AQA A-Level Physics/Scalars and vectors

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The term "scalar" means either that a quantity has no direction or to refer to such a quantity, whereas the term "vector" refers to a physical quantity or interaction that possesses both magnitude and direction.

Examples of scalars include:

  • Temperature
  • Energy
  • Distance
  • Speed
  • Mass
  • Charge

By contrast, the following quantities are vector quantities:

  • Velocity (This is the distinction between speed and velocity, hence why a negative velocity is possible but not a negative speed)
  • Displacement (Vectored distance)
  • Momentum (Equal to mass multiplied by velocity; a vector multiplied by a scalar remains a vector)
  • Impulse (Change in momentum)
  • Force (Not a physical quantity, but force remains an essential point in mechanics. Note that F = ma shows that force is a vector in the same way that p = mv or I = Δp does)
  • Acceleration

Vector quantities are typically represented by arrows in the correct direction on forces diagrams. Note that the type of arrow differs by the quantity in question. For example, acceleration is typically illustrated by way of an arrow with two non-filled heads along the body (e.g. ->->- 5ms -2 )

Two vectors quantities may be added if they are representative of/act upon the same body; this is usually done using a scale diagram.

A single vector may be broken up into a number of perpendicular parts equal to the number of dimensions in which it is acting. For example, a force of (√2) Newtons that acts at an angle of 450 to the horizontal may be split into a force of 1N acting vertically upwards and a force of 1N acting horizontally.