Moment inertia - theoretical problem

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Homework Help Overview

The discussion revolves around calculating the moment of inertia of a hollow cylinder with specified inner and outer radii. The original poster expresses uncertainty about the appropriate approach to derive the moment of inertia, particularly in relation to known formulas for non-hollow cylinders.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the idea of splitting the hollow cylinder into two overlapping parts to facilitate the calculation. There is also a question about the necessity of using definite integration to solve the problem, with some suggesting that known formulas for solid cylinders could be relevant.

Discussion Status

The discussion includes attempts to clarify the approach to the problem, with some participants providing hints about using known formulas for composite bodies. There is an acknowledgment of the challenges faced by the original poster, but no consensus has been reached regarding the method to be used.

Contextual Notes

Participants note the importance of careful consideration of mass in the calculations and the potential constraints of not using definite integration, which appears to be a common method referenced in external solutions.

silenzer
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Moment inertia -- theoretical problem

Homework Statement



Show that the moment inertia of a hollow cylinder with inner radius a and outer radius b is (1/2)*M*(a^2+b^2), calculated for the center axis.

Homework Equations



I know that the moment inertia of a non-hollow cylinder is I = (1/2) MR^2, but I don't know the moment inertia of a hollow one.

I = MR^2, generally.

Krotation = (1/2)Iw^2

The Attempt at a Solution



I'm not entirely certain on where to start. Should I split the cylinder into two parts and work from there?
 
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silenzer said:
Should I split the cylinder into two parts and work from there?
Yes. Consider overlapping cylinders. Subtract!

Be careful with the mass.
 
I'm sorry but I'm still having problems... I googled the problem and all of the solutions use definite integration. Can I solve this problem without using that?
 
silenzer said:
I'm sorry but I'm still having problems... I googled the problem and all of the solutions use definite integration. Can I solve this problem without using that?
All you need to know is the formula for the moment of inertia of a solid cylinder--which you already know.

Hint: For a composite body with parts a and b, Itotal = Ia + Ib.
 
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Sorry for the late reply. I did it! :D Thanks a lot.
 
silenzer said:
Sorry for the late reply. I did it! :D Thanks a lot.
:thumbs:
 

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