Scalars & Vectors (Oxford AQA IGCSE Combined Science Double Award)
Revision Note
Written by: Leander Oates
Reviewed by: Caroline Carroll
Scalars & Vectors
All quantities can be one of two types:
A scalar
A vector
Scalars
Scalars are quantities that have only a magnitude
Mass is scalar since it has magnitude without a direction
Energy and speed are also examples of scalar quantities
Vectors
Vectors have both magnitude and direction
Velocity is a vector since it has a magnitude and a direction
When describing the velocity of a car it is necessary to mention both its speed and the direction in which it is travelling
For example, the velocity might be 60 km per hour (magnitude) due west (direction)
Distance is a value describing only how long an object is or how far it is between two points - this means it is a scalar quantity
Displacement on the other hand also describes the direction in which the distance is measured - this means it is a vector quantity
For example, a displacement might be 100 km north
Table of Common Scalar & Vector Quantities
Scalar | Vector |
|---|---|
Distance | Displacement |
Speed | Velocity |
Mass | Weight |
Energy | |
Volume | |
Density | |
Temperature | |
Power | |
Force | |
Acceleration | |
Momentum |
Worked Example
An instructor is in charge of training junior astronauts. For one of their sessions, they would like to explain the difference between mass and weight.
Suggest how the instructor should explain the difference between mass and weight, using definitions of scalars and vectors in your answer.
Answer:
Step 1: Recall the definitions of a scalar and vector quantity
Scalars are quantities that have only a magnitude
Vectors are quantities that have both magnitude and direction
Step 2: Identify which quantity has magnitude only
Mass is a quantity with magnitude only
So mass is a scalar quantity
The instructor might explain to their junior astronauts that their mass will not change as their location in the Universe changes
Step 3: Identify which quantity has magnitude and direction
Weight is a quantity with magnitude and direction (it is a force)
So weight is a vector quantity
The instructor might explain that their weight - the force on them due to gravitational field strength - will vary depending on their location. For example, the force of weight acting on them would be less on the Moon than it is on Earth
Examiner Tips and Tricks
Make sure you are comfortable with the differences between similar scalars and vectors, the most commonly confused pairings tend to be:
Distance and displacement
Speed and velocity
Weight and mass
Vector arrows
A vector can be represented by using an arrow
The length of the arrow represents the magnitude of the vector
The direction of the arrow indicates the direction of the vector
Forces represented as vectors
Pairs of objects exerting a force on one another can be represented by vectors
Vector diagram for a pair of objects exerting a force on one another
In the example above:
The vectors are equal in length showing that the forces are equal in magnitude
The vectors are opposite in direction showing that the forces are acting in opposing directions
Worked Example
A tennis ball is thrown at an angle of 45° to horizontal at a speed of 5 m/s. A second tennis ball is thrown in the same direction at a speed of 10 m/s.
Draw the velocity vectors of the balls.
Answer:
Step 1: Draw the first tennis ball and its velocity vector
Measure the 45° angle with a protractor
Step 2: Draw the second tennis ball and its velocity vector
The second ball has a speed of 10 m/s, so the arrow will be twice as long
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