Physical quantities fall into two groups: scalars (magnitude only) and vectors (magnitude and direction). This distinction is tested in both Core and Extended papers, but Extended candidates must use it in calculations.
What is the difference?
A scalar has size (magnitude) only. A vector has both size and direction.
| Scalar examples | Vector examples |
|---|---|
| Speed | Velocity |
| Distance | Displacement |
| Mass | Weight (force) |
| Energy | Momentum |
| Temperature | Acceleration |
| Time | Force |
The classic exam pair is speed and velocity. A car travelling at 30 m/s has a speed of 30 m/s regardless of direction. Its velocity is 30 m/s north, 30 m/s south, or whatever direction it actually moves.
Why does the distinction matter?
Two forces of 3 N and 4 N can produce a resultant anywhere between 1 N (opposite directions) and 7 N (same direction). If the two forces act at right angles, the resultant is . This calculation only works because force is a vector.
For Extended candidates: a body moving in a circle at constant speed has a changing velocity because its direction changes continuously. This changing velocity means it has acceleration (centripetal acceleration) even though its speed is constant.
Common errors and how to correct them
- Calling mass a vector. Mass is always a scalar. Weight (the gravitational force on that mass) is a vector. They are related by but they are different quantities.
- Saying distance and displacement are the same. A runner completing one lap of a 400 m track has a distance of 400 m but a displacement of zero (they return to the start).
- Adding vectors without considering direction. Two 5 N forces acting on an object do not always produce 10 N. If they act in opposite directions, the resultant is 0 N.
How to apply this in an exam
When asked to classify a quantity, state whether it is a scalar or vector and give the reason (magnitude only, or magnitude and direction). For calculation questions involving vectors, always consider direction. Draw a diagram where possible.
Need help with this concept?
A 0625 specialist can work through the student's current question and help identify whether the difficulty is the concept, the calculation or the exam technique.