Fundamental SI units

• meter (m) – length
• kilogram (kg) – mass
• seconds (s) – time
• ampere (A) – electric current
• kelvin (K) – temperature, 0°C = 273 K
• mole (mol) – amount with same particles as atoms in 12g of carbon-12

Derived units

• Newton (N) – kgms⁻² – force
• Pascal (Pa) – kgm⁻¹s⁻² – pressure
• Hertz (Hz) – s⁻¹ – frequency
• Joule (J) – kgm²s⁻² – energy
• Watt (W) – kgm²s⁻³ – power
• Coulomb (c) – As – charge
• Volt () – kgm²s⁻³A⁻¹ – potential difference
• Ohm (Ω) – kgm²s⁻³A⁻² – resistance
• Weber (Wb) – kgm²s⁻²A⁻¹ – magnetic flux
• Tesla (T) – kgs⁻²A⁻¹ – magnetic field strength
• Becquerel (Bq) – s⁻¹ – radioactivity

Note: $x^{-1}$ is another way to write ‘per x’, like ‘meters per second’ can be written as ‘m/s’ or $ms^{-1}$. Similarly, ‘meters per second squared’ (like for acceleration) can be written as ‘m/s²’ or $ms^{-2}$.

Important numbers

• mass of H atom – $10^{-29}$ kg
• mass of electron – $10^{-30}$ kg
• radius of Earth – 10⁷ m
• diameter of atom – $10^{-10}$ m
• diameter of nucleus – $10^{-15}$ m
• age of universe – $10^{18}$ s

Errors

• Random: cannot be avoided, e.g. scale limits, human error
• Parallax: reading from incorrect position
• Systematic: consistently wrong, e.g. incorrect calibration

Accuracy is “correctness” (small systematic error).

Precision is “repeatability”

Uncertainties

If $y = a \pm b$, then $\Delta y = \Delta a + \Delta b$.

If $y = \frac{ab}{c}$, then $\frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}$.

If $y = a^n$, then $\frac{\Delta y}{y} = \left| n \left( \frac{\Delta a}{a} \right) \right|$

$\frac{\Delta y}{y} = \frac{\Delta x}{x}$: fractional

$\frac{\Delta y}{y} = \left( \frac{\Delta x}{x} \right) \times 100$: percentage

$\Delta y = y \left( \frac{\Delta x}{x} \right)$: absolute