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1.2.2Forces and Motion

Scalar and Vectors

5 min read 4 parts Lesson 11 of 26 1 quiz

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Section 1 of 4Definitions

1.2.2 Scalar and Vectors

Every physical quantity is either a scalar or a vector, and the difference is whether direction matters.

Scalar
  • A quantity with magnitude (size) only, and no direction associated with it.
Vector
  • A quantity that has both a magnitude and a specified direction.
Distance
  • A scalarthe total length of the path travelled, regardless of direction.
Displacement
  • A vectorthe straight-line change in position from the start to the end point.
Speed
  • A scalarthe rate of change of distance, with no direction given.
Velocity
  • A vectorthe rate of change of displacement, which includes the direction of motion.

Section 2 of 4Examples

Examples
Scalar examples
  • Mass, temperature, energy, time and speed are all scalar quantities.
Vector examples
  • Force, weight, acceleration, momentum and displacement are all vector quantities.
Direction matters
  • A vector quantity changes when its direction changes, even if its size stays the same.
Walking a loop
  • Walking a closed loop gives a distance travelled but a displacement of zero.

Section 3 of 4Deciding in an Exam

Ask the same question each time to identify a quantity correctly.

1
Ask whether the quantity could be fully described by a number and a unit alone.
2
If the quantity needs a direction to be complete, it is a vector.
3
Check whether the question asks for distance or displacement, which are different.
4
Write the answer with a direction, such as to the north, if the quantity is a vector.

Section 4 of 4Exam Checklist & Tips

1.2.2 – Key Points for the Exam

  • Scalar A quantity with magnitude only, such as mass or speed.
  • Vector A quantity with magnitude and direction, such as force or velocity.
  • Magnitude The size or numerical value of a quantity, without any direction.
  • Displacement The shortest straight-line distance from the start point to the end point, in a stated direction.

Common Mistakes

  • Describing speed as a vector; speed has no direction, but velocity does.
  • Saying displacement equals distance travelled; for a journey with turns, displacement can be much smaller.
  • Giving a vector answer without a direction, which loses marks in calculations involving forces.
  • Calling force a scalar because it has a size; a force also needs a direction to be fully described.
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