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## An Introduction to Newton's Laws of Motion

By Akshat B on August 24, 2021

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NEWTON’S LAWS OF MOTION, a collection of 3 axioms, which a student waits to enter grade 9 in order to learn about. But what if I told you that you already know these ‘laws’ ever since you were a child. Allow me to prove it to you.
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“Child is the Father of Man”  - William Wordsworth
Imagine the baby version of yourself (3-4 y/o) is playing with one of his/her toys. For my convenience, I will imagine that the baby is a girl named Gita. She is playing with one of her favorite classic cinderella dolls when she was called upon by her mother for dinner. She puts her doll on her table and goes for dinner. After completing her dinner, she wants to continue playing with the doll, where do you think she looks for the doll? Give it a thought.
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Did you think about it? Well, she would obviously look for it on the table where she left it. But why did she do that? Well let’s imagine that the doll isn’t there, what would be her reaction? She would look here and there, and if she didn't find it, she would go to her family members and ask “Mom,did you take my doll?”, “Daddy, did you take my doll?”, etc. Why is she doing so? Because deep inside her mind she knows that the doll cannot move on its own unless someone else does ‘something’ to it.
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Well now let’s just ask her to run as fast as she can and hit her head on the wall. Will she do it? No right, even if she agrees, she’ll slow down near the wall and would want to minimize the pain. Why is she doing this? Because she knows that the harder she’ll hit the wall, the wall will hit her back with the same strength.
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Let’s take a moment to appreciate the fact that all these laws, theories etc are already inbuilt in us from childhood only.
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Well as the creatures with an inbuilt fondness of observing patterns in this world, various human beings have come up with an explanation of such behaviour.
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Aristotle, a famous Greek philosopher,  (known as the “Father” of many sciences ranging from biology to social science and such a renowned thinker that throughout medieval Europe he was simply called “The Philosopher'') postulated that every object has a tendency to come to rest. This interpretation is not accepted in modern day physics, but let's give it a thought. Roll a ball, it will come to rest after some time; throw a ball up, it will return to ground, bounce once or twice, and then will come to a rest. We can give many examples which go hand in hand with this idea, but all we need is one counterexample so we can reject this theory (this is called proof by contradiction). I’ll leave it on you to come up with a counterexample on the matter.
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Another interpretation was formulated by yet another gentleman named Galileo Galilei. He did some practical experiments and a thought experiment. His practical experiment was concerned with two inclined planes connected end to end. What he observed was- irrespective of the steepness (or slope) of the inclined plane, if he releases a ball from a certain height, it keeps on moving until it reaches the same height on the other inclined plane. He verified it by a number of practical experiments. Now comes the thought experiment, what if we make the slope of the other inclined plane zero. The ball has a tendency to move until it reaches the same height, and since the ball cannot ‘know’ that it won’t be able to reach the height, it will end up in an infinite struggle of reaching the same height meaning that it will keep on moving forever and ever. But the main question which arises here is that when this thought experiment is done practically, we find that the ball stops after some time. This observation, again, can be explained using Aristotle’s interpretation.
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Well this is the time I introduce to you a legendary character, Sir Isaac Newton. (Most of Newton's major breakthrough work was done by him when he was quarantining himself due to an epidemic).
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In his book, Mathematical Principles of Natural Philosophy, he documented three statements which are called “Newton’s Laws of Motion.”
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In Newtonian terms, the fact that Gita knew that the doll won’t move up by herself until someone does ‘something’ to it amounts to fifty percent of what is called the Law of Inertia. The other fifty percent takes its roots from Galileo's experiments and essentially says that any object which is in motion will remain in motion until someone does ‘something’ to it.
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Moving on, realising the significance of that ‘something,’ Sir Isaac Newton went on to call that something as (drum roll) FORCE. If we ask Gita if she wants to throw a ball farther than previous attempt, assuming she is now old enough to speak, what will she do? We can expect her to reply that “I’ll put in some more effort”. But this leads to our observation that to get more acceleration, (rate of change of rate of change of position), we need to put even more effort. Also the bigger the body is, the more force we need to apply.
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From here, Sir Issac Newton concluded that Force is directly proportional to mass and acceleration.
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F∝ ma
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F = kma
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Now I would like to address a common myth that the value of k is experimentally determined to be equal to 1, which is not the case. If we tell this thing to Gita, she’d curiously ask what exactly is that experiment, and we don't have any answer to it, then why is k=1? Well since force is now defined as a completely new quantity, it doesn’t have any kind of relation with any other already existing quantity, Sir Isaac Newton had full liberty to ‘Choose’ the proportionality constant, which he, perhaps to make a life simpler, chose it to be 1. Could he have chosen 76, yes; could he have chosen 69.934467, again yes; did he choose, no. What if he had chosen some other number? It won’t have any qualitative impact, only quantitative numbers would change, the value of other linked constants (such as G) would change and we’ll have to add another constant to our list of fundamental constants, maybe named as Newton’s Constant. It should be noted that this type of choice could be made only once, we couldn’t choose the value of G as 1 because G is interlinked with the second law.
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To understand this, consider the fact that everyone has the right to define their own units. For example, I have 27 apples. I decide to call 3 apples as 1 guf, therefore I have 9 gufs of apples.
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Now, let's move to the case where Gita was skeptical about hitting her head on the wall. We know that the harder we hit the wall, it will hit us back with an equal force, which is enshrined in Newton’s third law.
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We have come a long way, now let's officially introduce Newton's laws of motions, in bit more quantitative terms.
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1. Acceleration of a body is zero, if and only if, net external force is 0 A = 0, if and only if, F
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net
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= 0 This law, kind of also formalises the concept of mass. Mass is a quantity defined as the measure of inertia. More the body resists change in velocity, the more will be its mass. We can deduce from here that this new unit which we have defined as force, is the cause of acceleration. So we have essentially 2 statements, a∝f a∝1/m Bringing above two equations together, we get a ∝ f/m.
2. Net external force is directly proportional to rate of change of momentum P ≡ mv F
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net
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= (kΔp)/t = km(Δv)/t Putting mΔv = a F
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net
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= kma (k = 1 as mentioned above)
3. Every action has an equal and opposite reaction F
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AB
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= -F
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BA
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Now addressing the elephant in the room, Aristotle's theory was disregarded because now we had a better theory which was even General than Galileo's. What we did was, in order to make Galileo's thought experiment possible, we added a new (actually a result of an already existing one) force called friction. Now we can easily explain the ball stopping after a while by saying that friction is the force which causes an acceleration in the opposite direction of the moving ball eventually causing it to stop. Now if we accept Newton's laws, we are obliged to reject Aristotle's theory.
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Well what is mentioned above is a simplified form of the laws which are very different from the original verbatim. I’d leave you with the original text of laws of motion from principia and invite you to frame your own interpretation out of it and if you’d want to share your insights, you can sign up for free live zoom sessions @ schoolhouse.world
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1. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.”
2. The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”
3. To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts” - principia, english translation by ANDREW MOTTE.