LucidSTEM
A-LEVEL 9702 · AS · TOPIC 1
Physical quantities and units
The chain of the topic: every quantity is a number with a unit, those units reduce to seven SI base units, every measurement carries an uncertainty, and quantities split into scalars and vectors. This is the shared language that all later mechanics, fields and waves topics are written in.
TOPIC 1: PHYSICAL QUANTITIES AND UNITS
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
√ GCSE measurement skills
Σ Basic algebra and geometry
10³ Standard form and significant figures
Topic 1 is the root: no physics topic comes before it.
1.1
1.2
1.3
1.4
TOPIC 1
QUANTITIES
& UNITS
1 · PHYSICAL QUANTITIES
Every quantity is a number times a unit.
Magnitude and unit together: 5.0 m, not just 5.0
The unit must match the quantity it labels
Estimate orders of magnitude for everyday values
quantity = number × unit
e.g. mass of a person ≈ 70 kg
5.0
m
a number (5.0) paired with a unit (m)
2 · SI UNITS & PREFIXES
Seven base units build every other unit.
Base units: kg, m, s, A, K (plus mol, cd)
Derived: N = kg m s−², J = kg m² s−²
Homogeneity: both sides must share the same units
Prefixes from pico (p) to tera (T)
p 10−¹² · n 10−⁹ · μ 10−⁶ · m 10−³
k 10³ · M 10⁶ · G 10⁹ · T 10¹²
10−³ m
10⁰
unit
10³ k
each step scales the base unit by a power of ten
3 · ERRORS & UNCERTAINTIES
Every reading carries a band of doubt.
Systematic error shifts all readings the same way
Random error scatters them; averaging reduces it
Accuracy is closeness to truth; precision is spread
sum or difference: Δy = Δa + Δb
product or quotient: %Δy = %Δa + %Δb
true value
accurate and precise: tight cluster on the centre
4 · SCALARS & VECTORS
Some quantities need a direction too.
Scalar: magnitude only (mass, time, energy)
Vector: magnitude and direction (force, velocity)
Add coplanar vectors tip to tail (parallelogram)
Resolve into two perpendicular components
Fx = F cosθ Fy = F sinθ
F
Fx
Fy
θ
one vector, two perpendicular components
LEADS TO
T2 Kinematics: displacement and velocity as vectors T3 Dynamics: forces add as vectors, F = ma T4 Forces: equilibrium by resolving components Every later topic inherits this language: SI units check each equation, and uncertainties travel with every measured result.
← Builds on IGCSE: Measurement