Drums rolling downhill scenario

1. Oct 15, 2007

Skhandelwal

All the drums weigh the same...one has greater surface area , one has center of mass in the middle...and one has center of mass at an end.

Which will get to the ground first?

When I think I am starting to understanding mechanics, I spot questions like these.... If I am having problem w/ this...what principle am I weak on?

2. Oct 15, 2007

rcgldr

The force is the component of gravity that is parallel to the angle of the inclined plane (cos(angle)). The resistance to this force is the inertia of the drums, which is a combination of the linear and angular inertias. Since the drums have the same mass, the linear inertia is the same for the drums, so the only difference is the angular inertia. See if you can figure it out from here.

3. Oct 16, 2007

Skhandelwal

The one w/ the bigger area will get at the bottom first...even though, it has to face more friction....the surface area makes up for it. Btw, is the center of mass faster or the one which has the mass at a corner?

Also, another similar question, if there is a drum, and then there is another drum but there is one difference. Assume the drum is a pizza made up of 16 slices. Well, every alternative slice has been taken out. Which one will get to the ground first?

4. Oct 16, 2007

rcgldr

The fastest drum is the one with it's mass at it's center. The surface area doesn't mattter unless you're including friction from the air. If the mass is at the center, then there's virtually no angular inertia.