OCR A-level Physics A (H556) · Module 2: Foundations of Physics
Mini-Lesson
Foundations of Physics
Module 2 is short but it underwrites the whole A level: physical quantities and units, prefixes and standard form, estimation, and scalars and vectors.
every quantity = number × unitSI base units: kg · m · s · A · K · mol (and the candela)
The skill that pays out for two years: checking an equation for homogeneity of units. If the base units do not match on both sides, the equation is wrong — no exceptions. It costs ten seconds and catches most algebra slips.
Work through each screen, answer the questions as you go (several are full A-level calculations) and collect ⭐ stars. Press Start when you're ready.
Module 2 · units
SI base units and derived units
OCR expects fluency with six of the seven SI base units:
kilogram (kg) mass · metre (m) length · second (s) time
ampere (A) current · kelvin (K) temperature · mole (mol) amount of substance
All other units are derived from these using a defining equation:
N = kg m s⁻² · J = N m = kg m² s⁻² · W = J s⁻¹ = kg m² s⁻³Pa = N m⁻² = kg m⁻¹ s⁻² · C = A s · V = J C⁻¹ = kg m² s⁻³ A⁻¹ · Ω = V A⁻¹
Homogeneity check in action
Is v² = u² + 2as dimensionally consistent?
LHS: (m s⁻¹)² = m² s⁻². RHS: (m s⁻¹)² = m² s⁻², and (m s⁻²)(m) = m² s⁻². Consistent ✓
(Beware: a check like this cannot detect a missing dimensionless factor such as ½ or 2π.)
Sort it
Base unit, derived unit, or prefix?
Tap an item, then tap the box it belongs in.
⚖️ SI base unit
🔧 Derived unit
🔢 Prefix
Quick check
Spot the base unit
?Which of these is an SI base unit?
Quick check
Unpacking a derived unit
?What is the pascal expressed in SI base units?
Module 2 · estimation
Prefixes, standard form and estimation
T (10¹²) · G (10⁹) · M (10⁶) · k (10³) · c (10⁻²) · m (10⁻³) · µ (10⁻⁶) · n (10⁻⁹) · p (10⁻¹²) · f (10⁻¹⁵)
Squares and cubes catch everyone: 1 cm² = 10⁻⁴ m² and 1 cm³ = 10⁻⁶ m³.
Estimation is examined explicitly. State your assumptions, use round numbers, and aim to be right to within an order of magnitude.
Worked estimate — seconds in a year
365 × 24 × 3600 = 31 536 000 ≈ 3.2 × 10⁷ s
The handy approximation π × 10⁷ s is accurate to under 0.5%.
Useful order-of-magnitude anchors: atom ≈ 10⁻¹⁰ m · nucleus ≈ 10⁻¹⁵ m · human ≈ 10⁰ m · Earth radius ≈ 10⁷ m · Earth–Sun ≈ 10¹¹ m · observable Universe ≈ 10²⁶ m.
Calculate
Your turn — unit conversion
1Convert 90 km h⁻¹ into m s⁻¹.
m s⁻¹
Hint: 90 km = 90 000 m and 1 hour = 3600 s. So 90 000 ÷ 3600.
Calculate
Your turn — density conversion
2A metal has a density of 2700 kg m⁻³. Convert this to g cm⁻³.
g cm⁻³
Hint: 1 kg = 1000 g and 1 m³ = 10⁶ cm³. So divide by 1000.
Calculate
Your turn — estimation
3Estimate the number of seconds in a year (365 days). Give your answer as a multiple of 10⁷ s to 2 significant figures.
× 10⁷ s
Hint: 365 × 24 × 3600 = 31 536 000 s. Express that as a multiple of 10⁷.
Module 2 · vectors
Scalars, vectors and vector addition
A scalar has magnitude only. A vector has magnitude and direction — and vectors must be added geometrically, never by simple arithmetic.
Scalars: mass, speed, distance, energy, work, power, temperature, time, density.
Vectors: displacement, velocity, acceleration, force, weight, momentum, field strength.
perpendicular vectors: R = √(x² + y²) · θ = tan⁻¹(y/x)resolving: x-component = F cos θ · y-component = F sin θ (θ from the horizontal)
Worked example
3.0 N east and 4.0 N north.
R = √(3.0² + 4.0²) = √25 = 5.0 N
θ = tan⁻¹(4.0 ÷ 3.0) = tan⁻¹(1.333) = 53.1° north of east
Two forces of equal magnitude F: the resultant can be anything from 0 (antiparallel) to 2F (parallel), depending on the angle between them. Never just add the numbers without checking the directions.
Calculate
Your turn — resultant force
4Two forces act on a point: 3.0 N due east and 4.0 N due north. Calculate the magnitude of the resultant. Give your answer in N.
N
Hint: They are perpendicular, so R = √(3.0² + 4.0²) = √(9 + 16).
Calculate
Your turn — the direction
5For those same two forces (3.0 N east, 4.0 N north), calculate the angle of the resultant north of east. Give your answer in degrees to 3 significant figures.