A cat story..

Consider a lonely cat on a straight and infinitely long pavement with no cars and traffic lights. The sky is murky and the city is silent. Actually a point on a line will do. This technique is called abstraction; it really doesn’t matter whether it is a cat or a dog, or if it is lonely, or if it is on a pavement.

We call this initial point the origin. It’s not that the cat is the first of its kind; the origin means that this is where our line is based. In physics terms, this is called our point of reference.

We still need to determine which direction is positive. As the cat leaps 1 meter to the right, you determine that that direction is the positive direction, denoted using +x. That is, the positive x axis direction.

This is our frame of reference, since we now have a direction as well. Mathematically, if we let the unit be in centimeters (cm), then we can denote the initial position as 0, and the terminal position as 5.

Just then, a kind man walked by. He notices the cute cat on the sidewalk, and approaches, trying to offer it food. However, the cat is scared as it thinks that this is just yet another police, possibly trying to chase it away. The cat runs to the left for 2 meters before the kind man places down cat food at the origin.

Above is an abstraction of what just happened. The black dot is the origin and the initial location, and the cat traveled a total distance of 3 meters, as seen by the purple arrows, from the initial location (black) to the terminal location (light grey). However, the difference in initial and terminal location is only 1 meter left. This is called the total displacement of the cat.

Scalars

Scalars are physical quantities that are defined by their magnitude (only). As shown in the example above, distance is a scalar value since every meter travelled adds on to it, even if the end is the same as the start. One other important way to differentiate scalars from vectors is to note that scalars do not have direction. Examples of scalars in real life include: volume, density, speed, energy, mass, and time.

Vectors

Vectors are quantities that are defined by both magnitude and direction. However, they do not have position, meaning that if we moved a copy of a vector 20 units to the right, they would still be the same vector. Vectors are calculated by subtracting the starting position from the final position. As shown in the example above, displacement is a vector value since it only looks at the final and initial position, and also has direction. Everyday examples of vectors include: velocity, force, pressure, displacement, and acceleration.

Scalars and vectors are two ways physicists describe quantities. Scalars have only magnitude, and every change in position matters, while vectors only consider the absolute change from the starting point to the ending point.

You can also find more videos on our YouTube, join our Discord for a helpful community, and check out our courses for more help!

Happy learning!