Physical quantities and measurement techniques

O Level / IGCSE Physics · Motion, forces and energy. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

Physics starts with measuring. Choose the instrument that suits the size: a tape for many metres, a ruler for lengths up to a metre (it reads to 1 mm), and a micrometer for very small lengths such as the diameter of a wire (it reads to 0.01 mm). A measuring cylinder gives the volume of a liquid, and the volume of a solid from how far the water level rises.

A very small length or a very short time is hard to measure once. Measure many together, then divide. This makes the error in each one much smaller.

A scalar has size only. A vector has size and direction.

Rules to remember

Common mistake

When timing a pendulum, students say "one" as they start the stopwatch, so they time one swing fewer than they think. Start the count at zero.

Worked example

Two forces act on a ring at right angles to each other. One is 5.0 N and the other is 12 N. What is the size of the resultant force?

  1. The forces are at right angles, so use resultant2 = a2 + b2.
  2. resultant2 = 5.02 + 122 = 25 + 144 = 169
  3. resultant = √169 = 13

Answer: 13 N (not 17 N: forces at right angles cannot simply be added).

Practice questions

Try each one, then open the answer.

1. A metre rule is used to measure the length of a pencil. Which reading is recorded to the correct precision for this instrument?

  1. A
    15 cm
  2. B
    15.2 cm
  3. C
    15.23 cm
  4. D
    15.234 cm
Show answer

Answer: B. A metre rule is marked in millimetres, so readings are given to 0.1 cm. Extra decimal places claim a precision the rule does not have.

2. A student starts a stopwatch as a pendulum passes the centre and says "1". She counts each time it passes the centre in the same direction, and stops the watch as she says "20". The watch reads 19.0 s. What is the period?

  1. A
    0.95 s
  2. B
    1.0 s
  3. C
    1.9 s
  4. D
    19 s
Show answer

Answer: B. Saying "1" at the start means no swing has been completed yet, so "20" marks 19 complete oscillations. Period = 19.0 ÷ 19 = 1.0 s. Dividing by 20 gives the wrong 0.95 s.

3. A student times 20 complete swings of a pendulum and gets 30.0 s. What is the period of the pendulum?

  1. A
    0.67 s
  2. B
    1.5 s
  3. C
    15 s
  4. D
    600 s
Show answer

Answer: B. Period = time for one swing = 30.0 ÷ 20 = 1.5 s. Timing many swings reduces the effect of reaction time.

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