Physical Quantities & Units

The language of physics - SI base units, derived units, prefixes, and checking equations by dimensional analysis.

Spec Points Covered
  • OCR.2.1.1 I can state the six SI base quantities and their base units.
  • OCR.2.1.1 I can express derived units in terms of SI base unitsThe fundamental units from which all other units are derived: kilogram (kg), metre (m), second (s), ampereThe SI unit of current. One ampere is a flow of one coulomb of charge per second. (A), kelvin (K), mole (mol). Defined by international agreement..
  • OCR.2.1.1 I can use SI prefixes from pico to tera and convert between them.
  • OCR.2.1.1 I can check the homogeneity of a physical equation using base units.
  • OCR.2.1.1 I can explain that a homogeneous equationAn equation where every term has the same base units. The units on the left-hand side must equal the units on the right-hand side. is not necessarily correct.
  • OCR.2.1.1 I can distinguish between a physical quantityA property of a material or system that can be measured. It consists of a numerical magnitude and a unit. and its unit.
  • OCR.2.1.1 I can make order-of-magnitude estimates of physical quantities.
  • OCR.2.1.1 I can use standard form and appropriate significant figures in calculations.
Notes
01 Physical quantity Physical quantity → 02 Derived unit Derived unit → 03 SI prefix SI prefix → 04 Homogeneous equation Homogeneous equation → 05 Homogeneous equations → 06 Order of magnitude Order of magnitude → 07 SI base units → 08 Standard form & significant figures →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Defining a derived unit from base units
$$[\text{derived}] = \text{combination of kg, m, s, A, K, mol}$$
Not a formula to memorise, but a technique. Replace each quantity in an equation with its SI base unit and simplify. This is how you check homogeneity or express derived units.
Newton in base units
$$1 \text{ N} = 1 \text{ kg m s}^{-2}$$
  • Where:
    • $N$ = kg m \(s^{-2}\)
From F = ma. The newton is the most commonly tested derived unit at A-Level.
Joule in base units
$$1 \text{ J} = 1 \text{ kg m}^{2} \text{ s}^{-2}$$
  • Where:
    • $J$ = kg \(m^{2}\) \(s^{-2}\)
From W = Fd = (kg m \(s^{-2}\))(m). Also the base units of all forms of energy.
Watt in base units
$$1 \text{ W} = 1 \text{ kg m}^{2} \text{ s}^{-3}$$
  • Where:
    • $W$ = kg \(m^{2}\) \(s^{-3}\)
From P = W/t = (kg \(m^{2}\) \(s^{-2}\)) / s.
Pascal in base units
$$1 \text{ Pa} = 1 \text{ kg m}^{-1} \text{ s}^{-2}$$
  • Where:
    • $Pa$ = kg \(m^{-1}\) \(s^{-2}\)
From p = F/A = (kg m \(s^{-2}\)) / \(m^{2}\). Commonly tested in thermal physics and materials.