Scalars and Vectors

You must know the definitions of a scalar and a vector.

A scalar is a quantity that has magnitude only (it has no direction). Common examples include; temperature, speed, mass and distance.

A vector is a quantity that has both magnitude and direction. Common examples include; forces, velocity, acceleration and electric current.

There are a few quantities that be expressed in either scalar or vector form. This can be a bit confusing so let’s look at one example.

When objects move, they change their position in both space and time. We can measure the change in location (position in space) and the change in time (the time it took to complete the change in location). If we measure the change in location as a distance and divide by the time taken, we get the speed of the object. This in turn gives us the common equation; speed (m/s) = distance (m) / time (s).

But for some moving objects, the distance moved is not very useful. Think about a pendulum that swings left and right. It is constantly covering more and more distance but it is not getting further and further away: all it is doing is moving a certain amount to the left then a certain amount to the right. We have a special word for distance that is in a specific direction, “displacement”. So a pendulum has a displacement to the left and to the right, both being equal amounts away from the centre position in opposite directions.

Clearly (I hope) displacement is a vector, because it is “how far in a specific direction”, whereas distance is just “how far” and is therefore a scalar quantity.

Speed and velocity are also a pair of similar scalar and vector quantities. In this case it’s easy to remember which is which since they both begin with the same letter as their quantity type (scalar speed and vector velocity).

For now this may sound as if it is unnecessarily complicated but when we come to look at how forces affect each other, and how velocities can also be combined (such as wind speed and an aircraft’s rate of movement) we will discover that the properties of vectors become very important – and extremely useful!