Now if you are a structural engineer, you cannot go far in your life without dealing with mechanics. So I decided to put up an article regarding the very basic entities of mechanics, the objects one uses to relate the physical quantities to mathematics, namely scalars, vectors and tensors. I’ll begin by giving you a sense of what these English words mean in the realm of mechanics.
So, think of a guy beating another random person with his bat (I will let the readers decide if it was a cricket bat or a baseball one). Now the guy getting beaten does not care where the punches are coming from; he is bound to be in bad shape at the end of it. All that he knows is how hard is he getting punched. This ladies and gentlemen is what we call scalar quantities. Now imagine the guy with a bat going on a cricket field (yes, I am an Indian so I’ll be prejudiced towards cricket). Now his strokes are measured in placement and power. Suddenly he wants to move his bat in a particular direction. So, this is what many of us are familiar with as vectors. Now imagine that the bat is now a hammer and the guy wants to hammer a nail on a surface. Also try to think that this nail for him is to hang his shirt. So now, along with power & direction, the orientation of the nail is also important. The guy will find a hard time hanging his clothes on a nail which is on the ceiling or the floor. So the same beating is now a tensor, where the magnitude, direction and the sense of orientation are equally important.
The story of scalars is pretty mundane if you ask a mechanics person. It’s more of a layman’s best shot at science. Every morning, you would hear swarms of people buzzing with the latest weather[dot]com temperature updates to try and sound cool. They do not know a thing about heat and heat transfer. But hey! Temperature is not a bad way to measure how ‘hot’ or ‘cold’ is it outside. In fact, that’s the first thing I personally check before stepping outside. But the thing is it has very little use in the more advanced science. So generally speaking, scalars are more of a newspaper quantity than a scientific one.
Vector is where most of the world lights up. We all love vectors- be it the displacement, force or your favourite player’s (Sachin Tendulkar) shot. This is what has kept the world buzzing and afloat. But the sad part is that, the discussions of these quantities are often limited to classrooms. How often do you see the wind speed and if you do, when was the last time you noticed that there was direction alongside the number. How cool would it be if some guy jogging daily would check what the wind speed was and from which direction and then plan his course likewise. Vectors are here to stay and are soon going to be the next talking point among people. So if you have no idea regarding vectors go familiarize yourself with it.
In this race for popularity, Tensor is the sorry guy who is far lacking behind scalars and vectors. He is like the Royal Crown of United Kingdom, the ultimate formal executive authority but having virtually no say on political matters. It is a very obscure entity describing very specific quantities like stress and stuff. It is so uncommon that not even engineering undergraduate students are taught about it until their senior year. And the fact that it is often represented as a three by three array (matrix if you will) often makes me relate it to a tic-tac-toe game- tepid and boring. But, it is what most mechanicians feel, the ultimate tool to represent everything in the mechanics realm. So, if you are an unfortunate graduate student like me, you’ll find yourself stuck with it for most of the time.
Well, so much information even makes me confused. So let’s have a summary sort of, so to speak. Scalars while are very useful in your day-to-day purposes is pretty humdrum. Just imagine if you are a scalar person, then you are the ones in the mobs enjoying the fight. Vectors get a bit exiting. Imagine yourself as an audience to a spectacular match if you are a vectors’ fan. Tensor holds some what a sympathetic position. Being a tensor guy is like having the job of a carpenter superintendent. Not even the carpenter himself, who by the way has a pretty interesting job.