Question

How do you do this question?

Answer 1

Explanation:

Assuming a uniform mass, let's say ρ is the mass per area density.

ρ = M / (πR²)

Let's look at this as the difference of two disks, a large one and a small one.

The moment of inertia of the large disk is:

I = 1/2 MR²

The mass of the small disk is:

m = ρ πr²

m = M / (πR²) πr²

m = M (r/R)²

Using parallel axis theorem, the moment of inertia of the small disk is:

I = 1/2 mr² + md²

I = 1/2 M (r/R)² r² + M (r/R)² d²

I = 1/2 M (r²/R)² + M (rd/R)²

The total moment of inertia is:

I = 1/2 MR² − 1/2 M (r²/R)² − M (rd/R)²