What are the Physics of a loop-the-loop

[AHUGEMUSHROOM]

What are the Physics of a "loop-the-loop"

I have to design an investigation that relates to the circular motion of a body executing a vertical "loop". Obviously, the physics involved varies quite significantly depending on the method of motion and the physical boundaries employed.

So, I was wondering if anyone one knew of some websites/links that would help with undertaking some background research before initiating the planning phase of the investigation.

 

[Khashishi]

Maybe check out
http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/shawna_sastamoinen/Roller_Coasters.htm

The main concept you need to know is centripetal acceleration.
$a=v^2/r$
The key insight is that the downward centripetal acceleration at the top of the track must exceed the gravitational acceleration for the coaster to stay on the rails. You can calculate the speed such that |a| > |g| at the top of the loop. The roller coaster ought to be moving faster than this.

You can calculate the speed by invoking energy conservation, and using the gravitational potential energy = mgh.