Physical quantities, units and measurement
Study quantities, SI units, scale, instruments, scalars, vectors and graphical vector addition.
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Before you begin
Measurement questions reward correct units, suitable instruments and a clear method. The skills here are used throughout mechanics and practical work.
New to the topic? Start with base quantities and SI units. If you are already confident with units, start at measurement of length.
Learning goals
- Represent a physical quantity with a numerical magnitude and unit
- Recall the six prescribed SI base quantities and their units
- Use the prescribed SI prefixes from nano to tera
- Compare orders of magnitude from a typical atom to the Earth
- Select and justify measuring instruments by range and precision
- Distinguish scalar and vector quantities and give examples
- Add two vectors graphically to determine a resultant
Syllabus statements covered
- show an understanding that physical quantities typically consist of a numerical magnitude and a unit
- recall the following base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)
- use the following prefixes and their symbols to indicate decimal sub-multiples and multiples of the SI units: nano (n), micro (µ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T)
- show an understanding of the orders of magnitude of the sizes of common objects ranging from a typical atom to the Earth
- select and explain the use of appropriate measuring instruments to measure or determine physical quantities listed in “Summary of key quantities, symbols and units” taking into consideration the range and precision of the instrument
- state what is meant by scalar and vector quantities and give common examples of each
- add two vectors to determine a resultant by a graphical method
Lessons
Work through them in order.
Lessons
- Base quantities and SI unitsRecall the six base quantities and their SI units, and tell base units from derived units.
- Prefixes and unit conversionsRead the prescribed prefix symbols and express the same quantity in different units.
- Area, volume and compound unit conversionsApply unit factors to every dimension and treat numerator and denominator conversions separately.
- Orders of magnitude: from atoms to EarthCompare familiar length scales and distinguish exponent gaps from actual size ratios.
- Choosing instruments and measuring lengthChoose a tape, rule, digital caliper or digital micrometer by range and precision.
- Measuring time intervals and periodsTime intervals with a digital stopwatch and measure a period reliably from repeated oscillations.
- Accuracy, precision and measurement errorsTell accuracy from precision, and reduce systematic, random, parallax and zero errors.
- Scalar and vector quantitiesTell scalars from vectors, and state a vector's direction as well as its magnitude.
- Vector addition by graphical methodsAdd two vectors by a scale drawing and state the resultant magnitude and direction.
Calipers and micrometers
- Digital and vernier calipersChoose the jaws or depth rod, zero a digital caliper and record its reading; read an analogue vernier scale if you meet one.
- Digital micrometers and screw gaugesZero a micrometer, close it with the ratchet and record every digit; read an analogue screw gauge if you meet one.
Beyond the syllabus: analogue vernier practice
- Practice: reading a vernier caliperRead main and vernier scales on caliper diagrams with no zero error.PracticalBeyond the syllabus
- Practice: finding the zero error of a vernier caliperFind positive and negative zero errors from closed-jaw readings.PracticalBeyond the syllabus
- Practice: reading a vernier caliper with zero errorSubtract the zero error from each observed reading.PracticalBeyond the syllabus
Practise and check
Or choose
Topic reference
Calipers and micrometers
G3 Physics and O-Level practical work uses digital calipers and digital micrometers. Each lesson also shows the analogue scale in case your school or a question uses one.
Revision
High-value checks
- Write every measurement as a number and a unit.
- Use mutually consistent units in an equation and give the requested output unit.
- Choose an instrument whose range includes the value and whose precision is suitable.
- Record all digits justified by the instrument display or scale.
- Correct a zero error using: corrected reading = observed reading − zero error.
- Repeat measurements to reveal scatter and calculate a mean when appropriate.
Six base quantities to recall
| Base quantity | SI unit | Symbol |
|---|---|---|
| mass | kilogram | kg |
| length | metre | m |
| time | second | s |
| electric current | ampere | A |
| temperature | kelvin | K |
| amount of substance | mole | mol |
The complete SI system has a seventh base quantity, luminous intensity, measured in candela. For this course, recall the six quantities above.
Going further
O-Level practical skills applies measurement to planning and evaluation. Useful applications within later topics include: