Hello and greetings for the day! I'm pleased to see you interested in learning the Fundamentals of Classical Physics. Let's tune in to a fantastically simplified article of the very complex postulates and objects above us, a special one and a basic one made just for you by Physics Simplified.
Now let's dive right in.
We start with the basic concept of Distance and Displacement. We often use these terms in real-life(that is questionable if life is real, but that's nothing to do with us mortals at least for now) scenarios. So, what is the difference between the two? What are their characteristics?
Distance, is basically a quantity that only has a size. So let's say I travelled from India, and went all the way to Spain by travelling 7900 Kilometers, I then relax in the kingdoms of Scotland after a distance of 1954 kilometers, and then all the way back to India by a massive 12954 kilometers in 7 days. So what is the distance I travelled? Well, it is simply:
Amazing, I travelled a lot of distance, and what was my displacement? Well, when you hear the term 'Displacement', what do you think of? It is basically "Dis-Place-ment" or you are getting moved away, or 'placed' elsewhere. After the whole travel did I get placed elsewhere? No! I ended up back in my beautiful home country, India. Therefore, the displacement was 0! Yes, 0! Simply because my 'Place' was the same(Well, this is untrue if I started off from Delhi but ended up in Mumbai, but we do not need to go to that MICROSCOPIC level for now and can stay at the global level).
Therefore, we can come up with a quick definition, the distance travelled by the body is the actual path covered by the body. It's simple, the path by the body which it covered, we do not mess with the path or anything, its 'actual' and 'real' and 'authentic'.
Displacement can be defined as the 'Unreal path travelled by the body'. No, no way, we cannot insult displacement in such a manner. Displacement can actually be defined as 'The change in position of the body'. Again, it's simple, the-change(changes are good and bad, but let's assume its neutral) in-position(it's location even though according to Issac Newton's equations there is no particular absolute location but that's not our business right now) of the body(or the mass).
We did level one at the easiest it can be, so let's proceed one step higher. Level 2.
Here we'll understand the difference between speed and velocity.
We have a perfectly amazing car on a perfectly horizontal road with perfectly no friction and on a perfectly fine day. This car travels a distance of 10 kilometers in only 10 hours, what a fast car right? So, if that's the case, what is the speed?
The speed is basically the distance travelled by a body d in some amount in time t.
Let's look at this car's business together. This superior car who claims to be the fastest of all travels 10 kilometers in 10 hours. To determine the speed, we must understand how much distance it travelled in time t. Thus, the formula of speed is:
v=d/t, where 'v' is the velocity, 'd' is the distance, and 't' is the time.
So, now, if the car travels 10 kilometers in 10 hours, we have:
v=10/10, or, in other words, the car travels 1 kilometer in 1 hour.
In your car, the speed-meter tells you the speed in kilometers per hour. In this case, 'the fastest car in the world' claimer travels at the fastest speed of 1 kilometer per hour! Can you imagine?! The car can travel a whole of 1 kilometer in only 1 hour, or take a round around my society!
Now the velocity is basically the same formula as that of speed, just with displacement instead of distance. So it is basically how much the body is displaced per unit time. The formula of velocity is also identical, just with an arrow above the 'v' in speed.
This is specially for the Physics definition interested ones, so others, please skip this-
Definition of speed: The rate of change of distance travelled by the body.
Definition of velocity: The rate of change in position by the body.
Just a quick note for those who are renowned for messing up their Physics, distance is always positive, because you cannot have 'negative' distance. I myself find it odd to have negative distance, because, what does it mean? You can have 0, but if you move anywhere, you travelled some distance.
And in the case of displacement, yes, you can have 'negative' displacement. This is because displacement is a vector quantities and vector quantities are upgraded scalar quantities with a new feature(not paid) direction. The negative symbol would resemble the object being 'displaced'(hopefully not misplaced) in the negative direction, or in case of linear motion, backwards.
Scalar and Vector Quantities.
OK, this is no joke. This is a very serious topic so don't dare to laugh. Scalar are quantities that need a scale. Vector are quantities that need a scale in a particular direction. In other words, scalar quantities are those quantities that only have a size, or the 'scale'. Vector quantities are those quantities that have both a size, and a direction.
And of course, all great physicists framed in the walls do not love using these simple terms such as 'size' since that's a bit too much related to real-life, and thus use the word 'magnitude' instead, and it means the exact same thing!
So in the above case, which is scalar and which is vector in terms of distance and displacement. Well, distance is scalar because we need a scale and the direction is useless for the distance, and on the other hand, displacement is vector, since we speak a lot about position, which involves the scale in a particular direction.
Thus, we have:
Scalar=Magnitude(Degraded version of vector)
Vector=Magnitude+Direction(New feature, upgraded version, totally free and only for enthusiasts!)
Quickly, let's look at force. Force, in classical physics is simply a push or a pull. A push, like pushing a car, or a pull, like pulling a box, that simple!
But let's complicate it for impressing those who love such complications(it's not that complex, so you may read this):
A force can be defined as an external element that causes a change in the state of the body in terms of motion and/or shape/size. This is the best defintion I can provide you in classical physics, but of course, if you'd like to complicate it to the highest possible, welcome to our Quantum Mechanics.
I'm sorry for switching topics abruptly, but the whole idea of this article is to quickly arrive here one fine day and check for some fundamentals if required. I aim to help you quickly cover up the fundamentals and that's exactly what I'm doing at this point in known time(in my clock because time is not absolute, but again, that's Einstein's business and not ours).
So this time, we look at dot product. A dot product is a special kind of multiplication, in which the vector quantities are converted into a scalar quantity. So the direction is often removed and of course, it cannot just be removed, and thus is mostly present in the form of 'cos', if you'd like more information about cos, e-mail us at email@example.com.
Moving on, the dot product is used in various cases to degrade these vectors and to make our wonderful lives simpler. For example, in case of work, no one wants to keep the direction and we want a scalar value at the end and therefore we do a dot-product. Again, if your brain is still curious, e-mail firstname.lastname@example.org.
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Author: Rishabh Pal
Publisher: Physics Simplified
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