The moment of inertia is:

I = 6(-3)2 + 5(-2)2 + 9(1)2 + 2(8)2

= 54 + 20 + 9 + 128

= 211

To find R, we use:

I = (m1 + m2 + m3 ... + mn)R2

211 = (6 + 5 + 9 + 2)R2

So `R ≈ 3.097`

This means a mass of `22` units placed at `(3.1, 0)` would have the same rotational inertia about O as the 4 objects.

Please support IntMath!