Scalars & Vectors

• Scalars & Vectors:

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

  
• • Some vectors and scalars are similar to each other
  • For example, the scalar quantity distance corresponds to the vector quantity displacement
• Table showing the difference between vector and scalar quantities:

  
• Difference between distance and displacement:

  • Distance is a measure of how far an object travels
  • It is a scalar quantity - it has a size (magnitude), but the direction is not important
  • Consider a 300 m race:
  • From start to finish, the distance travelled by the athletes is 300 m
• The athletes run a total distance of 300 m:

  
• Displacement is a measure of how far something is from its starting position, along with its direction

  • It is a vector quantity - it describes both magnitude and direction
  • Consider the same 300 m race again
  • The athletes still run a total distance of 300 m (indicated by the red arrow)
  • However, at the end of the race, their displacement is 100 m to the right of the starting point (indicated by the green arrow)
  • If they had run the full 400 m, their displacement would have been zero
• The athletes run a total distance of 300 m, but end up 100 m from where they started: