Section 1 of 5What Is a Physical Quantity?
A physical quantity is a property that can be measured, and it is always expressed as a number multiplied by a unit.
Magnitude
- The numerical part of a quantity, such as 12 in a measurement of 12 m s⁻¹.
Unit
- The standard reference in which a quantity is measured; a number alone has no physical meaning.
Symbol
- A letter, such as v for velocity, that represents the quantity in equations.
Same letter
- A single letter can stand for several quantities, so the context and units must be checked.
Section 2 of 5Base and Derived Quantities
Base and Derived Quantities
Base quantity
- A quantity defined independently of others, such as length, mass, time, current or temperature.
Derived quantity
- A quantity obtained by combining base quantities, such as speed, force or density.
Speed
- Speed is length divided by time, so its unit is built from the base units metre and second.
Force
- Force is mass multiplied by acceleration, so its unit is built from the kilogram, metre and second.
| Quantity | Symbol | Type |
|---|---|---|
| Length | l, s or x | Base |
| Mass | m | Base |
| Time | t | Base |
| Density | ρ | Derived |
| Force | F | Derived |
Section 3 of 5Writing Quantities Properly
1
State the quantity by name, for example the time taken for one oscillation.
2
Give its symbol and, in the notation of graphs and tables, separate the symbol and unit with a slash.
3
Write the value with the unit, for example t = 2.4 s, never the value on its own.
4
Use powers of ten with prefixes to keep numbers a sensible size, such as 3.2 mm rather than 0.0032 m.
5
Check that quantities being added or equated have the same unit, converting first if they differ.
Section 4 of 5Worked Example
Question Express the density of a block of mass 0.240 kg and volume 3.0 × 10⁻⁵ m³ as a physical quantity.
- Density = mass ÷ volume = 0.240 ÷ 3.0 × 10⁻⁵.
- 0.240 ÷ 3.0 × 10⁻⁵ = 8000.
- The unit is kg m⁻³, because the base unit of mass is divided by the unit of volume.
Answer Density ρ = 8.0 × 10³ kg m⁻³.
Section 5 of 5Exam Checklist & Tips
2.1.1 – Key Points for the Exam
- Physical quantity A measurable property expressed as a numerical value and a unit.
- Base quantity One of the quantities from which all others are derived, such as length or time.
- Derived quantity A quantity formed by combining base quantities through multiplication or division.
- Magnitude The size of a quantity, given by its numerical value.
- Unit The standard in which a quantity is measured.
Common Mistakes
- Writing an answer as a bare number with no unit.
- Confusing the symbol for a quantity, in italics, with the symbol for its unit, which is upright.
- Treating capital V as always meaning potential difference, when it can also mean volume.
- Adding or equating quantities in different units without converting first.