Scalars & Vectors (Edexcel GCSE Physics: Combined Science)

• 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 since it is a quantity that has magnitude without a direction
  • Distance is also a scalar since it only contains a magnitude, not a direction

Vectors

• Vectors have both magnitude and direction
• Velocity, for instance, is a vector 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, 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

• 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

• The worked example below illustrates how to determine whether a quantity is a scalar or a vector

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