Question

What is the moment of inertia of a half solid disc along its base(diameter)

Answer 1

The moment of inertia of a semi-circular disk is simply half the moment of inertia of the entire disk.

The moment of inertia of a circular disk about any diameter is I=14mR2

where m = mass of the entire disk

∴ the moment of inertia of a semi-circular disk is:

I12=12I=(12)14mR2=18mR2

Let’s write this in terms of the mass of a semi-circular disk:

let m12 = mass of the semi-circular disk = m2

or

m=2m12

∴ I12=18mR2=18(2m12)R2

or

I12=14(m12)R2

Answer 2

its MR^2/4 . Applr perpendicular axis theorem