Physical quantities

AS Level Physics · Physical quantities and units. 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

A physical quantity is something that can be measured, such as a length, a mass or a force. Every physical quantity has two parts: a numerical magnitude and a unit. The number alone means nothing. Writing "1.8" for a length does not tell anyone whether it is 1.8 m or 1.8 cm.

You must also be able to make a sensible estimate of everyday quantities. Start from values you know (an adult has a mass of about 70 kg, a car about 1000 kg), put them into a formula you know, and give the answer as an order of magnitude. In an estimate question the options usually differ by a factor of 10 or 100, so a rough calculation is enough.

Rules to remember

Common mistake

Students guess the answer instead of calculating. Always choose sensible values, put them into the formula, and then pick the option nearest to your result.

Worked example

Estimate the gravitational potential energy gained by an adult who climbs one floor of a building.

  1. Choose sensible values: mass about 70 kg, height of one floor about 3 m, g = 9.81 m s−2.
  2. gain in potential energy = mass × g × height = 70 × 9.81 × 3
  3. = 2060 J, which is about 2 × 103 J.

Answer: About 2 × 103 J (2 kJ).

Practice questions

Try each one, then open the answer.

1. A student records the length of a bench in her notes simply as "1.8". What is wrong with this record?

  1. A
    it has too many significant figures
  2. B
    it should include a direction
  3. C
    the unit is missing, so the value alone does not state the length
  4. D
    nothing, because lengths in SI are always in metres
Show answer

Answer: C. A physical quantity must be written as a magnitude with a unit: 1.8 m and 1.8 cm are very different lengths.

2. Which is the best estimate of the kinetic energy of a car travelling on a motorway?

  1. A
    5 × 102 J
  2. B
    5 × 103 J
  3. C
    5 × 105 J
  4. D
    5 × 107 J
Show answer

Answer: C. Mass about 1000 kg, speed about 30 m/s: KE = ½ × 1000 × 302 = 4.5 × 105 J.

3. Which statement about a physical quantity is correct?

  1. A
    it consists of a numerical magnitude together with a unit
  2. B
    it is a number that has no unit when written in SI
  3. C
    it must always have a direction
  4. D
    it can only be measured with an electronic instrument
Show answer

Answer: A. A physical quantity is a number and a unit, for example 3.2 m. Without the unit the number has no physical meaning; only some quantities (vectors) also need a direction.

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