Physical Quantities, Units and Measurement

This guide covers Topic 1, Physical quantities and units, in full — subtopics 1.1 Physical quantities, 1.2 SI units, 1.3 Errors and uncertainties and 1.4 Scalars and vectors — from Cambridge International AS & A Level Physics 9702, 2025–2027 series. This is the first topic of the AS Level course and assumes only the physics covered at Cambridge IGCSE or O Level.

Before studying this

You should already be comfortable with basic SI units (metres, kilograms, seconds) and simple measurement from IGCSE or O Level Physics. Nothing else is assumed — this topic is deliberately foundational, setting up the vocabulary and conventions used throughout the rest of 9702.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 — AS Level, Topic 1

1.1 Physical quantities — understanding that every physical quantity has a numerical magnitude and a unit; making reasonable estimates of quantities included in the syllabus.

1.2 SI units — the five SI base quantities and units used at this level (mass in kg, length in m, time in s, current in A, temperature in K); expressing derived units as products or quotients of base units; using SI base units to check the homogeneity of equations; the prefixes pico, nano, micro, milli, centi, deci, kilo, mega, giga and tera.

1.3 Errors and uncertainties — the effects of systematic errors (including zero errors) and random errors; the distinction between precision and accuracy; assessing the uncertainty in a derived quantity by simple addition of absolute or percentage uncertainties.

1.4 Scalars and vectors — the difference between scalar and vector quantities, with syllabus examples of each; adding and subtracting coplanar vectors; resolving a vector into two perpendicular components.

Base and derived units

Every physical quantity has a numerical magnitude and a unit — “20” on its own means nothing until you attach metres, seconds or newtons. At 9702, the SI base quantities you need are:

Base quantity	SI unit	Symbol
mass	kilogram	kg
length	metre	m
time	second	s
electric current	ampere	A
temperature	kelvin	K

Every other unit used in this syllabus is derived — built from these five by multiplication or division. Speed, for example, is distance ÷ time, so its unit is m s⁻¹. Force, from F = ma, has the unit kg m s⁻², which is given its own name, the newton (N). You can check whether an equation is even dimensionally possible by confirming both sides reduce to the same combination of base units — useful as a quick sanity check on any formula you’re unsure of.

Prefixes

You need to recall and use these prefixes and convert between them:

Prefix	Symbol	Factor
pico	p	10⁻¹²
nano	n	10⁻⁹
micro	μ	10⁻⁶
milli	m	10⁻³
centi	c	10⁻²
deci	d	10⁻¹
kilo	k	10³
mega	M	10⁶
giga	G	10⁹
tera	T	10¹²

Errors and uncertainties

A systematic error shifts every reading in the same direction by roughly the same amount — a ruler with a worn end causing every length measured to read short is a classic example, and a zero error (an instrument that doesn’t read zero when it should) is a specific case of this. Systematic errors affect accuracy, not precision, and cannot be reduced by repeating the measurement and averaging.

A random error causes readings to scatter unpredictably above and below the true value — for example, human reaction time when starting and stopping a stopwatch. Random errors affect precision, and repeating a measurement and averaging genuinely reduces their effect.

Precision is how close repeated measurements are to each other; accuracy is how close a measurement is to the true value. A set of tightly clustered readings that are all wrong in the same direction is precise but not accurate.

Combining uncertainties

At this level, you’re expected to combine uncertainties by simple addition of absolute or percentage uncertainties — not the more advanced quadrature method used at A Level in the Practical assessment section. If a quantity is calculated by multiplying or dividing measured quantities, add the percentage uncertainties; if it’s calculated by adding or subtracting measured quantities, add the absolute uncertainties.

Worked example. A rectangular block has length l = (12.0 ± 0.1) cm and width w = (5.0 ± 0.1) cm. The percentage uncertainty in l is (0.1/12.0) × 100 ≈ 0.83%, and in w is (0.1/5.0) × 100 = 2.0%. Since area = l × w, the percentage uncertainty in the area is the sum: 0.83% + 2.0% ≈ 2.8%.

Scalars and vectors

A scalar has magnitude only (mass, distance, speed, energy, temperature); a vector has both magnitude and direction (displacement, velocity, acceleration, force). Whether a quantity is a scalar or a vector matters for how you combine two of them — you can’t just add speeds together if they act in different directions.

Adding coplanar vectors. Vectors in the same plane can be added by drawing them tip-to-tail (a vector diagram) or by resolving each into perpendicular components and adding the components separately.

Resolving a vector. Any vector at an angle θ to a reference direction can be split into two perpendicular components: one along the reference direction (magnitude × cos θ) and one perpendicular to it (magnitude × sin θ). This is the technique you’ll use repeatedly from Topic 3 (Dynamics) onwards, whenever a force or velocity acts at an angle.

Common mistakes

• Quoting a calculated answer to more significant figures than the data justifies. If your least-precise measurement has 2 significant figures, your answer shouldn’t claim 5.
• Confusing precision and accuracy. A precise result can still be inaccurate if there’s a systematic error present — precision is about repeatability, accuracy is about closeness to the true value.
• Adding percentage uncertainties when a calculation involves addition or subtraction, not multiplication. Match the combination method (absolute vs. percentage) to the operation.
• Forgetting that resolving a vector always uses cos θ for the component along the vector’s own reference direction and sin θ for the perpendicular component — mixing these up is the single most common error carried forward into Topics 3 and 4.

Quick revision checklist

• The five SI base quantities and units used at this level, and the ten required prefixes
• Checking equation homogeneity using base units
• Systematic vs. random error, and precision vs. accuracy
• Combining uncertainties by simple addition (absolute or percentage, matched to the operation)
• Scalar vs. vector, and resolving a vector into perpendicular components

Related resources

• Kinematics: Equations of Motion — the next AS topic, applying vectors to motion
• Dynamics: Newton’s Laws and Momentum — vector resolution applied to forces
• Cambridge AS & A Level Physics hub

Written against Cambridge International AS & A Level Physics 9702, 2025–2027 series. Always check the current syllabus for your examination year.