1.1 Physical quantities and measurement techniques
- Syllabus
- 0625–2026–2027
- Topic
- 1.1
- Level
- —
Learning objectives
1.1.1Use of rulers and measuring cylinders• Describe the use of rulers and measuring cylinders to find a length or a volume1.1.2To measure a variety of time intervals• Describe how to measure a variety of time intervals using clocks and digital timers1.1.3An average value for a small distance• Determine an average value for a small distance and for a short interval of time by measuring multiples (including the period of oscillation of a pendulum)1.1.4A scalar quantity has magnitude (size)• Understand: a scalar quantity has magnitude (size) only and that a vector quantity has magnitude and direction1.1.5Distance, speed, time, mass, energy• Know scalar quantities: distance, speed, time, mass, energy and temperature1.1.6Force, weight, velocity, acceleration• Know vector quantities: force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength1.1.7Determine, by calculation or• Determine, by calculation or graphically, the resultant of two vectors at right angles, limited to forces or velocities only
Measure length and volume accurately
Use a scale that is suitable for the size of the quantity, read it at eye level and obtain the result from the difference between the final and initial readings when the object does not start at zero.
| Quantity | Method | Accuracy check |
|---|---|---|
| length with a ruler | align the object with the scale; read both ends and subtract start from end | ruler parallel to the object; eye perpendicular to the scale to avoid parallax |
| liquid volume | place the measuring cylinder upright on a level surface and read the bottom of the concave meniscus | choose the smallest cylinder that safely contains the volume |
| irregular solid volume | record initial water volume, fully submerge the solid, record final volume | displaced volume = final − initial; remove trapped air |
Do not assume the first end is at zero. A ruler gives length directly; a measuring cylinder gives liquid volume or solid volume by displacement.
Measure a time interval
A time interval is the difference between the readings at two clearly defined events.
| Step | Action |
|---|---|
| choose | use a clock for long intervals and a digital timer for short intervals |
| define | decide the exact start and finish events before measuring |
| measure | start and stop at those events, or record both clock readings |
| calculate | interval = finish reading − start reading |
| improve | repeat when possible and use a mean; for very short repeated events, time several together |
The timer reading is meaningful only when the start and finish events are consistent. Human reaction time is a larger fraction of a very short interval.
Measure small distances and short times by using multiples
When one distance or interval is too small to measure precisely, measure many identical copies or cycles together and divide by their number.
averagevalue=totalmeasuredvalue÷numberofidenticaldistancesorintervals
| Small quantity | Multiple measurement | Final value |
|---|---|---|
| coin thickness | measure the height of a stack of touching identical coins | stack height ÷ number of coins |
| wire or thread diameter | wind many close turns around a cylinder and measure their total width | total width ÷ number of turns |
| pendulum period | time many complete oscillations from the same marker and direction | total time ÷ number of oscillations |
Count complete intervals, not marker crossings. One oscillation returns the pendulum to the same position moving in the same direction.
Distinguish scalars from vectors
A scalar quantity has magnitude only. A vector quantity has both magnitude and direction.
| Feature | Scalar | Vector |
|---|---|---|
| magnitude | required | required |
| direction | not part of the quantity | required |
| complete statement | 20 m/s speed | 20 m/s east velocity |
| combination | ordinary signed arithmetic where appropriate | direction must be included, often using vector geometry |
A unit does not decide whether a quantity is scalar or vector. Speed and velocity can share units, but velocity includes direction and speed does not.
Recognise the six scalar quantities
The syllabus scalar quantities are distance, speed, time, mass, energy and temperature. Each is completely specified by its magnitude and unit.
| Scalar quantity | What its magnitude states |
|---|---|
| distance | total path length |
| speed | rate of distance travelled |
| time | duration |
| mass | quantity of matter |
| energy | capacity transferred or stored in a process |
| temperature | thermal state measured on a temperature scale |
Distance is scalar even when a route has direction; velocity, force and momentum are not scalar. This card classifies the six named quantities rather than defining their later equations.
Recognise the seven vector quantities
The syllabus vector quantities are force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength. Each requires magnitude and direction.
| Vector quantity | Direction describes… |
|---|---|
| force | the direction of the push or pull |
| weight | the direction of gravitational force |
| velocity | the direction of motion |
| acceleration | the direction of change of velocity |
| momentum | the direction of velocity |
| electric field strength | the force direction on a positive test charge |
| gravitational field strength | the force direction on a mass |
Speed is not velocity, and mass is not weight: the first in each pair is scalar, while the second is vector.
Find the resultant of two perpendicular vectors
The resultant is the single force or velocity with the same combined effect as two perpendicular component vectors.
R=A2+B2
tanθ=adjacent componentopposite component
For perpendicular components A and B, use Pythagoras to find the magnitude. Use trigonometry to find the angle, then state the angle from a named direction so the vector is complete.
| Graphical step | Action |
|---|---|
| 1 | choose and state a scale |
| 2 | draw the two vectors to scale at right angles, head-to-tail, preserving arrow directions |
| 3 | draw the resultant from the tail of the first to the head of the second |
| 4 | measure its length and angle, then convert length using the scale |
This method is limited here to two perpendicular forces or two perpendicular velocities. Do not add magnitudes directly unless the vectors point along the same line and direction.