Scalars & Vectors

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Scalars and Vectors

Scalars are quantities with a magnitude (size) only. Vectors have a magnitude (size) and a direction.

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  • Mass is a scalar.
    • Mass describes how much of something there is.
    • Mass has no direction.
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Distance vs displacement

  • Distance is a scalar.
    • Distance describes how far something has travelled.
  • Displacement is a vector.
    • Displacement describes the distance from one place to another.
    • Displacement also describes the direction from the start to the end.
  • E.g. If an ant travels 6 metres east then 2 metres west:
    • Distance = 8 metres.
    • Displacement = 4 metres east.
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Speed vs velocity

  • Speed is a scalar.
    • Speed describes how fast something is travelling but says nothing about direction.
  • Velocity is a vector.
    • Velocity describes how fast something is going and in what direction.
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  • Force is a vector.
    • We need to know the magnitude (size) of the force and also the direction it acts.
  • Weight is an example of a force and so weight is a vector.
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  • Acceleration is a vector.
    • We must know the magnitude (how quickly something is speeding up) and the direction (in which direction it is speeding up).

Addition of Vectors - Drawing

In physics, it is often important to add vectors together. For example, when calculating the resultant force on an object.

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Head to tail

  • We can add vectors together by drawing them head to tail.
  • Consider these two velocities acting on a man who is walking on a moving train.
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Resultant force

  • By accurately drawing the two vectors head to tail, we can measure the resultant velocity of the man.

Addition of Vectors - Calculation

Instead of using a drawing, we can sometimes use a right-angled triangle to add vectors.

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Resultant force

  • Consider the forces acting on this object.
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Right-angled triangle

  • We can form a right-angled triangle with these two vectors head to tail.
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Pythagoras and trigonometry

  • Vectors can be added by visualising the vectors forming a closed triangle.
  • Pythagoras and trigonometry can then be used to find a missing side.

Jump to other topics

1Measurements & Errors

2Particles & Radiation


4Mechanics & Materials


6Further Mechanics & Thermal Physics (A2 only)

7Fields & Their Consequences (A2 only)

8Nuclear Physics (A2 only)

9Option: Astrophysics (A2 only)

10Option: Medical Physics (A2 only)

11Option: Engineering Physics (A2 only)

12Option: Turning Points in Physics (A2 only)

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