Scalar & Vector Quantities
Physics: Cambridge International GCSE Supplement, topic 1.1.4
Scalar & Vector Quantities
A quantity is anything that can be measured, such as length, mass, or time. They can be divided into two groups: scalars and vectors.
What are quantities?
- Quantities are things we can measure.
- Example: length, mass, force
- Quantities can be divided into two groups:
- Scalars
- Vectors
- The difference in scalars and vectors lies in whether the quantity has direction as well as size.
Scalar quantities
- A scalar quantity has magnitude (size) only. They do not include direction.
- Example: The mass of a ball is 2 kg (we do not need to know its direction).
- Examples of scalar quantities:
- Distance
- Speed
- Time
- Mass
- Energy
- Temperature
Vector quantities
- A vector quantity has both magnitude and direction.
- Example: A force of 10 N acting downwards.
- Vectors are often represented by arrows.
- The length of the arrow shows the size of vector (magnitude), and the direction it points shows the direction of vector.
- Examples of vector quantities:
- Force
- Weight
- Velocity
- Acceleration
- Momentum
- Electric field strength
- Gravitational field strength
Comparing scalars and vectors
- Scalar = Magnitude only (e.g. “60 km/h”)
- Vector = Magnitude + direction (e.g. “60 km/h north”)
- Distance vs. Displacement:
- Distance is a scalar (e.g. you walk 5 km).
- Displacement is a vector (e.g. you are 5 km north of your starting point).
- Speed vs. Velocity:
- Speed is a scalar.
- Velocity is a vector.
Test yourself on Scalar & Vector Quantities
Which of the following is a scalar quantity?
In a vector diagram, what does the direction of the arrow represent?
A car travels at 60 km/h north. Why is this an example of a vector quantity rather than a scalar quantity?
In a vector diagram, what does the length of the arrow represent?
A student records that she walked 5 km. Why is this a scalar quantity rather than a vector quantity?