physics

[cipher]

imagine a ramp, there are 4 objects that are going to roll down the ramp.
assume all objects have same mass, all are let go at the same time, and all have to travel the same distance.
these objects are: a solid cylinder, a hollow cylinder, a solid sphere, and a hollow sphere.
which of these objects would roll down the ramp fastest (hit the bottom first)?

EDIT:
all have the same radii (thanks xyphet)

[Adron]

Obviously the solid sphere, everyone knows a good solid ball is going to roll much faster than a hollow one, you know, simply the weight of it being solid will outdo it. And cylinders can roll nowhere as fast as a good ball, just think about a basketball vs a log, the basketball rolls much better. And then think of a solid bowling ball and it's obvious that the solid one rolls heavier and faster instead of bouncing around all over and slowing down.

And yes, there's a completely different motivation too

[jigsaw]

thats a real toughy. Word play is gay btw.

[cipher]

a good solid ball is going to roll much faster than a hollow one, you know, simply the weight of it being solid will outdo it.

Well, since I've allowed enough time to pass... even though I answered this question in op [vl] (didn't really give anyone a chance heh) I'll now give my explanation for the answer.
While you're right Adron, the solid ball would roll fastest, the first thing I noticed in your explanation was that you assumed the weight of the solid ball would have an influence on the situation; I believe it is incorrect to assume this as all the objects have the same mass (I believe I said this).
The explanation of having a Log vs a Basketball a valid example except for A) The log and the Basketball would need to be the same mass and therefore weight (we're assuming these objects are influenced by the same force--gravity) B) a basketball and a log are very different materials, of course a rigid object, such as a bowling ball would do better than a bouncing ball. Therefore, in that respect, I should have said all these objects are made of rigid materials.
My explanation would go sort of along these lines:
Firstly, moment of inertia plays a large role in the reasoning in this situation. Imagine an ice skater while spinning around in place. If this ice skater were to have her arms out, and then slowly pull them closer to her body, then she would begin to spin faster--this relies heavily on the fact that friction is very low on ice and stuffs. Similarly, in a hollow cylinder or hollow sphere, the mass is being directed outward... to the edges, which makes it more difficult to spin. Another example might be if you were to imagine a barbel being spun on the floor. With weights distributed at the direct end of the barbel, one would have a tough time spinning it, but if all that weight were at the center, it'd be much easier. So that eliminates that hollow objects. Next the selection of a sphere versus a cylinder. A better explanation can be given that involves some calculus, but I'm just about to hit the sack, so maybe I'll add that when I get home from school tomorrow. But here is a quick way to prove it, and I'll show the longer, more drawn out way later.
Kinetic Energy (rotational) = 1/2 (moment of inertia) * (angular velocity)^2
Using this equation, we can see that [(2 * KE) / (moment of inertia)]^(1/2). Therefore, there is an inverse relationship between angular velocity and moment of inertia (the higher the moment of inertia, the slower you spin, and vice versa).
The sphere happens to have a lower moment of inertia, so that's why it spins faster.. the proof for this will come later, when I have more time.
This was my first post to this neato Math forum--and it will not be my last. Next time however, I will need to be much more specific, because it's my fault that I didn't take the time to properly set the conditions.

[j0k3r]

I guessed the solid ball simply because it had the least amount of surface touching the ramp, and would have less friction being applied to it.

[Adron]

I guessed the solid ball simply because it had the least amount of surface touching the ramp, and would have less friction being applied to it.

Why solid instead of non-solid?

[Tuberload]

I guessed the solid ball simply because it had the least amount of surface touching the ramp, and would have less friction being applied to it.

Why solid instead of non-solid?

If both the solid ball, and the non-solid ball had the same mass, wouldn't the non-solid ball's perimeter have to be bigger to make up for it's hallow center?

[Adron]

If both the solid ball, and the non-solid ball had the same mass, wouldn't the non-solid ball's perimeter have to be bigger to make up for it's hallow center?

Think non-solid gold or solid cork...

[j0k3r]

I guessed the solid ball simply because it had the least amount of surface touching the ramp, and would have less friction being applied to it.

Why solid instead of non-solid?

Well I was assuming the hollow ball would be bigger, in which case there would be a bit more surface touching... If they were the same size and mass, I don't see how one would be faster than the other.

[cipher]

Because of the distribution of the mass... that's the point =P Read my explanation above.

[Tuberload]

If both the solid ball, and the non-solid ball had the same mass, wouldn't the non-solid ball's perimeter have to be bigger to make up for it's hallow center?

Think non-solid gold or solid cork...

Hmmm, I was thinking they had to be the same material. Thanks for the wake up call.