Scalars & Vectors (Edexcel International A Level Physics)

• 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

Scalars	Vectors
distance	displacement
speed	velocity
mass	acceleration
time	force
energy	momentum
volume
density
pressure
electric charge
temperature

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