# In a race down inclined plane why does a cube reach bottom first?

1. Oct 21, 2005

### positron

In a race down inclined plane why does a cube reach bottom first? The other object is a solid cylinder. The cylinder rolls without slipping, and the cube slides. The cylinder has radius R, and a cube has radius R. Does this depend on the mass of the objects? Is it because since the cube doesn't slide, none of its energy is converted into rotational KE as happens in the case of the cylinder?

2. Oct 21, 2005

### Staff: Mentor

That's right. Of course you have to "cheat" a bit and assume that the cube slides down a frictionless surface, while the cylinder rolls down a surface with friction. (Otherwise the cylinder would just slide down also.)

For fun: Solid cylinder versus hoop--which wins that race? Does it depend on mass? On radius? (Figure it out.)

3. Oct 21, 2005

### positron

It be the one with the smaller moment of inertia. I for a solid cylinder of the same radius and mass as the hoops is larger, so it would go down faster. I for the solid cylinder is 1/2*M*R^2 and I for the hoops is just M*R^2. If the moment of inertia of the cube were greater than the cylinder, would it reach the bottom second?

4. Oct 21, 2005

### Staff: Mentor

Right. The one with the smallest rotational inertia per unit mass would win. (Note: It doesn't depend on mass or radius as long as the object rolls without slipping.)
Cubes don't roll very well.

5. Oct 21, 2005

### vanesch

Staff Emeritus
You should use a tetraheder ; it eliminates one bump

6. Oct 23, 2005

### Tide

How about an icosahedron so the bumps are smaller?