From the circular disc let us consider an elemental hollow disc of inner radius and outer radius
The area of this hollow disc will be,
Since is very small, can be neglected.
Let the circular disc be uniform so that the areal density is same for the whole disc and the hollow disc whose mass is
Given that is areal density. So,
The hollow disc is just a ring, so its moment of inertia is,
Then moment of inertia of the circular disc is,
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From the circular disc let us consider an elemental hollow disc of inner radius
and outer radius ![\sf{r+dr.} \sf{r+dr.}](https://tex.z-dn.net/?f=%5Csf%7Br%2Bdr.%7D)
The area of this hollow disc will be,
Since
is very small,
can be neglected.
Let the circular disc be uniform so that the areal density is same for the whole disc and the hollow disc whose mass is![\sf{dM.} \sf{dM.}](https://tex.z-dn.net/?f=%5Csf%7BdM.%7D)
Given that
is areal density. So,
The hollow disc is just a ring, so its moment of inertia is,
Then moment of inertia of the circular disc is,