# How is centrifugal force derived?

So far, I've understood the meaning and derivation of centripetal acceleration as $v²/r.$ Centrifugal force is therefore basically mass times the centripetal acceleration. But how exactly is the connection made, so that we know the inertia of an object is pulling it outwards with that force?

• This is meant to be a simple non-rigorous comment. Using Cartesian coordinates $(x,y)$ you know how to write out $\vec{F} = m\vec{a}$. You see a bunch of accelerations $\ddot{x}$'s, $\ddot{y}$, and $\ddot{z}$'s. Now label space with polar coordinates $(r,\phi)$. Writing out Newton, you will see a bunch of accelerations $\ddot{r}$'s and $\ddot\phi$'s, but also velocity terms $\dot{r}$ and $\dot{\phi}$. That's strange. I though forces were connected to accelerations. Anyways, one does physics in inertial reference frames most of the time. Inertial Cartesian, inertial polar, whatever – DWade64 Apr 13 '18 at 16:54
• However an inertial polar frame happens to be essentially the same as a rotating cartesian reference frame. But just looking at Newton in polar coordinates, move the velocity terms to the other side to make them into forces. And that's essentially the centrifugal and coriolis forces – DWade64 Apr 13 '18 at 16:57