4.1.1

# 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.

### 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.

• 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.

### 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.

### 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.

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