• 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

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