State the SI base quantities and units, use common prefixes, distinguish scalars and vectors, and select suitable instruments to measure length, time and other quantities

What this dot point is asking

SEAB wants you to know the SI base quantities and their units, to use common prefixes such as kilo, centi, milli and micro, to tell the difference between scalar and vector quantities, and to choose a sensible instrument for measuring length, time and other everyday quantities. The skill being tested is partly knowledge and partly the practical judgement of picking the right tool and reading it without error.

The answer

SI base quantities and units

Physics is built on a small set of base quantities, each with an agreed SI unit:

• length, metre ($\text{m}$)
• mass, kilogram ($\text{kg}$)
• time, second ($\text{s}$)
• electric current, ampere ($\text{A}$)
• temperature, kelvin ($\text{K}$)

All other units are derived from these. For example, speed is metres per second ($\text{m/s}$), and force is the newton ($\text{N}$), which is $\text{kg}\,\text{m/s}^2$.

Prefixes

Prefixes scale a unit up or down so we avoid awkward numbers:

So $5\ \text{km} = 5000\ \text{m}$ and $2\ \text{mm} = 0.002\ \text{m} = 2 \times 10^{-3}\ \text{m}$.

Scalars and vectors

A scalar has magnitude (size) only: mass, time, temperature, energy, speed. A vector has both magnitude and direction: force, velocity, acceleration, displacement. The simplest exam test is to ask whether a direction is needed to describe the quantity fully. Velocity needs a direction; speed does not.

Choosing and reading an instrument

Match the instrument to the size you are measuring:

• a metre rule for lengths of a few centimetres to a metre,
• a micrometer screw gauge for very small lengths such as the diameter of a wire ($0.01\ \text{mm}$ precision),
• a measuring cylinder for the volume of a liquid,
• a stopwatch for time.

Read a scale with your eye level with the mark to avoid a parallax error, and check for a zero error before you start.

Examples in context

Example 1. Measuring a sheet of paper. A single sheet is too thin to measure with a ruler. Stack one hundred identical sheets, measure the total thickness, and divide by one hundred. This averaging trick reduces the percentage error of a tiny measurement, the same idea used to time a fast pendulum by timing many swings.

Example 2. Why units matter in a formula. When you compute density as $\rho = m/V$, putting mass in grams and volume in $\text{cm}^3$ gives $\text{g/cm}^3$, while kilograms and $\text{m}^3$ give $\text{kg/m}^3$. The number changes completely, so the unit you quote is part of the answer.

Try this

Q1. State the SI unit of mass and of time. [2 marks]

• Cue. Mass is measured in the kilogram ($\text{kg}$); time is measured in the second ($\text{s}$).

Q2. Convert $250\ \text{cm}$ to metres, giving your answer in standard form. [2 marks]

• Cue. $250\ \text{cm} = 2.50\ \text{m} = 2.5 \times 10^{0}\ \text{m}$, since $1\ \text{cm} = 10^{-2}\ \text{m}$.

Q3. Explain why force is a vector but mass is a scalar. [2 marks]

• Cue. Force needs a direction as well as a size to be fully described, so it is a vector; mass has size only, so it is a scalar.