Singapore-Cambridge O-Level Physics

## Physical quantities and SI units A **physical quantity** is something that can be measured, and it is written as a numerical magnitude together with a unit. A length of 4.2 means nothing until it is given as 4.2 m or 4.2 cm, and the same quantity can be written in different units with different numbers. The SI system is built on base quantities, each with its own unit. | Base quantity | Unit | Symbol | |---|---|---| | mass | kilogram | kg | | length | metre | m | | time | second | s | | current | ampere | A | | temperature | kelvin | K | | amount of substance | mole | mol | Every other unit is derived from these. The newton, for example, is the force that gives a mass of 1 kg an acceleration of $1\,\mathrm{m\,s^{-2}}$, so $1\,\mathrm{N} = 1\,\mathrm{kg\,m\,s^{-2}}$. ### Prefixes Prefixes scale a unit by a power of ten, which keeps very large and very small numbers readable. | Prefix | Symbol | Factor | |---|---|---| | tera | T | $10^{12}$ | | giga | G | $10^{9}$ | | mega | M | $10^{6}$ | | kilo | k | $10^{3}$ | | deci | d | $10^{-1}$ | | centi | c | $10^{-2}$ | | milli | m | $10^{-3}$ | | micro | µ | $10^{-6}$ | | nano | n | $10^{-9}$ | To convert, substitute the prefix for its factor. A wavelength of 650 nm is $650 \times 10^{-9}\,\mathrm{m} = 6.5 \times 10^{-7}\,\mathrm{m}$, and a frequency of 2.4 GHz is $2.4 \times 10^{9}\,\mathrm{Hz}$. Area and volume units need more care, because the conversion factor is squared or cubed. Since $1\,\mathrm{m} = 100\,\mathrm{cm}$, $$…