Quantities and Units

• Quantities in SI units

  • 4 km = 4000 m
  • 0.32 g = 3.2 × 10⁻³ kg
  • 5.1 × 10³ km h⁻¹ = 1.42 × 10² m s⁻¹
• Vector quantities


  Quantities which have both magnitude and direction
• Examples of vector quantities


  • Displacement
  • Velocity
  • Acceleration
• Scalar quantities


  Quantities which have magnitude only
• Examples of scalar quantities


  • Distance
  • Speed
  • Time
  • Mass
• 1. j notation


  Used to describe vectors, where i and j are the unit vectors in the positive x and y directions
• Finding speed and angle from velocity vector


  1. Calculate speed using Pythagorean theorem

  2. Calculate angle using inverse tangent
• Modelling in mechanics


  Mathematical models can be constructed to simulate real-life situations, but simplifying assumptions are often needed
• Modelling basketball motion


  • Use equation h = 2 + 1.1x - 0.1x² to find height at different horizontal distances
• The model is not valid when the predicted height is negative
• Common modelling assumptions


  • Smooth surface (no friction)
  • Rough surface (friction)
  • Negligible air resistance
  • Uniform gravity (g = 9.8 m/s²)
• Base SI units used in mechanics


  • Mass (kg)
  • Length/displacement (m)
  • Time (s)
• Derived SI units used in mechanics


  • Speed/velocity (m/s)
  • Acceleration (m/s²)
  • Weight/force (N)
• Common force diagrams


  • Weight
  • Normal reaction
  • Friction
  • Buoyancy
  • Air resistance