Physical Quantities

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand that all physical quantities consist of a numerical magnitude and a unit
  2. Make reasonable estimates of physical quantities included within the syllabus

What is a Physical Quantity?

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A physical quantity is anything that can be measured. Examples include speed, mass, time, temperature, length, and energy.

Every physical quantity must have two parts:

  1. A numerical magnitude (the number)
  2. A unit (what you're measuring in)

Without both parts, the measurement is incomplete and meaningless.

Why Do We Need Both Parts?

Imagine someone tells you "the distance to the shop is 5." This statement doesn't make sense because you don't know if they mean 5 metres, 5 kilometres, or 5 miles. The number alone tells you nothing useful.

Similarly, just saying "metres" without a number doesn't tell you anything about the actual distance.

You always need both the number AND the unit to describe a physical quantity properly.

Examples of Physical Quantities

Let's look at some common examples:

Speed

  • With both parts: 30 metres per second (30 m s⁻¹)
  • Just magnitude: "30" — doesn't tell you if it's fast or slow
  • Just unit: "metres per second" — doesn't tell you the actual speed

Mass

  • With both parts: 70 kilograms (70 kg)
  • Just magnitude: "70" — could be grams, kilograms, or tonnes
  • Just unit: "kilograms" — doesn't tell you how heavy something is

Time

  • With both parts: 25 seconds (25 s)
  • Just magnitude: "25" — could be seconds, minutes, or hours
  • Just unit: "seconds" — doesn't tell you the duration

Temperature

  • With both parts: 300 kelvin (300 K)
  • Just magnitude: "300" — meaningless without knowing the scale
  • Just unit: "kelvin" — doesn't tell you how hot or cold

Volume

  • With both parts: 0.5 cubic metres (0.5 m³)
  • Just magnitude: "0.5" — could be cubic centimetres or litres
  • Just unit: "cubic metres" — doesn't tell you the actual volume

The Same Symbol Can Mean Different Things

In physics, we use letters to represent physical quantities. However, the same letter can represent different quantities depending on the context. The unit tells you which quantity is being discussed.

For example, the letter v could represent:

  • Velocity — unit: m s⁻¹ (metres per second)
  • Volume — unit: m³ (cubic metres)

The letter V (capital V) could represent:

  • Potential difference (voltage) — unit: V (volts)

This is why including the unit is essential — it removes any confusion about what you're actually measuring.

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