Foundations of Physics

• Physical quantities


  Have a numerical value and a unit
• Physical quantities


  • Mass
  • Length
  • Temperature
  • Time
• Estimates of physical units can be made
• S.I. Units


  Systeme Internationale - a set of base units and a scientific method of expressing the magnitudes of quantities of important natural phenomena
• S.I. Units are used to reduce confusion between different units that are used to measure the same natural phenomena
• S.I. base quantities and units

  • Mass - Kilogram (kg)
  • Length - Metre (m)
  • Time - Second (s)
  • Current - Ampere (A)
  • Temperature - Kelvin (K)
  • Amount of Substance - Moles (mol)
• Derived units


  Units which may be expressed in terms of base units by means of mathematical symbols of multiplication and division
• Derived units


  • Momentum = kgms-1
  • Density = kg/m3
• Homogeneity of physical equations

  An equation is homogenous if both sides can be simplified to the same base unit or set of base units
• If an equation is not homogenous then it is incorrect
• Metric prefixes in everyday use

  • tera (T) - 1012
  • giga (G) - 109
  • mega (M) - 106
  • kilo (k) - 103
  • (none) - 1
  • deci (d) - 10-1
  • centi (c) - 10-2
  • milli (m) - 10-3
  • micro (μ) - 10-6
  • nano (n) - 10-9
  • pico (p) - 10-12
• Accuracy


  An experiment is accurate if the quantity being measured has a value that's very close to the commonly accepted or true value
• Precision


  The results of an experiment are precise if they are close together and have a small range
• Systematic error


  An error that is not due to chance but is introduced by an inaccuracy in the apparatus or its use
• Systematic errors


  • Zero error
  • Parallax error
• Random error


  An experimental error caused by unknown or unpredictable changes to the apparatus or conditions
• Random errors can be reduced by improving techniques, making multiple measurements or using instruments with a higher degree of precision
• Systematic errors can be reduced or eliminated by the use of better techniques and instruments
• Resolution (precision)


  The smallest change in a quantity that an instrument can measure
• Reliability


  If a measurement or test is reliable, it gives consistent results each time the activity is repeated
• Absolute uncertainty


  The size of the range of values in which the "true value" of the measurement probably lies
• Absolute uncertainty


  • Length = (295 ± 1) mm
• Percentage uncertainty


  Calculated as (Uncertainty/Average value) x 100
• For multiple readings, half the range of the readings is the uncertainty
• Stopwatch uncertainty is typically 0.1s to 0.6s due to human reaction time
• Parallax errors can make it difficult to measure length accurately
• Rules for determining percentage uncertainties


  If y = ab, % uncertainty in y = % uncertainty in a + % uncertainty in b

  If y = a/b, % uncertainty in y = % uncertainty in a + % uncertainty in b

  If y = an, % uncertainty in y = n x % uncertainty in a
• Determining uncertainty in gradient

  Draw best fit line and worst acceptable line

  Uncertainty = |gradient of best fit - gradient of worst acceptable|

  % uncertainty = (Uncertainty/Gradient of best fit) x 100
• Determining uncertainty in y-intercept

  Draw best fit line and worst acceptable line

  Uncertainty = |y-intercept of best fit - y-intercept of worst acceptable|

  % uncertainty = (Uncertainty/y-intercept) x 100
• Percentage difference


  Calculated as (Experimental value - Accepted value)/Accepted value x 100
• Scalar quantity


  A quantity with only magnitude, not direction
• Vector quantity


  A quantity with both magnitude and direction
• Vector quantities


  • Displacement
  • Force
  • Velocity
  • Acceleration
  • Momentum
• Vectors can be added together to find the resultant vector
• Finding resultant vector for vectors at right angles

  Draw vectors head-to-tail, then use Pythagoras' Theorem
• Finding resultant vector for non-right angle vectors

  Use cosine rule and sine rule

  
• Finding vector components


  Fx = F cos Θ

  Fy = F sin Θ