Parametric equations for vertical and horizontal circular motion

[Flin]

Hello. I apologize if I put this in the wrong section.

I got this problem with the assignment I am currently working with. I have to set the position function for motion as a parametric equation for motion in circular motion, horizontal and vertical respectively.

While I do know the position function for uniform circular motion as a parametric equation I am unsure how this translates to these two types of cicurlar motions. This is rollercoaster physics, so it can be seen as how to set up parametric equations for motion in the merry go round and a loop (circular).

Thank you in advance!

 

[LCKurtz]

I would start with the parametric equation of a torus, which involves a couple of angles and the two radii. Then give the angles angular velocities.