Patrick Elliott wrote:
> So.. guess I am trying to work this out myself after all. lol

My apologies.  Real life conspired to take from me all but about five hours of
sleep for a while.

If I understand what you are trying to do, I think you can boil it all down to
figuring the "swing angle" (theta) of the car.  I'm assuming a rigid connection
(a "bar" with length L) between the center of mass (m) of the car and the track.
 The position of the track-end of the bar is given at any point in time, and
from this you can figure the car's velocity and acceleration in the direction
tangent to the track.

You have five "forces" acting on the car.

 * Gravity pulls it downward.
   |F_g| = m*g

 * Centrifugal force pulls it away from the center of the disc.
   |F_disc| = m*r_disc*omega_disc^2

 * Centrifugal force pulls it away from the center of curvature of the track.
   |F_track| = m*|v|^2/r_track

 * Centrifugal force pulls it away from the track-end of the bar as it swings.

 * The bar pulls it toward the track.

This can be further simplified, since the bar will counteract all force
components EXCEPT the component that can cause the car to swing from
side-to-side.  This component is tangent to the swinging arc at the car's
current position.  So, figure out the component of F_g, F_disc, and F_track that
is in this direction.  (You can use trig or direction vector dot products for
this, whichever you prefer.)

Now that you have the total tangential force (F_tan), calculate the tangential
acceleration (a_tan) it would cause from F_tan = m*a_tan.  Then, figure the
angular acceleration (alpha = a_tan/L).  Integrate over time to get the angular
velocity (omega), and again to get the angular position (theta).

Don't forget to calculate and then add the tangential velocity (v_tan) vector to
the total velocity (v) vector when computing F_track.  You will also probably
want to include some kind of frictional force (angular velocity damping) so the
car does not keep swinging forever.

I hope this helps.

http://en.wikipedia.org/wiki/Centripetal_force
http://en.wikipedia.org/wiki/Angular_acceleration

P.S. Your intuition that "forces" don't exist as such is a good one, especially
at the macro scale of everyday life.  They are, however, extremely useful
abstractions.

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