Introduction:
We have two circular discs, A and B, which have equal masses and thickness. However, they are made of metals with different densities, where the density of disc A (Da) is greater than the density of disc B (Db). We need to determine the moments of inertia about an axis passing through the centers and normal to the circular faces, denoted as IA and IB respectively.

Understanding Moments of Inertia:
The moment of inertia of an object is a measure of its resistance to rotational motion about a particular axis. It depends on the mass distribution of the object and the axis of rotation. For a rotating body, the moment of inertia is given by the formula:

I = m * r^2

Where I is the moment of inertia, m is the mass of the object, and r is the perpendicular distance of each mass element from the axis of rotation.

Calculating Moments of Inertia:
To calculate the moments of inertia of discs A and B, we need to consider their mass distributions and how their densities affect their moments of inertia.

Disc A:
Since the density of disc A is greater than that of disc B, it means that disc A has a greater mass per unit volume. Therefore, the mass distribution of disc A will be more concentrated towards the center compared to disc B.

Disc B:
Disc B has a lower density compared to disc A, which means it has a lower mass per unit volume. Consequently, disc B will have a more uniform mass distribution throughout its volume.

Effects on Moments of Inertia:
The moments of inertia of discs A and B will be influenced by their mass distributions due to differences in their densities.

Moment of Inertia for Disc A (IA):
Since disc A has a greater concentration of mass towards its center, it will have a higher moment of inertia compared to disc B. This is because the mass elements close to the axis of rotation will have a smaller perpendicular distance (r) and contribute more to the moment of inertia.

Moment of Inertia for Disc B (IB):
Disc B, with a more uniform mass distribution, will have a lower moment of inertia compared to disc A. The mass elements at larger perpendicular distances (r) will contribute more to the moment of inertia for disc B.

Conclusion:
In summary, the moments of inertia of discs A and B will differ due to their different mass distributions caused by their densities. Disc A, with a higher density, will have a greater concentration of mass towards its center, resulting in a higher moment of inertia (IA). On the other hand, disc B, with a lower density, will have a more uniform mass distribution and a lower moment of inertia (IB).

Compare the moement of inertia ?