Loop the loop: Sphere, hoop, disk rolled down a looped track.

Loop the Loop: Moment of Inertia. To make it completely around the loop, at the top of the loop the velocity of the object must be great enough so that v^2/r = g. We must also take into account rotational kinetic energy because the objects are rolling without slipping. Also, total energy at the top of the loop must equal potential energy at point A. The difference in rotational energy are enough to cause the hoop to not have the necessary velocity to stay on the track.
UCB Index: 
A+25+10
Demo Diagram: 
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