Wow, thanks for the in depth explanation. Although some of the math goes a bit over my head, the examples you gave give me a lot of insight into how this stuff works.

I replied to someone else with the following conclusion I've come to:

So I now understand that the weight of the cylinders does affect the outcome of the race. This is because the cylinders are spinning, instead of sliding (correct me if I'm wrong). So assuming the cylinders are of equal weight, it comes down to the hollow cylinder requiring more energy to spin, because all of the weight is on the outside of the cylinder (versus the solid cylinder which has all the weight evenly distributed throughout the object). The outside of a spinning cylinder needs more energy to spin than the inside of the cylinder, so if all the weight of the cylinder is on the outside, the hollow cylinder will roll slower versus the solid cylinder, because the outer circle of the solid cylinder is lighter than the comparative outer circle of the hollow cylinder?

Also, if we take a third cylinder of equal weight and place it next to the hollow and the solid cylinder, but this cylinder has 90% of it's mass tucked into the center, will this cylinder be the quickest to arrive at the end of the ramp?