How to Calculate Moment of Inertia for a Disk Using Calculus?

AI Thread Summary
The moment of inertia for a disk about an axis perpendicular to its plane is given by I=1/2 MR^2, while the perpendicular axis theorem states that the moment of inertia about another axis is I=1/4 MR^2. A user sought to derive the second result using calculus but encountered difficulties during integration. They initially considered the mass of a disk section as pyr dx, leading to complex calculations. Ultimately, the user resolved their issue without further elaboration.
jeremy5561
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I know that the moment of inertia of a disk about the axis perpendicular to the plane of the disk is

I=1/2 MR^2

and by the perpendicular axis theorem the moment of inertia about the other axis is

I=1/4 MR^2

I want to get the 2nd result with calculus. I can't get the right answer. What am I doing wrong?

I know the moment of inertia of a rod is 1/12 MR^2
I take the mass of a section of the disc to me pyr dx where y is the depth of the disc
but when I integrate it gets really messy.

What's the correct way to do this?

http://individual.utoronto.ca/jeremyli/moi.jpg
 
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I got it

OH nevermind I got it.
 

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