A length is measured as (5.0 0.1)\ cm. State its percentage uncertainty. [1 mark]

WJEC Eduqas Eduqas 2019-style practice: The drag force on a sphere falling through a fluid is given by F = 6π r v, where r is the radius and v the speed. Use base units to determine the base units of the viscosity .

Rearrange for : = F6π r v, so the units are [F][r][v]. Force has base units kg\,m\,s^-2, radius m, speed m\,s^-1. So [] = kg\,m\,s^-2m × m\,s^-1 = kg\,m^-1\,s^-1. Markers reward rearranging for , substituting the base units of force, radius and speed, and the correct answer kg\,m^-1\,s^-1.

WJEC Eduqas Eduqas 2021-style practice: Two forces of 6.0\ N and 8.0\ N act on a point at right angles to each other. Calculate the magnitude and direction of the resultant force.

The forces are perpendicular, so combine them with Pythagoras: F = sqrt(6.0^2 + 8.0^2) = sqrt(36 + 64) = sqrt(100) = 10\ N. The direction relative to the 8.0\ N force: θ = tan^-1\!(6.08.0) = tan^-1(0.75) = 37^. Markers reward using Pythagoras for perpendicular vectors, the resultant 10\ N, and an angle of 37^ from the larger force (or 53^ from the smaller, if clearly stated).

EnglandPhysicsSyllabus dot point

How do physicists describe quantities precisely using units, scalars and vectors, and how do they handle measurement uncertainty?

Basic physics: SI base and derived units, homogeneity of equations, scalars and vectors, resolving and adding vectors, and the treatment of measurement uncertainty.

A focused answer to the Eduqas A-Level Physics Component 1 basic physics content, covering SI base and derived units, checking the homogeneity of equations by units, distinguishing scalars from vectors, resolving and adding vectors, and the treatment of measurement uncertainty.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Have a quick question? Jump to the Q&A page

Quick answer

The seven SI base units are the metre, kilogram, second, ampere, kelvin, mole and candela; every other unit is derived from these (for example the newton is $\text{kg}\,\text{m}\,\text{s}^{-2}$ ). An equation must be homogeneous, meaning both sides have the same base units, which is a quick way to spot an error. Scalars (mass, energy, speed) have magnitude only; vectors (displacement, velocity, force) have magnitude and direction. A vector at angle $\theta$ resolves into components $F\cos\theta$ and $F\sin\theta$ , and perpendicular vectors add by Pythagoras. Every measurement carries an uncertainty, combined by adding absolute uncertainties when quantities are added or subtracted, and adding percentage (fractional) uncertainties when they are multiplied or divided.

Jump to a section

What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

Eduqas wants you to use the seven SI base units and build derived units from them, check whether an equation is homogeneous (balanced) in its units, distinguish scalar from vector quantities, resolve a vector into perpendicular components and add vectors, and express a measured value with a sensible uncertainty.

The answer

SI base and derived units

A common Eduqas task is to find the base units of an unfamiliar quantity by rearranging the defining equation and substituting the base units of each term. Prefixes scale units in powers of ten: pico ( $10^{-12}$ ), nano ( $10^{-9}$ ), micro ( $10^{-6}$ ), milli ( $10^{-3}$ ), kilo ( $10^{3}$ ), mega ( $10^{6}$ ) and giga ( $10^{9}$ ).

Homogeneity of equations

Scalars and vectors

Resolving and adding vectors

For two perpendicular vectors this reduces to Pythagoras for the magnitude and a single inverse-tangent for the direction. Resolving is the standard route into inclined-plane, projectile and equilibrium problems later in the course.

Measurement uncertainty

Combining uncertainties in a density measurement

A cube has side $(2.00 \pm 0.01)\ \text{cm}$ and mass $(64.0 \pm 0.5)\ \text{g}$ . Find the density and its percentage uncertainty.

step 1: Calculate the central value

Volume $= (2.00)^3 = 8.00\ \text{cm}^3$ . Density $= \dfrac{64.0}{8.00} = 8.00\ \text{g cm}^{-3}$ .

step 2: Percentage uncertainty in each quantity

Side: $\dfrac{0.01}{2.00} = 0.5\%$ . Mass: $\dfrac{0.5}{64.0} = 0.78\%$ .

step 3: Combine for the density

Volume depends on side cubed, so its percentage uncertainty is $3 \times 0.5\% = 1.5\%$ . Density is mass divided by volume, so add the percentages: $0.78\% + 1.5\% = 2.3\%$ .

So the density is $8.00\ \text{g cm}^{-3} \pm 2.3\%$ , i.e. $(8.00 \pm 0.18)\ \text{g cm}^{-3}$ .

Examples in context

Dimensional checking catches algebra slips before they cost marks: if a derived expression for a period came out with units of metres, you have made an error. Engineers carry uncertainties through every calculation so they can quote a tolerance, for example the load a cable can safely bear. GPS positioning resolves a satellite signal into components to locate a receiver, and surveyors combine vector displacements to map terrain.

Try this

Q1. State the SI base units of the joule. [2 marks]

Cue. From $W = Fs$ and $F = ma$ , $1\ \text{J} = 1\ \text{kg}\,\text{m}^2\,\text{s}^{-2}$ .

Q2. A force of $12\ \text{N}$ acts at $30^\circ$ above the horizontal. Find its horizontal and vertical components. [2 marks]

Cue. $F_x = 12\cos 30^\circ = 10.4\ \text{N}$ ; $F_y = 12\sin 30^\circ = 6.0\ \text{N}$ .

Q3. A length is measured as $(5.0 \pm 0.1)\ \text{cm}$ . State its percentage uncertainty. [1 mark]

Cue. $\dfrac{0.1}{5.0} \times 100 = 2\%$ .

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20193 marksThe drag force on a sphere falling through a fluid is given by

F = 6\pi\eta r v

, where

r

is the radius and

v

the speed. Use base units to determine the base units of the viscosity

\eta

Show worked answer →

Rearrange for $\eta$ : $\eta = \dfrac{F}{6\pi r v}$ , so the units are $\dfrac{[F]}{[r][v]}$ .

Force has base units $\text{kg}\,\text{m}\,\text{s}^{-2}$ , radius $\text{m}$ , speed $\text{m}\,\text{s}^{-1}$ .

So $[\eta] = \dfrac{\text{kg}\,\text{m}\,\text{s}^{-2}}{\text{m} \times \text{m}\,\text{s}^{-1}} = \text{kg}\,\text{m}^{-1}\,\text{s}^{-1}$ .

Markers reward rearranging for $\eta$ , substituting the base units of force, radius and speed, and the correct answer $\text{kg}\,\text{m}^{-1}\,\text{s}^{-1}$ .

Eduqas 20214 marksTwo forces of

6.0\ \text{N}

and

8.0\ \text{N}

act on a point at right angles to each other. Calculate the magnitude and direction of the resultant force.

Show worked answer →

The forces are perpendicular, so combine them with Pythagoras: $F = \sqrt{6.0^2 + 8.0^2} = \sqrt{36 + 64} = \sqrt{100} = 10\ \text{N}$ .

The direction relative to the $8.0\ \text{N}$ force: $\theta = \tan^{-1}\!\left(\dfrac{6.0}{8.0}\right) = \tan^{-1}(0.75) = 37^\circ$ .

Markers reward using Pythagoras for perpendicular vectors, the resultant $10\ \text{N}$ , and an angle of $37^\circ$ from the larger force (or $53^\circ$ from the smaller, if clearly stated).

Related dot points

Sources & how we know this

Eduqas GCE AS/A Level Physics specification (A720QS) — WJEC Eduqas (2015)