Use of SI units and their prefixes: Fundamental (base) units.

The idea

Fundamental, or base, units are the small set of independently defined SI units from which every other unit is built. In AQA A-level Physics the seven base quantities are mass, length, time, electric current, thermodynamic temperature, amount of substance and luminous intensity, with units kilogram (kg), metre (m), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd). A derived unit is formed by combining base units, for example speed in m s⁻¹ or force in kg m s⁻². When checking an equation, replace each symbol by its base units and compare both sides; this is the basis of dimensional analysis. For instance, the potential difference unit volt reduces to kg m² s⁻³ A⁻¹, showing it is derived, not fundamental.

What earns the marks

• State that fundamental units are the independently defined SI units from which all other units are derived.
• List the seven base quantities and their SI units: mass (kg), length (m), time (s), electric current (A), thermodynamic temperature (K), amount of substance (mol) and luminous intensity (cd).
• Distinguish base units from derived units, giving examples such as m s⁻¹ for speed and kg m s⁻² for force.
• Use base units to check the homogeneity of a physical equation by substituting units for each quantity.
• Recognise that prefixes such as kilo, milli and micro modify a base unit without changing its fundamental character.

Common mistakes and how to put them right

• Treating the newton or joule as a fundamental unit.

  Put it right by expressing each in base units, for example N = kg m s⁻² and J = kg m² s⁻².

• Writing the unit of mass as gram rather than kilogram.

  Put it right: The SI base unit of mass is the kilogram, and gram is a prefixed form.

• Omitting the ampere or kelvin from the list of base units.

  Put it right: Both are fundamental, with the kelvin used for thermodynamic temperature.

• Confusing amount of substance with mass.

  Put it right: Amount of substance is measured in moles, while mass is measured in kilograms.

Exam tips

• Learn the seven base quantities and their units as a fixed list so you can recall them without a data sheet.
• When asked to show a unit is derived, substitute the defining equation and cancel to base units rather than quoting the named unit alone.
• In dimensional checks, treat numerical factors and pure numbers as dimensionless and compare only the unit combinations.
• Write units with correct spacing and index notation, for example kg m s⁻², so the examiner can follow your reasoning.