Rotational Inertia: Pipe Reaches Bottom First?

[NoHeart]

if a ball, a solid cylinder, and a hollow pipe each with equal masses and radius are released simultaneously from an inclined plane, which will reach the bottom first?
i would say the pipe would reach the bottom first, because the rotational inertia of the pipe is greater than that of the other two. can anyone tell me if I'm correct? if not, how do i go about answering this question (if inertia has nothing to do with it)?

 

[dextercioby]

It has everything to do with principal moments of inertia.I'm assuming they roll without slipping and there's no friction on the incline.(Since the problem doesn't say so,it's better to assume it,for simplicity).So u'd have to compare the linearvelocities once they reach the ground...

Daniel.

 

[OlderDan]

You have identified the important property of the objects, but you have come to the wrong conclusion. Think about energy conservation.

 

[NoHeart]

inert

yeah, I'm totally backwards. so the object with the least amount of inertia would have the greatest velocity, that would be the cylinder...but you are saying it has to do with energy conservation- why?
using potential energy=kinetic energy, the ball has the fastest speed. I'm going to say that's the answer, but why?

 

[OlderDan]

When an object rolls without slipping, all the little pieces of mass are moving at different speeds, which makes calculating kinetic energy different than when all the pieces are moving at the same speed. Fortunately, the mathematics permits a separation of the problem into a kinetic energy of translation plus a kinetic energy of rotation. I assume you know how to calculate these. All three objects will have the same kinetic energy at the bottom of the incline, but their rotational kinetic energies will all be different and their translational kinetic energies will all be different. The one with the greatest rotational energy is going to be the one with the greatest moment of inertia, so it will have the lowest translational kinetic energy and the lowest speed. You should be able to calculate the final speeds of all three objects if you know the height of the incline.

 

[NoHeart]

the height is not given, only the things i mentioned are given. no numerical values of anything.
so if i find the relative translational kinetic energies, the one with the highest is the correct answer?

 

[OlderDan]

Right. You are not given the height, but you could find an algebraic expression for final velocity in terms of the initial height. It is not needed for this problem. A relative comparison is all you need to do, and yes, the one with the highest translational kinetic energy is the one that gets to the bottom first.