# Newton’s Laws

## Description and application of the Newton’s Laws, in the ambit of the classic Mechanical.

I wish to make some useful explanation to the Newton’s Laws.

The laws are three:

• The law of inertia
• The law of forces
• The law of interaction

1) INERTIAThe firt of the Newton’s Laws are the explanation of Inertia. But, what is this?
Inertia is the idea that everything mantains the same velocity in the universe, you don’t see that strange? No? Try to think about a ball on space, if we push it, accordingly to the First Newton’s Law, the ball continue float in a direction at the same speed forever! You can say: “I know, I’ve seen a lot of science/fantascience videos!”. What if I told you that the thing goes in this way anytime and everywhere?
Yeah, it seem strange, but when you push a ball on Earth, it really want to continue to fly with same speed, but it can’t, because of a moltitude of forces! We will talk about these forces in the Second Law, for now, our First Law is: “Things want to mantain constant velocity”.
FAQ:
Q: “What if these things aren’t moving?” A: “Zero is a velocity!”Q: “So in space there are no forces?”A: “Yes, there are, but we usually approximate them to null (The gravity force, is the major force in space, and the weaker in Universe!)”
2)FORCESThe forces are the name associated to the “action” that we make or we see made on an object, for example, pushing a ball, a car, a chair, a bomb, is a force! Ok, we know what is a force, but how can we predict the movements of the bodies, knowing that?
Law Two advance.Here is the most famous Newton’s Law in math terms:
F = m * aLet explain: F stands for: “The sum of all the forces”= stands for… equal! (But you already know that, meh?)m stands for “The inertial mass of the object”a stands for “The acceleration of the object”Let me explain better:
The sum of the forces is referred of a vector sum because when we push things we make a direction and a verse of the force, not only the value.
The inertial mass isn’t a strange type of mass, but the same that we can mesure with a balance.
#Little thing, the mass that we mesure with balance is called gravitational mass, the fact that these two mass are proportional is a very important thing in Einstein theory for example, and is not so obvious#The acceleration(is vector too) permit us to determine the movements of the body.
So we now have joined the forces with the acceleration, we can describe the movements of the body!So whit this new rule, we can explain because the thing slow down when pushed on Earth: The friction, the friction is a force opposite to the speed of the body that occours with the contact of two body, like pen on table, ball on camp, ball on air, the friction, according to the second law make a negative acceleration and slow down the object!
3)INTERACTIONThe last and more subtle of the Newton’s Laws are the famous: “If I interact with a force on an object, the object interact with a force equal and opposite to the mine”. Can be described mathematically in this way:
F1 = -F2Where F1 is the force with that I push an object, and F2 is the force with that object push me! It’s seems simply, but hide a little problem, i the first Newton formulation, the forces are instantaneous, but now we know that exist a speed limit for everything (The well know speed of light), so modern theory renewed this Law, and now we use the conservation of momentum and angular momentum instead!FAQ:A: “If I push a ball, and that ball push me, why the ball move?”Q: “Because the forces F1 and F2 are applied to different corpse, so the acceleration change however (the thing that don’t move, or better, that maintain his velocity, is the so called: center of mass of the sistem)”
Finally:I want to summarize all these laws in a simple way: The math way, the simplest and more elegant ever.
First & Second Laws:
F = m * a  (Second)F = 0 => m * a = 0 => a = 0 => v = constant  (First)Third Law:F1 = -F2
or in modern way:
dQ/dt = 0 => m * a = F1 + F2 = 0 => F1 = -F2  (Same forces)
dP/dt = 0 => M1 = -M2 => |F1|b = |F2|b => b = 0  (Same directions)
where: Q = momentum, P = angular momentum

So, I wanted to make a brief summary of the Newton’s Laws to help remembering for study, hope this help! Bye!

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