# Force

Once upon a time, a misanthropic teenager named Isaac Newton decided to be a genius.
The genius decided that he’d be interested in the physical properties and relations between stuff, and he’d try and describe it using mathematics. It was a wild success, and he became the father of physics or whatever.

Same guy decided to turn, like, 21 or something, and invent differential calculus for some odd reason (to describe planetary motion, I believe). Strange guy, I guess there was less light pollution back then. I’m hardly conscious of the planet’s existences up in the sky. At best, I see Venus or whatever standing out like a drama queen.

So Newton was a cool guy, among the many things he churned out was the concept of Forces in dynamical systems.

A quick run through of Kinetics – you can describe a physical system in terms of its physical coordinates. Here comes the SUVAT Equations to save the day.

When it comes to forces though, you enter the realm of Dynamics, and you encounter Newton’s III Laws:

1. In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force – incoming the concepts of Inertia, and Inertial Frames of Reference.
2. In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.
3. When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Forces are Vector quantities, so they have both direction and magnitude tied to them. For instance, you can imagine your own weight (a force) as an arrow (a common representation of a vector) pointing straight down, whose length is the magnitude of your weight. A 200lb man will have an arrow twice as long as the 100lb girl, and so on, but that direction will always be pointing to the center of the Earth (or wherever the center of mass of the Earth happens to be).

Formally, the force applied to an object is defined as being equivalent to the change in the object’s Momentum with respect to time: $\vec{F}=\frac{d\vec{p}}{dt}=m\frac{d\vec{v}}{dt}=m\vec{a}$

The m there is the mass of the object – but Newton didn’t quite think of it that way. Actually, that was just his lil physics-maths Constant of Proportionality, because as far as I know, all Isaac knew at the time was that forces accelerated bodies, and conversely, that accelerated bodies were acted upon by forces. That’s it.

Newton thought of that lil m as something called Inertia, an object’s ability to resist change in momentum (refer to N.Law #3). Something with a large inertia (say, a car) acted upon by a force F would accelerate less than an object of small inertia (say, a speck of dust). Obviously that dust speck will go flying with a gust of wind, but it’d take a tornado or something to do the same to the car.

It was later then, that I think inertia was tied to an object’s Mass. Of course, it makes sense now, but whatever, history lesson over.

This all comes in handy when you’re trying to pass physics exams, and also if/when you decide to be an engineer, because it describes the world pretty gd well.

Newton used the idea of forces to describe a number of phenomena in his Principia Mathematica, and one example he gave in that text was his Universal Law of Gravitation: $\vec{F}=G\frac{m_1m_2}{\vec{r}^2}$
Which does a pretty gd good job of describing the force of Gravity.

Philosophical aside here: why does gravity follow an Inverse Square Law? I’mma look this up, see what I dig up, and update this post with a brief later. For a more “derivational”, more “grassroots” post, go check out the Universal Law of Gravitation, it’ll probs be more explicit (parents be advised, too much physics at a young age may result in social exclusion).

— Ah, it’s because we assume the effects of gravity is evenly radiated outwards, and the surface area of a sphere is proportional to the radius squared ($A=4{\pi}r^2$). So if you imagine the “intensity” at a distance r from the “source”, it drops off inversely to the radius squared.