Mesurements and errors

• SI units


  International System of Units, used worldwide
• Base units


  • Mass
  • Length
  • Time
  • Amount of something
  • Temperature
  • Current
• Units for base quantities

  • Mass: kilograms
  • Length: meters
  • Time: seconds
  • Amount: moles
  • Temperature: Kelvin
  • Current: amps
• Derived units


  Units derived from combinations of base units, e.g. velocity (m/s), acceleration (m/s^2), force (N = kg·m/s^2), energy (J = kg·m^2/s^2)
• Prefixes


  • Tera (10^12)
  • Giga (10^9)
  • Mega (10^6)
  • Kilo (10^3)
  • Milli (10^-3)
  • Micro (10^-6)
  • Nano (10^-9)
  • Pico (10^-12)
  • Femto (10^-15)
• Electron volt


  Energy required to accelerate an electron through a potential difference of 1 volt
• Kilowatt hour


  Energy transferred by a power of 1 kilowatt over 1 hour
• Random error


  Spread of data around the true value, reduced by repeating measurements
• Systematic error


  Consistent difference from the true value, addressed by changing method or equipment
• Key terms


  • Accuracy
  • Precision
  • Repeatability
  • Reproducibility
  • Resolution
• Uncertainty


  Absolute uncertainty (with units) and percentage uncertainty, account for errors in measurements
• Reading vs Measurement


  Reading is a single judgement (e.g. thermometer), measurement involves two judgements (e.g. ruler)
• Analog meters


  Meters where you have to set the dial at the beginning to a zero point
• Absolute uncertainty


  Plus or minus half of the smallest scale division
• Percentage uncertainty (single reading)

  Absolute uncertainty / Measured value x 100
• Percentage uncertainty (repeated readings)

  Half the range / Mean value x 100
• Drawing graphs


  1. Choose appropriate scale

  2. Label axes with quantity and units

  3. Plot data points

  4. Draw line of best fit

  5. Add error bars
• Line of best fit (LoB)


  Line that goes through the centre of the data points
• Worst acceptable line of best fit (LoB)


  Line that still goes through the error bars but is not as good as the LoB
• Percentage uncertainty in gradient

  (Gradient of LoB - Gradient of worst LoB) / Gradient of LoB x 100
• Percentage uncertainty in y-intercept

  (y-intercept of LoB - y-intercept of worst LoB) / y-intercept of LoB x 100
• Combined/final uncertainty


  Absolute uncertainty in Y + absolute uncertainty in Z

  OR

  Percentage uncertainty in Y + percentage uncertainty in Z
• Estimation


  Using known typical values to estimate unknown quantities
• Examples of typical values: Wavelength of light ~10^-7 m, Mass of Earth ~10^24 kg, Mass of Sun ~10^30 kg
• Force = Rate of change of momentum = Mass x Velocity / Time