Physical Quantities And Measurement TechniquesCopy

Cheat Sheet: Measurement Techniques & Scalars vs Vectors (O Level / IGCSE Physics)

1. Measuring Lengths

• Ruler or Metre Rule
  • Precision: ±0.1 cm (1 mm)
  • Read at eye level to avoid parallax error
  • Ensure zero error is checked (start from 0 mark)
• Measuring Tape
  • Used for long distances (≥1 m)
  • Less precise due to flexibility and possible stretching
• Micrometer Screw Gauge
  • Precision: ±0.01 mm
  • Measures very small thicknesses (e.g. wires)
  • Reading an analogue micrometer:
    • Main scale: shows mm and half-mm
    • Thimble scale: shows hundredths of a mm (0–50)
    • Total reading = main scale + thimble scale
    • Always check for zero error before use

2. Measuring Volume

• Measuring Cylinder (Liquid)
  • Read bottom of the meniscus at eye level
  • Precision depends on cylinder (usually ±1 cm³)
• Displacement Method (Solid)
  • For irregular solids
  • Use a measuring cylinder:
    1. Measure initial volume of water
    2. Submerge object completely
    3. Measure final volume
    4. Volume of object = final volume − initial volume

3. Measuring Time Intervals

• Stopwatch/Digital Timer
  • Precision: ±0.01 s (digital), ±0.1 s (manual)
  • Use for timing repeated events, oscillations, reaction times
  • Start/stop with quick reaction to reduce human error

4. Average Value Measurements

• Small Distance (e.g. pendulum swing)
  • Measure distance over multiple swings
  • Divide total distance by number of swings to get average
• Short Time Interval
  • Measure total time for n events (e.g. 10 swings)
  • Average time = total time ÷ n
  • Period of pendulum = time for one complete swing

5. Scalar vs Vector

• Scalar Quantity: Only magnitude (size), no direction
• Vector Quantity: Has both magnitude and direction

6. Examples of Scalars

• Distance
• Speed
• Time
• Mass
• Energy
• Temperature

7. Examples of Vectors

• Displacement
• Force
• Weight
• Velocity
• Acceleration
• Momentum
• Electric Field Strength
• Gravitational Field Strength

8. Resultant of Two Vectors at Right Angles

• Graphical Method (scale diagram):
  • Draw vectors at 90°
  • Resultant = diagonal of the right-angled triangle
• Calculation (Pythagoras):
  • If A and B are vectors at right angles:
    Resultant, R = √(A² + B²)
• Direction (Angle θ):
  • θ = tan⁻¹(opposite / adjacent) = tan⁻¹(B / A)
    (where A and B are the components)