SI units

Physical quantities are measured using standard units. The International System of Units (SI) provides a set of base units from which all other units (derived units) are formed.

SI Base Quantities and Units

There are five SI base quantities you need to know at AS Level:

A minimalist table or grid showing five icons, each representing one SI base quantity: a weight for mass (kg), a ruler for length (m), a clock for time (s), a simple electric circuit for current (A), and a thermometer for temperature (K). Each icon is labeled with the quantity name and symbol. Use clean lines and a modern UI style.

QuantitySymbolSI Unit NameSI Unit Symbol
Massmmkilogramkg
Lengthllmetrem
Timettseconds
Electric currentIIampereA
TemperatureTTkelvinK
Definition

SI base units are the fundamental units defined by the International System of Units, from which all other units are derived.

Derived Units

Derived units are combinations of base units, formed by multiplication or division.

Examples:

  • Speed: metres per second (m s−1^{-1})
  • Acceleration: metres per second squared (m s−2^{-2})
  • Force: newton (N), where 1 N=1 kg m s−21\,\text{N} = 1\,\text{kg m s}^{-2}
  • Energy: joule (J), where 1 J=1 kg m2s−21\,\text{J} = 1\,\text{kg m}^2\text{s}^{-2}

A clean, modern flowchart or diagram showing how derived units are built from SI base units. For example, show 'Force (N)' branching from 'Mass (kg)', 'Length (m)', and 'Time (s)' with multiplication/division symbols. Use minimalist arrows and typography.

Formula
F=maF = ma

Force (N) = mass (kg) × acceleration (m s−2^{-2})

Expressing Derived Units:

Write derived units as products or quotients of base units. For example, pressure (pascal, Pa):

Pressure=ForceArea=kg m s−2m2=kg m−1s−2\text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{\text{kg m s}^{-2}}{\text{m}^2} = \text{kg m}^{-1} \text{s}^{-2}

Checking Homogeneity of Equations

An equation is homogeneous if all terms have the same units. This is a useful way to check if an equation could be correct.

Example:

For s=ut+12at2s = ut + \frac{1}{2}at^2:

  • utut has units: (m s−1^{-1}) × (s) = m
  • at2at^2 has units: (m s−2^{-2}) × (s2^2) = m

All terms have units of metres (m), so the equation is homogeneous.

A minimalist equation check: show the equation s = ut + ½at², with each term annotated with its units (m) in a clean, modern style. Use subtle color or boxes to highlight the matching units.

Exam Tip

Always check the units in each term of an equation to ensure they are consistent.

SI Prefixes

Prefixes are used to indicate multiples or submultiples of units. Learn the following:

A clean, horizontal scale or ladder showing SI prefixes from pico (10^-12) up to tera (10^12), with each prefix, symbol, and factor. Use minimalist icons or color blocks for visual separation, and align with a modern UI look.

PrefixSymbolFactor
picop10−1210^{-12}
nanon10−910^{-9}
microμ\mu10−610^{-6}
millim10−310^{-3}
centic10−210^{-2}
decid10−110^{-1}
kilok10310^{3}
megaM10610^{6}
gigaG10910^{9}
teraT101210^{12}

Examples:

  • 1 km = 10310^3 m
  • 1 ms = 10−310^{-3} s
  • 1 μA = 10−610^{-6} A
Important

Always include units with every physical quantity.

Summary:

  • SI base units: kg, m, s, A, K
  • Derived units are combinations of base units
  • Use prefixes to express very large or small quantities
  • Check equations for homogeneity using SI units
← Physical quantitiesErrors and uncertainties →

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