Which Object Will Roll Farther: Solid Cylinder or Hoop on an Incline?

[Keissterr]

Homework Statement

This is a question I have for a presentation on rotational motion: "A solid cylinder rolls down an incline faster than a hoop [or say an open cylinder], whether or not they have the same mass or diameter. The hoop has greater rotational inertia relative to its mass than a cylinder does." Now my question is when they reach the bottom of the incline to a flat surface, which one will roll the farthest? (if their masses are the same) Suppose the amount of friction and air resistance are the same for both.

Homework Equations

The Attempt at a Solution

I'm guessing that the hoop will since it has greater rotational inertia to keep it rolling, but another professor thinks it may be the solid cylinder.

 

[drvrm]

I'm guessing that the hoop will since it has greater rotational inertia to keep it rolling, but another professor thinks it may be the solid cylinder.

calculate the total energy of the hoop and the solid cylinder and see which is larger so one having the larger energy will traverse larger distance on the flat surface after completing the rolling down on the incline.

 

[haruspex]

calculate the total energy of the hoop and the solid cylinder and see which is larger so one having the larger energy will traverse larger distance on the flat surface after completing the rolling down on the incline.

Better still, consider where that energy came from in the first place,
@Keissterr , you mentioned friction. I assume you meant rolling resistance.
With regard to drag (air resistance), it depends what you mean by being the same. Do you mean the same force, or the same coefficient but varying according to speed?