All physical quantities can be classified as either a scalar or a vector. Scalar and vector quantities require different mathematical treatment.
Key Concepts
A scalar quantity is a measurement with magnitude (and usually a unit), e.g. 5 cm, 27 000 elephants or -0.0036 A. Energy is an example of a scalar.
A vector quantity is a measurement with magntiude, direction (and usually a unit), e.g. 10 ms-1 North or 6.35 N to the right. Vectors are usually drawn with an arrow in the correct direction, where the length of arrow represents the magnitude. A force is an example of a vector.
Some quantities have scalar and vector equivalents:
- Distance is a scalar and displacement is a vector
- Speed is a scalar and velocity is a vector
- Acceleration can be either (but is usually the consequence of a resultant force - vector)
Scalar quantities can be added or subtracted like normal, provided they are measuring the same thing. However, directions must be considered when adding vectors.
Two forces of 3 N and 4 N act on a body. What is the largest possible resultant force? What is the smallest possible resultant force?
If the forces combine in exactly the same direction, the resultant force is 7 N (maximum). If the forces are in exactly the opposite direction, they mostly cancel, leaving 1 N remaining (minimum).It is possible to add any vectors in 2 (or more) dimensions by considering the magnitude of these vectors in 2 perpendicular directions (e.g. vertical and horizontal). Similarly, any combined vector can be resolved (split) into 2 perpendicular components. Scale drawings or trigonometry are required.
How much of Scalars and vectors have you understood?
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