Physical quantities and measurement techniques
SI units and prefixes, measuring length, volume and time, and the difference between scalars and vectors.
Learning objectives
What you need to be able to do
Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.
- 1.1.1Describe how to measure length, volume and time intervals, including the use of multiple readings to improve accuracy.
- 1.1.2Understand that a scalar quantity has magnitude only and a vector quantity has both magnitude and direction.
- 1.1.3Determine the resultant of two vectors at right angles, graphically or by calculation.Supplement
7 minute read
Units, prefixes and vectors
Every physical quantity is a number and a unit. Drop the unit and the number means nothing — an answer of "12" is worth zero marks.
The SI base units you need
- metre (m) for length
- kilogram (kg) for mass
- second (s) for time
- ampere (A) for current
- kelvin (K) for temperature
Everything else is built from these. A newton, for example, is really kg m/s².
Prefixes
Prefixes scale a unit by a power of ten. The ones that appear in 0625 papers are:
- nano (n) = ×10⁻⁹
- micro (µ) = ×10⁻⁶
- milli (m) = ×10⁻³
- centi (c) = ×10⁻²
- kilo (k) = ×10³
- mega (M) = ×10⁶
- giga (G) = ×10⁹
The single most common mark loss in the whole paper is converting these the wrong way. Ask yourself: is the new number bigger or smaller than the old one? 5 km must be 5000 m, not 0.005 m.
Scalars and vectors
A scalar has size only: distance, speed, mass, time, energy. A vector has size and direction: displacement, velocity, acceleration, force, momentum, weight.
Two vectors at right angles combine with Pythagoras for the magnitude and trigonometry for the direction. Two vectors along the same line simply add, taking one direction as positive.
Measuring well
- Take several readings and average them.
- For a small length (like the thickness of paper), measure many together and divide.
- For a pendulum, time 20 swings and divide by 20 — this reduces the effect of your reaction time.
Think of it like this
Speed is "how fast" — velocity is "how fast, and which way". A car going round a roundabout at a steady 20 km/h has constant speed but constantly changing velocity.
Worked examples
Method, step by step
A student measures the time for 20 swings of a pendulum as 31.4 s. Find the time for one swing.
- 1The time for one swing (the period) is the total time divided by the number of swings.
- 2T = 31.4 / 20
T = 1.57 s
A force of 3.0 N acts north and 4.0 N acts east on the same object. Find the resultant.
- 1The forces are perpendicular, so use Pythagoras for the magnitude.
- 2R = √(3.0² + 4.0²) = √25
- 3Direction: tan θ = 4.0 / 3.0, so θ = 53° east of north.
5.0 N at 53° east of north
Common misconceptions
- Thinking distance and displacement are the same. Walk 3 m east then 3 m west: distance is 6 m, displacement is 0.
- Multiplying instead of dividing when converting prefixes. Always sanity-check whether the number should get bigger or smaller.
- Treating mass and weight as the same quantity — mass is a scalar in kg, weight is a vector in N.
In the exam
- Write the unit on every line of working, not just the final answer.
- If a question says "state", one short sentence is enough — no marks for extra prose.
- When asked to improve accuracy, "repeat and average" and "measure a larger quantity and divide" are the two standard answers.