Do heavy and light cylinders roll the same?

[Gary_1]

I understand why a heavy item and a light item both fall a given distance in the same time - in a vacuum, etc.

What happens in the case of a cylinder rolling down an inclined plane with no slippage? Would a heavy cylinder reach the bottom at the same time as would a light cylinder? What if the cylinders were of differing radii? What if the cylinders had a differing moment of inertia, e.g., one cylinder with homogeneous density versus another that was of higher density nearer the surface of the cylinder?

Thansk for helping me understand.

 

[Gerenuk]

I once wrote a derivation. See
https://www.physicsforums.com/showthread.php?t=346336

 

[Gary_1]

I once wrote a derivation. See
https://www.physicsforums.com/showthread.php?t=346336

Gerenut, thanks very much.

 

[Gerenuk]

Thinking about it more, I'm actually not entirely sure if that statement generalizes to arbitrarily *curved* slopes. For cylindrical objects my calculation is correct. The catch is that the height refers to the center of mass and the center of mass might trace out shorter or longer paths (depending on the radius of the cylinder) if the slope isn't flat but curved. Hmm...