Moment of Inertia

Hi, if anyone could guide me as to what I'm doing wrong with this question it would be appreciated
"Use calculus to find the moment of inertia of a thin hollow uniform right circular cylinder of mass M, radius R, and height H about a diameter of an end circle. The cylinder is open at both ends"



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What is the moment of inertia of the small ring about the diameter? (Use the perp and parallel axis theorems)

Also where you crossed out area and put volume, it should be surface area

I understand that I could find the result by considering the inertia about the vertical axis of symmetry of the cylinder, use the perpendicular axis theorem, and then use the parallel axis theorem to shift it down.

However, I'm not sure why I get a different result from trying it this way.

And yeah I know it's the surface area, I initially missed the word hollow and had a bit of a moment of inertia


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Hi, if anyone could guide me as to what I'm doing wrong with this question it would be appreciated
"Use calculus to find the moment of inertia of a thin hollow uniform right circular cylinder of mass M, radius R, and height H about a diameter of an end circle. The cylinder is open at both ends"



Posted from TSR Mobile

It is very difficult to help you with this without me providing a full solution (very time consuming)

look at page 11 here for a similar question with a cone

I understand the method, it is just I thought I found a quicker alternative and I couldn't understand why it was not working. I've figured it out now though, turns out I was not considering the distance due to the depth of the cylinder - rather silly.
Thanks though and @gome44 ,your resources are brilliant btw


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what answer did you get?

Apologies if it's hard to follow, I didn't expect to be showing anyone


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