Thick cylindrical ring find inertia help

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Homework Help Overview

The problem involves calculating the moment of inertia of a thick cylindrical ring with specified inner radius, thickness, and mass. The context is centered around understanding the appropriate formulas for moment of inertia in relation to the geometry of the object.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the correct formula for the moment of inertia, with some confusion regarding the relationship between the thick cylindrical ring and solid cylinders. There are attempts to clarify the definitions of inner and outer radii, as well as the implications of the ring's thickness.

Discussion Status

Some participants have offered guidance on the relationship between the thick cylindrical ring and solid cylinders, while others express uncertainty about the application of the formulas. There is an ongoing exploration of the correct approach to calculating the moment of inertia, with multiple interpretations being discussed.

Contextual Notes

Participants are navigating the definitions of inner and outer radii, as well as the implications of the thickness of the ring. There is mention of the mass distribution and density, which may influence the calculations but are not fully resolved in the discussion.

blackbyron
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Homework Statement



A thick cylindrical ring of inner radius 29.0cm and thickness 2.8cm has a mass of 10.0kg. What is the moment of inertia of this cylinder about its central axis?

Homework Equations



I = (.5)(m)(ri^2+ro^2)

The Attempt at a Solution


I tried to use hollow cylinder formula, but the answer says it's wrong.
I don't know if I use the right inertia formula. I don't know if thickness is the outer radius. I confused.

Thanks
 
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The thickness is the difference between the outer radius and the inner one. Use the formula of the solid cylinder. The thick cylindrical ring is made from a solid cylinder by removing a thinner cylinder from its inside.

ehild
 
Ah okay, yeah cause I thought the formula I mention is the one I have to use. But thanks for your help.
 
Sorry, but I think I'm lost here. How does solid cylinder relate to the thick cylindrical ring? Because when I use solid cylinder formula, it didn't work on the answer tho.

And also

"The thick cylindrical ring is made from a solid cylinder by removing a thinner cylinder from its inside."
So you're saying that the inner solid cylinder is removed right? And the thick cylindrical ring is the only thing left. Is that correct.


outer radius .29meters, thickness is .028m mass is 10 kg.

I = (1/2)(M)(R)^2
 
blackbyron said:
So you're saying that the inner solid cylinder is removed right? And the thick cylindrical ring is the only thing left. Is that correct.


outer radius .29meters, thickness is .028m mass is 10 kg.

I = (1/2)(M)(R)^2

The outer radius is R=(0.29 + 0.028) m, the inner radius is r=0.29 m. The mass of the ring is 10 kg. If the mass of the thinner cylinder is m, that of the thick one is

M=10+m.

The density of both cylinders is the same as that of the ring.

The moment of inertia is

I = 1/2 (MR2-mr2)

ehild
 
Oh I see, I forgot to add the thickness by radius to get the outer radius.

Sorry about that

Thanks for your help

Now I'm getting it.
 

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