Scalars & Vectors
Physics: AQA A Level, topic 4.1.1
Scalars and Vectors
Scalars are quantities with a magnitude (size) only. Vectors have a magnitude (size) and a direction.
Mass
- Mass is a scalar.
- Mass describes how much of something there is.
- Mass has no direction.
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.
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.
Force
- 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.
Acceleration
- 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.
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.
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.
Test yourself on Scalars & Vectors
What is a vector quantity?
Which of the following is NOT an example of a vector quantity?
Which of the following is a scalar quantity?
Adding Vectors Graphically
How do we find the resultant vector?