Inertial Paths, Fake Forces, and Rotating Spaceships

Recently I just read a whole bunch of relatively shabby explanations from students of why rotating spaceships can simulate gravity.  These are seniors who have taken a full year of physics and are currently in my astronomy class so they are well equipped to give a decent explainer, but most of them just said something like "centripetal centrifugal, blah blah blah".  As I was looking over their work, I realized that one of the major conceptual problems is that a true understanding of why this works involves a tale of two fake forces:

Fake force #1: 

Gravity

You don't actually ever feel the force of gravity pulling you down into the ground (contrary to what I teach my student to draw on free body diagrams!).  Rather, you only feel the normal force pushing up on you (the opposite direction!).  This was one of Einstein's key insights in revealing the General Theory of Relativity.  Since gravity is really just an alteration of your inertial path ("warping of spacetime"), it is not a force. What you feel is the ground pushing up against your inertial path so you assume something is pulling down on you.

Fake force #2:

Centrifugal forces

You don't actually ever feel a force pulling you out of a circle (or a turn).  Rather you feel a force directed towards the center of the arc of the circle of the turn you are making (the opposite direction!).  The force is required to keep you from following your inertial path (which is tangent to the circle).   Since you feel the force pushing inwards on you against your inertial path, you assume something is pulling outward on you.

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So, "artificial gravity" on space stations (accomplished by walking on the inside of the outer surface of rotation) is really the swapping of one fake force for another.  Either way, what you feel is a force on your feet preventing your from following your inertial path (the one you would take without any forces).

According to Einstein, we've been experiencing gravity as an upward acceleration on our feet our entire lives.  So, if you stand on the inside of a rotating surface, a 9.8 m/s/s centripetal acceleration to keep you going in a circle will substitute quite nicely for a gravitational field of 9.8 N/kg.  In one case we are accelerating inward to curve through space and in the other we are accelerating upward to curve through time.

The movie we were discussing was "Interstellar"

"If a person falls freely, he will not feel his own weight" - Einstein's 'happiest thought'