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Measuring, scalars and vectors Cambridge IGCSE Physics (9–1) revision

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In plain words

Some quantities are just an amount: 5 kg, 20 seconds. Those are scalars. Others only make sense with a direction as well: 5 N pushing down, 20 m/s heading north. Those are vectors.

When something is too small or too quick to measure well, measure lots of them together and divide.

Three things to know

  1. A scalar has size only (distance, speed, mass, energy, time). A vector has size and direction (displacement, velocity, force, acceleration, momentum).
  2. Measure a small length or time by measuring many and dividing: the thickness of 100 sheets, the time for 20 swings.
  3. Two vectors at right angles combine by Pythagoras: resultant² = a² + b².

Worked example

A student times 10 swings of a pendulum as 14.5 s. What is the time for one swing?

  1. Ten swings were timed, so divide by 10.
  2. 14.5 ÷ 10 = 1.45 s.

Tips and tricks

  • Vector or scalar? Ask "does it have a direction?" Weight pulls downwards, so it's a vector. Mass doesn't point anywhere, so it's a scalar.
  • Reading a ruler or a measuring cylinder: put your eye level with the mark, and say so in practical questions. It's a standard mark.
6 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Measuring, scalars and vectors: 6 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. Which of these is a vector?
    • energy
    • mass
    • force (the answer)
    • time

    A force acts in a direction. Energy, mass and time only have a size.

  2. A student times 10 swings of a pendulum instead of 1. Why?
    • It makes the pendulum swing more slowly.
    • It makes the reaction-time error a smaller fraction of the reading. (the answer)
    • It makes each swing take the same time.
    • Stopwatches cannot measure one swing.

    The reaction-time error is about the same either way, so spreading it over 10 swings makes it matter less.

  3. Which instrument is best for measuring the diameter of a wire about 1 mm thick?
    • a metre rule
    • a measuring cylinder
    • a micrometer screw gauge (the answer)
    • a tape measure

    A micrometer reads to 0.01 mm. A rule only reads to the nearest millimetre.

  4. Forces of 6 N and 8 N act at right angles on an object. What is the resultant force?
    • 2 N
    • 10 N (the answer)
    • 14 N
    • 48 N

    √(6² + 8²) = √100 = 10 N.

  5. 30 cm³ of water is in a measuring cylinder. A stone is lowered in and the level reads 42 cm³. What is the volume of the stone?
    • 12 cm³ (the answer)
    • 30 cm³
    • 42 cm³
    • 72 cm³

    The stone pushes aside its own volume of water: 42 − 30 = 12 cm³.

  6. Which list contains only scalars?
    • velocity, mass, time
    • force, energy, speed
    • distance, speed, energy (the answer)
    • weight, distance, acceleration

    Distance, speed and energy have no direction. Velocity, force, weight and acceleration all do.

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