Scalar & Vector Quantities (DP IB Physics): Revision Note

Scalar & vector quantities

Scalars

• Scalars are quantities that have magnitude only

  • 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 length 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 the 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 and vectors

• Some common scalar and vector quantities are shown in the table below:

Table of scalars and vectors

Representing vectors

• Vectors are represented by an arrow

  • The arrowhead indicates the direction of the vector

  • The length of the arrow represents the magnitude

The force vector F has both a direction and a magnitude

• Component vectors are sometimes drawn with a dotted line and a subscript indicating horizontal or vertical

  • For example, F_x is the horizontal component and F_y is the vertical component of the force F