Scalar quantity
Scalars & Vectors - OCR A-Level Physics
Key Definition
Scalar quantity
A quantity that has magnitude (size) only. It has no direction. Two scalars are added by simple arithmetic.
A quantity that has magnitude (size) only. It has no direction. Two scalars are added by simple arithmetic.
Key Definition
Vector quantity
A quantity that has both magnitude and direction. Vectors must be combined by triangle, parallelogram, or component methods, never by simple arithmetic unless they act along the same line.
A quantity that has both magnitude and direction. Vectors must be combined by triangle, parallelogram, or component methods, never by simple arithmetic unless they act along the same line.
Diagram pending
Side-by-side: a number line showing a scalar (a single value, e.g. mass $= 5 \text{ kg}$) next to a vector arrow with labelled magnitude and direction (e.g. $5 \text{ N}$ at $30^\circ$ above horizontal). Length of arrow shown to scale.
Will be replaced with a GeoGebra SVG in stream 2.
- ScalarA quantity that has magnitude only. examples (with SI units): mass (kg), temperature (K), speed ($\text{m s}^{-1}$), distance (m), time (s), energyThe capacity to do work. Measured in joules (J). (J), powerThe rate of energy transfer. Measured in watts (W). (W), pressureForce per unit area. Measured in pascals (Pa). (Pa), potential difference (V), volume ($\text{m}^3$).
- VectorA quantity that has both magnitude and direction. examples (with SI units): force (N), velocityThe rate of change of displacement. ($\text{m s}^{-1}$), displacementThe distance moved in a particular direction from a starting point. (m), acceleration ($\text{m s}^{-2}$), momentum ($\text{kg m s}^{-1}$), weight (N), momentThe turning effect of a force about a pivot. Measured in N m. (N m).
- Speed is scalar; velocity is the vector equivalent (speed in a stated direction).
- Distance is scalar; displacement is the vector equivalent (straight-line distance from start to finish in a stated direction).
- Vectors are represented by arrows: the length is proportional to magnitude, the arrowhead shows direction. In print, vectors are written in bold ($\mathbf{F}$) or with an arrow ($\vec{F}$); magnitude alone is written in italic ($F$).
Common Mistake
MEDIUM
Wrong: Saying "weight is a scalar because it is just a number in kg". Confusing weight with mass.
Right: Weight is a VECTOR. It has magnitude (in newtons) AND direction (always vertically downward, towards the centre of the Earth). Mass is the scalar quantity measured in kg. A 5 kg bag has weight $5 \times 9.81 = 49 \text{ N}$ downward.
Right: Weight is a VECTOR. It has magnitude (in newtons) AND direction (always vertically downward, towards the centre of the Earth). Mass is the scalar quantity measured in kg. A 5 kg bag has weight $5 \times 9.81 = 49 \text{ N}$ downward.
Examiner Tips and Tricks
- A common 1-mark OCR question asks you to classify a list of quantities as scalar or vector.
- The single test: does it require a direction to be fully specified?
- Energy, power, and temperature are the quantities students most often get wrong. All three are scalars.
- If asked to "give one example of a vector quantity," do not name two and lose the mark on the second if it is wrong. One clean example.