Solve Hoop and Disk Inertia Homework

[lc99]

Homework Statement

Hoop and disk with uniform mass distribution have the same radius but the total masses are not known. They both roll down ramp without slipping, reaching the bottom in the same time. What can you deduce about the relative masses?
1) disk is heavier, twice the mass of loop
2) the hoop is heavier, twice the mass of disk.
3) hoopi is heavier, twice the mass of disk
4) disk is lighter, 3/4 mass of hoop
5) hoop and disk have same mass

Homework Equations

The Attempt at a Solution

I'm thinking that the answer is 2) because hoop = MR^2 while disk is 1/2MR^2

But, i don't think this is that easy because they both roll without slipping, and they reach the bottom at the same time. If this is the case, mass does not really matter for they time they reach the bottom of the ramp? I'm kinda stuck ;/

 

[haruspex]

mass does not really matter for they time they reach the bottom of the ramp

Ignoring air resistance, that is true. The same is true for the radii - it is irrelevant whether they are the same.
My only explanation for the stated facts is that they were positioned at different heights on the ramp.

 

[collinsmark]

Homework Statement

Hoop and disk with uniform mass distribution have the same radius but the total masses are not known. They both roll down ramp without slipping, reaching the bottom in the same time. What can you deduce about the relative masses?
1) disk is heavier, twice the mass of loop
2) the hoop is heavier, twice the mass of disk.
3) hoopi is heavier, twice the mass of disk
4) disk is lighter, 3/4 mass of hoop
5) hoop and disk have same mass

Homework Equations

The Attempt at a Solution

I'm thinking that the answer is 2) because hoop = MR^2 while disk is 1/2MR^2

But, i don't think this is that easy because they both roll without slipping, and they reach the bottom at the same time. If this is the case, mass does not really matter for they time they reach the bottom of the ramp? I'm kinda stuck ;/

Is this a problem for your coursework, or is it rather something you are curious about? If it is for the coursework, is there something missing from the problem statement?

I suspect the problem statement itself, as-is, has a fallacy within it. [Edit: or at least is incomplete.]

 

[lc99]

Is this a problem for your coursework, or is it rather something you are curious about? If it is for the coursework, is there something missing from the problem statement?

I suspect the problem statement itself, as-is, has a fallacy within it. [Edit: or at least is incomplete.]

It's not homework or anything. Its a question from a quiz i took, and i got the question wrong of. I know I've been posting a lot of questions, but they are sadly all the ones I am getting wrong and want to understand!

 

[collinsmark]

It's not homework or anything. Its a question from a quiz i took, and i got the question wrong of. I know I've been posting a lot of questions, but they are sadly all the ones I am getting wrong and want to understand!

As @haruspex alluded to, the radii and mass shouldn't matter. So when the problem statement said that they reach the bottom at the same time has me scratching my head because that shouldn't be possible (I'm assuming they started at the same time, from rest, and that the slope is the same for both, and no air resistance).

But if you really want to understand, I don't suggest merely memorizing these sorts of outcomes. Analyze them properly with what you know about Newton's laws (both for translational and the rotational versions; you'll need both) complete with equations. Once you work through them and find simple equations describing the motion, you'll likely have an "Ah, ha!" moment.

You'll naturally build up a better intuition as you progress. But when in doubt, trust the fundamental physics and your math.

 

[lc99]

Ignoring air resistance, that is true. The same is true for the radii - it is irrelevant whether they are the same.
My only explanation for the stated facts is that they were positioned at different heights on the ramp.

Hmmm. Its not missing any information. Maybe the focus is on not slipping? Since there is no friction in no slipping? and gravity is the only force?

I kinda guess that they have the same mass. Is this question really invalid? It appeared on my midterm exam for college physics

Edit: wait, if mass and radii doesn't matter here, would it be same to assume that the inertia formula would dictate the masses?

 

[haruspex]

assume that the inertia formula would dictate the masses?

No. If you do the algebra you will find that both the mass and the radius cancel out. The acceleration only depends on g, the slope, and a dimensionless constant associated with the shape, e.g. 5/7 for the uniform solid sphere, 1/2 for the hollow cylinder, etc.