For the love of God, please stop calling centrifugal force a "fake" force; it confuses the fuck out of people. When you say that, students take it as "centrifugal force is fake, therefore I shouldn't include it on any of my diagrams".
Please call it an "apparent", "emergent" or "reaction" force.
Ex: You are at the bottom of a dip sitting in a roller coaster. Relative to a rotating frame of reference, you are in equilibrium.
This is what happens all the time: Students draw the diagram. Force of gravity down, normal force(only to gravity) up, centripetal force up. You end up with a net force up and you get stuck because you thought you were in equilibrium.

Smug high school physics teachers that say "Ackchyually centrifugal force doesn't really exist" make me want to off myself.