AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Scalars and vectors: Nature of scalars and vectors.
A scalar is a physical quantity that has magnitude only, such as mass, time, speed, distance, energy or temperature.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 1 of 10
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A scalar is a physical quantity that has magnitude only, such as mass, time, speed, distance, energy or temperature. A vector has both magnitude and direction, such as displacement, velocity, acceleration, force, momentum or electric field strength. Direction may be given as an angle, a bearing, or a sign in one dimension. Scalars add by ordinary arithmetic, but vectors must be combined by vector addition, for example using a scale diagram or resolving into perpendicular components. For instance, walking 3 m east then 4 m north gives a distance of 7 m but a displacement of 5 m at 53° north of east. Recognising whether a quantity is scalar or vector is essential before choosing the correct method for a calculation.
What earns the marks
- A scalar quantity has magnitude only and no direction.
- A vector quantity has both magnitude and direction.
- Examples of scalars include mass, time, speed, distance, energy and temperature.
- Examples of vectors include displacement, velocity, acceleration, force, momentum and electric field strength.
- Vectors are added by taking direction into account, for example by drawing a vector triangle or by resolving into components.
- Scalars are added using ordinary arithmetic because direction is not involved.
- In one dimension, direction can be represented by a positive or negative sign.
Common mistakes and how to put them right
Treating speed as a vector.
Put it right: Use velocity when direction matters.
Adding vector magnitudes arithmetically without considering direction.
Put it right: Use a vector triangle or components to find the resultant magnitude and direction.
Confusing distance with displacement.
Put it right: State the direction when giving displacement.
Exam tips
- When asked to classify a quantity, state whether it has direction as well as magnitude, and give a brief reason.
- For vector addition, always state both the magnitude and direction of the resultant, using an angle or bearing as appropriate.
- Use a clear scale diagram or resolve into perpendicular components; show the direction of each component with an arrow or sign.
Try the lesson
The start of the Scalars and vectors: Nature of scalars and vectors. lesson, made from checked teaching notes for this specification point.
Have a go first
Which of the following quantities is a vector?
Listen
A scalar is a physical quantity that has magnitude only, such as mass, time, speed, distance, energy or temperature. A vector has both magnitude and direction, such as displacement, velocity, acceleration, force, momentum or electric field strength. Direction may be given as an angle, a bearing, or a sign in one dimension. Scalars add by ordinary arithmetic, but vectors must be combined by vector addition, for example using a scale diagram or resolving into perpendicular components. For instance, walking 3 m east then 4 m north gives a distance of 7 m but a displacement of 5 m at 53° north of east. Recognising whether a quantity is scalar or vector is essential before choosing the correct method for a calculation. A strong answer earns marks for these points. A scalar quantity has magnitude only and no direction. A vector quantity has both magnitude and direction. Examples of scalars include mass, time, speed, distance, energy and temperature. Examples of vectors include displacement, velocity, acceleration, force, momentum and electric field strength. A common slip: Treating speed as a vector: speed is scalar because it has magnitude only, whereas velocity is a vector because it includes direction. Instead, use velocity when direction matters. Exam tip: When asked to classify a quantity, state whether it has direction as well as magnitude, and give a brief reason.
See it
Key words
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Scalar
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Vector
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Vector addition
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Direction in one dimension
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See every definition
- Scalar
- A physical quantity that has magnitude only, such as mass, time, speed, distance, energy or temperature.
- Vector
- A physical quantity that has both magnitude and direction, such as displacement, velocity, acceleration, force, momentum or electric field strength.
- Vector addition
- Combining vectors by taking direction into account, for example using a scale diagram or resolving into perpendicular components.
- Direction in one dimension
- Represented by a positive or negative sign.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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