What is a physical quantity?
A physical quantity is any property of a body or phenomenon that can be measured. Every physical quantity is written as a numerical value together with a unit, for example a length of 2.5 m. Physical quantities are divided into base quantities and derived quantities.
There are five base quantities in the SI system that you meet in SPM Physics: length (metre, m), mass (kilogram, kg), time (second, s), temperature (kelvin, K) and electric current (ampere, A). A derived quantity is obtained by combining base quantities through multiplication or division, such as speed, density and force.
Scalars and vectors
A scalar quantity has magnitude only (mass, distance, speed, energy). A vector quantity has both magnitude and direction (displacement, velocity, force, momentum). Direction matters when adding vectors.
Key formula / Key idea
Density is a derived quantity: ρ = m / V. Its unit is kg m⁻³, derived from kg ÷ m³.
Prefixes
Very large or very small values use prefixes: kilo (k, 10³), centi (c, 10⁻²), milli (m, 10⁻³) and micro (μ, 10⁻⁶). So 5 mm = 5 × 10⁻³ m.
Worked example
A metal block has mass 240 g and volume 30 cm³. Find its density in kg m⁻³.
First convert: m = 0.240 kg, V = 30 × 10⁻⁶ m³ = 3.0 × 10⁻⁵ m³.
ρ = m / V = 0.240 ÷ (3.0 × 10⁻⁵) = 8000 kg m⁻³.
Remember
- Always state a physical quantity as a number AND a unit.
- Base quantities cannot be broken down; derived quantities come from them.
- Vectors need direction; scalars do not.