Using Calculus to Find the Centripetal Acceleration Formula v²/r (proof, derivation)

Found this pretty easy myself too. If you have the mathematical toolset and a correct intuition about the world, it is very easy to find a mathematical formula to represent your intuition. The hard part in pioneering physics is not putting your ideas into math, it’s having and finding that idea or intuition about the world around you in the first place, and then being able to create the mathematical tools to help you represent the world in math. In this video I already had knowledge of the Cartesian Coordinate system, which is something we take for granted, something we think as “rudimentary” simply because we learned it in elementary school, when it took many millennia of human existence for Descartes to invent it. Likewise, we think algebra as a “basic” thing everyone should know, and therefore we take it for granted, when in reality it took a lot of ingenuity and effort to invent it. And now about physics. I probably would’ve never even thought up of such a thing like F=MA, seeing that not even the Ancient Greeks discovered it, and furthermore it took more than a 1000 years after the Greeks for Newton to discover it. Much less would I be likely to think of rotational motion as being caused by a center-seeking force, despite how easy it is for me now to understand it.