg/m3
Force	Newton	N	N = kg·m/s2
Pressure	Pascal	Pa	Pa = kg/m·s2 = N/m2
Energy, heat, or work	Joule	J	J = kg·m2/s2 = N·m
Velocity	Meters per second	m/s
Power	Watt	W	W = kg·m2/s3 = J/s
Electric charge	Coulomb	C	C = A·s
Electric potential difference	Volt	V	V = kg·m2/(A·s3) = J/C
Frequency	Hertz	Hz	Hz = 1/s

In scientific notation, when measuring quantities much larger or smaller than the base unit, a prefix is added (without a space) to indicate the multiple or submultiple of the unit.

Example: A centimeter (cm) is one-hundredth of a meter. A millimeter (mm) is one-thousandth of a meter. A kilometer equals a meter multiplied by 10³.

And so on.