Scalar & Vectors (Edexcel IGCSE Physics)

• All quantities can be one of two types:
  • A scalar
  • A vector

Scalars

• Scalars are quantities that have only a magnitude
  • For example, mass is a scalar quantity since it is a quantity that has no direction to it

Vectors

• Vectors have both a magnitude and a direction
• Velocity is a vector quantity since it is described with both 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, 60 km per hour in a Westerly 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, 100 km in a Northern direction

Examples of Scalars & Vectors

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

Scalars & Vectors Table

• Some vectors and scalars are similar to each other
  • For example, the scalar quantity distance corresponds to the vector quantity displacement

• Corresponding vectors and their scalar counterparts are aligned in the table where applicable

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
    • Blu might explain to his junior astronauts that their mass will not change if they travel to outer space

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
    • Blu might explain that to his junior astronauts that their weight - the force on them due to gravity - will vary depending on their distance from the centre of the Earth

• Force is a vector quantity because it describes both magnitude and direction
  • The length of the arrow represents the magnitude of the force
  • The direction of the arrow indicates the direction of the force

A free body diagram of an object with two forces acting on it

• Not all forces are directed perfectly horizontally or vertically and thus need to have an angle described
  • It is useful to describe an angle with respect to the vertical or the horizontal

A force of magnitude 100 N directed 40° to the horizontal