Scalar and Vector quantities

All physical quantities in the study of physics can be classified as scalar and vector quantities. You will need to know the differences between them and be able to identify whether a particular quantity is one or the other. Simply put, a scalar is a quantity without a direction. A vector, on the other hand, is a quantity or process that has both a value, which we call a “magnitude” and a direction.

To explain the difference more clearly, let us look at the quantities: speed and velocity. Speed is a scalar. By itself, speed simply refers to how fast something is going. It gives us no indication of which direction that quantity is being directed towards. Velocity is a vector. It is the rate of motion of an object in a given direction.

For example, consider a boy who walked 4 km towards the east in 1 hour. He would have a speed of 4/1 = 4 km/h. But to describe his velocity, you will have to include the direction of movement, in this case, east. Therefore, his velocity is 4 km/h, east.

But consider if the boy walks 2 km towards the east, then walks 2 km in the opposite direction (the west), in 1 hour. His speed remains unchanged because he still travelled 2 + 2 = 4 km in 1 hour. However, his velocity is now 0 as he has not travelled any distance in any given direction.

Here are some other examples of scalars and vectors:

Scalars – Temperature, distance, mass, mass, frequency, pressure

Vectors – Displacement, velocity, acceleration, weight, field strength, force, momentum

Adding and resolving coplanar vectors

An important concept to understand in tandem with scalar and vector quantities are coplanar vectors. Coplanar vectors are vectors which lie on the same plane. They need not be in the same direction. Collinear vectors are a subset of coplanar vectors which act along the same line, i.e. they act in the same or opposite direction of one another.

We will first look at how to add collinear vectors.

In the above case, the two force vectors are acting in the same direction. This means we can simply add them to find the resultant (the overall effect of the vectors on an object). The resultant here is 6N + 2N = 8N

Now, the vectors are acting in opposite directions. However, since they are collinear, the calculation remains the same, simple addition. If we assign the direction of the 6N vector to be positive, the resultant is simply 6N + (- 2N) = 4N.

In the case where you have two coplanar (not collinear) vectors acting at a right angle, you will need to use the Pythagoras’ theorem. In the above image, you can use the Pythagoras’ theorem to calculate the force of the resultant vector (x) from the two vectors which are at a right angle to each other.

x = √ 3²+4²= 5N

Conversely, any vector can be resolved into a vertical and horizontal component which are at a right-angle to each other. Here, you would need to know the angle at which the vector is acting to the particular reference point. In the above image, we assume that the angle is 30°. From there, we can use trigonometry to calculate the vertical component (y) and the horizontal component (x).

x = 6cos(30°) = 5.20N (3 s.f.)

y = 6sin(30°) = 3N

While scalars and vectors quantities are basic concepts, it is normal to have trouble grasping them for a start. If you need additional help, consult us for high-quality physics tuition, so that you can understand the concepts you need to ace your exams.