understand that all physical quantities consist of a numerical magnitude and a unit

Published by Patrick Mutisya · 14 days ago

Physical Quantities – Cambridge A-Level Physics 9702

Physical Quantities

Objective

To understand that every physical quantity is expressed as a product of a numerical magnitude and a unit.

What is a Physical Quantity?

A physical quantity describes a property of the physical world that can be measured. It is represented mathematically as

\$Q = N \times U\$

where Q is the quantity, N is the numerical value (a pure number), and U is the unit that gives the quantity its meaning.

Components of a Physical Quantity

  • Numerical magnitude – the number obtained from measurement (e.g., 5, 12.3, 0.007).
  • Unit – the standard name or symbol that defines the scale of measurement (e.g., m, s, kg).

Standard Units – The SI System

The International System of Units (SI) provides a consistent set of base units from which all other units are derived.

QuantitySymbolSI UnitUnit Symbol
Length\$L\$metrem
Mass\$m\$kilogramkg
Time\$t\$seconds
Electric current\$I\$ampereA
Temperature\$T\$kelvinK
Amount of substance\$n\$molemol
Luminous intensity\$I_v\$candelacd

Derived Quantities

Derived quantities are formed by combining base quantities according to physical laws. Their units are products or quotients of base units.

Derived QuantitySymbolDefinitionSI Unit (symbol)
Velocity\$v\$\$v = \dfrac{s}{t}\$metre per second (m s⁻¹)
Acceleration\$a\$\$a = \dfrac{v}{t}\$metre per second squared (m s⁻²)
Force\$F\$\$F = m a\$newton (N)
Energy\$E\$\$E = F s\$joule (J)
Power\$P\$\$P = \dfrac{E}{t}\$watt (W)

Expressing a Quantity

When writing a measured quantity, the numerical value and unit must be together, e.g.,

  • Length: \$12.5\ \text{m}\$
  • Mass: \$0.85\ \text{kg}\$
  • Time: \$3.2\ \text{s}\$
  • Force: \$45\ \text{N}\$

Omitting the unit removes the physical meaning and can lead to serious errors (e.g., the Mars Climate Orbiter failure).

Common Mistakes

  1. Writing only the number without a unit.
  2. Using inconsistent units in a calculation (mixing centimetres with metres).
  3. Confusing symbols for different quantities (e.g., \$I\$ for current vs. \$I_v\$ for luminous intensity).

Practice Questions

  1. Express the speed of a car travelling 150 km in 2 h in SI units.
  2. Calculate the force required to accelerate a 2 kg mass from rest to \$5\ \text{m s}^{-1}\$ in 3 s. State the answer with the correct unit.
  3. Identify the base units that compose the unit of pressure (pascal). Write the derived unit in terms of base units.

Suggested diagram: A simple illustration showing a ruler (length), a balance (mass), and a stopwatch (time) with arrows pointing to their respective units.