Moment of Inertia of a cylinder

  • Thread starter loup
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  • #1
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Main Question or Discussion Point

When I am reading a book, I find it is listed that the moment of Inertia of a cylinder is
MR^2/4 + Ml^2/12

It is a cylinder with rotation axis passing through the curve surface and its centre of mass. And its density is constant. With the circile surface raius = R and height = l

Can anybody show me the procedure of the integration? I have tried several times but fail. I just cannot get that answer. It is not homework but I am interested in the process. You know, usually, moment of Inertia is provided in the book, integration is not required. But I am really curious about it. Could anybody please help me?
 

Answers and Replies

  • #2
tiny-tim
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Hi loup! :smile:

Slice the cylinder into discs.

Use the moment of inertia formula for a disc about its diameter, combined with the parallel axis theorem, and integrate. :wink:
 
  • #3
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The problem is I don't know about how to integrate a disc.
 
  • #4
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And I think the integration of disc actually comes from cylinder. I expected once I finished this cylinder I could do the disc.
 
  • #5
tiny-tim
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The problem is I don't know about how to integrate a disc.
Slice it into strips parallel to a diameter, and integrate …

what do you get? :smile:
 
  • #6
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The r requires a cosine and there are more than one variable, what I should do?
 
  • #7
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I cannot use parallel axis theorem. I think it is too tricky.
 
  • #8
tiny-tim
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The r requires a cosine and there are more than one variable, what I should do?
uhh? what equation are you using? :confused:
 

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