Lesson 1 of 6
Physical quantities and units
I can interpret a physical quantity using its numerical value and unit where applicable.Syllabus
Syllabus K223 / K224, 1(a). Interpret a physical quantity using its numerical value and unit where applicable.
I can use the specified base quantities and their SI units.Syllabus
Syllabus K223 / K224, 1(b). Use the specified base quantities and their SI units.
In short
- A physical quantity has a number and a unit, for example 2.5 m.
- Base quantities include length (m), mass (kg), time (s), current (A) and temperature (K).
- Other units are built from these, such as m/s for speed.
A physical quantity describes something measurable, such as a length, a time or a mass. Its unit tells us what the number means.
25 cm and 0.25 m describe the same length. Changing the unit changes the numerical value, but does not change the object. Writing just "25" would leave the length unclear: 25 millimetres, centimetres and metres are very different.
A physical quantity is usually expressed as a numerical value and a unit. Some quantities are dimensionless: for example, a ratio of two lengths has no unit because the length units cancel.
Base quantities and SI units
SI is the international system of units. Use these six base quantities and their SI units in this course. Other quantities can be formed by combining base quantities.
| Quantity | SI unit | Unit symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Thermodynamic temperature | kelvin | K |
| Amount of substance | mole | mol |
Write the kelvin as K, without a degree sign. The SI base unit of mass is the kilogram, kg, even though the gram is also a familiar mass unit. One kilogram is 1000 g.
A quantity symbol is different from a unit symbol
In m = 2.0 kg, the first m is a symbol for the quantity mass; kg is its unit. In l = 2.0 m, lowercase l represents length and m is the unit metre. Read the meaning given in the question instead of deciding what a letter means on its own.
Worked example
Getting a unit from a calculation
A trolley travels a total distance of 2.4 m in 0.80 s. Let d represent the total distance, t the elapsed time and v the average speed.
v = d / t = 2.4 m / 0.80 s = 3.0 m/s
Dividing distance by time gives metres per second. The result means that travelling steadily at 3.0 metres each second would cover the same distance in the same time. The unit follows from the quantities in the calculation.
Make a guess. You are not marked.
You want the period of a pendulum, the time for one complete swing, as accurately as possible with a stopwatch. Which is better: timing one swing, or timing twenty swings and dividing by twenty?
Show the answer
Time twenty swings and divide by twenty.
Your reaction time error is about the same either way, about 0.2 s. Spread over twenty swings it becomes 0.01 s per swing, instead of 0.2 s on a single swing.
For more journeys, see distance, speed and velocity. To change the units before calculating, use prefixes and physical scales.