Scalars & Vectors (Edexcel International A Level Physics)

Scalars & Vectors

• All quantities can be one of two types:

  • a scalar

  • a vector

Scalars

• Scalars are quantities that have magnitude but not direction

  • For example, mass is a scalar quantity because it has magnitude but no direction 

Vectors

• Vectors are quantities that have both magnitude and direction

  • For example, weight is a vector quantity because it is a force and has both magnitude and direction

Distance and displacement

• Distance is a measure of how far an object has travelled, regardless of direction

  • Distance is the total length of the path taken

  • Distance, therefore, has a magnitude but no direction

  • So, distance is a scalar quantity

• Displacement is a measure of how far it is between two points in space, including the direction

  • Displacement is the length and direction of a straight line drawn from the starting point to the finishing point

  • Displacement, therefore, has a magnitude and a direction

  • So, displacement is a vector quantity

What is the difference between distance and displacement?

Displacement is a vector quantity while distance is a scalar quantity

• When a student travels to school, there will probably be a difference in the distance they travel and their displacement

  • The overall distance they travel includes the total lengths of all the roads, including any twists and turns

  • The overall displacement of the student would be a straight line between their home and school, regardless of any obstacles, such as buildings, lakes or motorways, along the way

Speed and velocity

• Speed is a measure of the distance travelled by an object per unit time, regardless of the direction

  • The speed of an object describes how fast it is moving, but not the direction it is travelling in

  • Speed, therefore, has magnitude but no direction

  • So, speed is a scalar quantity

• Velocity is a measure of the displacement of an object per unit time, including the direction

  • The velocity of an object describes how fast it is moving and which direction it is travelling in

  • An object can have a constant speed but a changing velocity if the object is changing direction

  • Velocity, therefore, has magnitude and direction

  • So, velocity is a vector quantity

Examples of scalars & vectors

• The table below lists some common examples of scalar and vector quantities

Table of scalars and vectors

Vector notation

• Sometimes, vector quantities are written in a certain way to distinguish them from scalar quantities

• Some examples of scalar and vector notation are shown below:

The arrow on vector notation does not indicate an actual direction, just that the quantity has a direction

• This means writing the quantity to make it clear that it is a vector

• In textbooks, vectors are often shown as bold and italic, for example, F or s

• Another form of notation, and easier to do in handwriting, is putting an arrow over the top of the quantity, for example, or 

  • The arrow does not indicate the actual direction of the vector, only that it has a direction