Measurement: Complete A Level H2 Physics Cheatsheet

Base quantities, SI units and homogeneity

The SI base quantities you need at A Level: mass (kilogram, kg), length (metre, m), time (second, s), electric current (ampere, A), thermodynamic temperature (kelvin, K), and amount of substance (mole, mol). Every other quantity is derived from these.

An equation is homogeneous (dimensionally consistent) if every term has the same combination of base units. Checking this is a quick way to spot whether a given formula could possibly be correct, though it can't confirm a formula is correct, only rule out ones that definitely aren't.

Prefixes you should recognise instantly: pico (p, ×10⁻¹²), nano (n, ×10⁻⁹), micro (μ, ×10⁻⁶), milli (m, ×10⁻³), kilo (k, ×10³), mega (M, ×10⁶), giga (G, ×10⁹).

Trap: Students moving up from O Level often list only 5 base quantities, forgetting the mole (amount of substance), which becomes essential once the Ideal Gas topic is reached. It's still examinable here as part of the base-quantity list.

Precision, accuracy, and systematic vs random errors

Accuracy describes how close a measurement is to the true value. Precision describes how close repeated measurements are to each other, regardless of whether they're close to the true value at all.

A systematic error shifts every reading by the same amount in the same direction (e.g. a zero error, a badly calibrated instrument, or a consistent reaction-time delay when starting a stopwatch). It affects accuracy, not precision, and cannot be reduced by repeating the measurement.

A random error causes readings to scatter unpredictably above and below the true value (e.g. parallax error, natural variation in what's being measured). It affects precision, and can be reduced by taking repeated readings and averaging.

Trap: A very common wrong answer: 'repeat the reading and average it' as a fix for a systematic error. Repeating and averaging only reduces random error. A systematic error needs a different fix entirely, correcting for a known zero error, or recalibrating/replacing the instrument.

Propagating uncertainties in a calculated quantity

If a result is found by adding or subtracting measured quantities, add the absolute uncertainties.

If a result is found by multiplying, dividing, or raising a quantity to a power, add the percentage uncertainties, multiplying by the power first if one is present. This is the rule you'll use in almost every practical-paper calculation.

Identifying the dominant uncertainty: once every quantity's percentage uncertainty is found, the single largest one usually dominates the total, useful for deciding which measurement would most improve the result if remeasured more carefully.

Trick: Before combining anything, write out the percentage uncertainty of every individual measured quantity first, doubling (or tripling, etc.) it if that quantity appears as a square (or cube) in the formula. Only add them together as the very last step, this avoids losing track of which power applies to which term.

Scalars, vectors, and resolving vectors

A scalar has magnitude only (e.g. mass, speed, energy, temperature). A vector has both magnitude and direction (e.g. displacement, velocity, force, momentum).

To add two or more vectors acting at different angles, resolve each one into perpendicular (usually horizontal and vertical) components first: Fx = F cosθ, Fy = F sinθ. Sum all the x-components together, and separately sum all the y-components together.

The magnitude of the resultant is found using Pythagoras' theorem on the summed components, and its direction using trigonometry (tan⁻¹ of the ratio of the components).

Trick: When three or more vectors are involved, resolving into components and adding algebraically is far more reliable than trying to add them 'by eye' or with repeated sine/cosine rule applications, which only works cleanly for two vectors at a time.

Worked Example

In an experiment to find the resistivity ρ of a wire, a student measures its diameter using a micrometer as d = (0.42 ± 0.02) mm, its length using a metre rule as l = (80.0 ± 0.1) cm, and its resistance using a multimeter as R = (2.50 ± 0.05) Ω. Resistivity is given by ρ = πRd²/4l.

Why this question is a good test of the topic: the diameter's uncertainty dominates the final answer, even though it's a smaller absolute uncertainty than R's, because it's squared in the formula and its percentage uncertainty (from a small measured value) is already the largest. This is exactly the reasoning examiners look for when a question asks which measurement to improve.

Frequently Asked Questions