AQA A-Level Physics

## SI units Every physical quantity is a number multiplied by a unit, and the whole of physics is built on a small set of base units from which every other unit is derived. The base quantities you need are mass (kilogram, kg), length (metre, m), time (second, s), amount of substance (mole, mol), temperature (kelvin, K) and electric current (ampere, A). A derived unit is a combination of base units. The newton is the force that gives a mass of 1 kg an acceleration of $1\,\mathrm{m\,s^{-2}}$, so $1\,\mathrm{N} = 1\,\mathrm{kg\,m\,s^{-2}}$. The joule is a newton metre, $1\,\mathrm{J} = 1\,\mathrm{kg\,m^2\,s^{-2}}$, and the watt is a joule per second, $1\,\mathrm{W} = 1\,\mathrm{kg\,m^2\,s^{-3}}$. Writing an equation's units in base units is a quick check that the equation can be right: both sides must reduce to the same combination. ### Prefixes and standard form Prefixes scale a unit by a power of ten, so that very large and very small values can be written without long strings of zeros. | Prefix | Symbol | Factor | |---|---|---| | tera | T | $10^{12}$ | | giga | G | $10^{9}$ | | mega | M | $10^{6}$ | | kilo | k | $10^{3}$ | | centi | c | $10^{-2}$ | | milli | m | $10^{-3}$ | | micro | $\mu$ | $10^{-6}$ | | nano | n | $10^{-9}$ | | pico | p | $10^{-12}$ | | femto | f | $10^{-15}$ | Standard form writes a number as $a \times 10^n$ with $1 \le a < 10$, so $0.000\,047\,\mathrm{m}$ is $4.7\times10^{-5}\,\mathrm{m}$ or $47\,\mu\mathrm{m}$. ### Converting between units Some units…