Strategy for composite bodies:

1. Break the body into simple shapes whose MOI you know
2. Find MOI of each part about the required axis (use parallel axis theorem if needed)
3. Add MOIs if the part is present; subtract if the part is removed $\frac{hole}{cavity}$

Example — Disc with a hole: If a disc of mass M, radius R has a hole of radius R/2 centered at distance R/2 from the centre:

• Mass of removed disc: $M_{hole}$ = M * $\frac{R}{2}$^2/$R^2$ = M/4
• MOI of full disc about centre: $I_{full}$ = $MR^2$/2
• MOI of removed portion about centre (parallel axis): $I_{hole}$ = \frac{M}{4}$$\frac{R}{2}^2/2 + \frac{M}{4}$$\frac{R}{2}^2 = $MR^2$/32 + $MR^2$/16 = 3$MR^2$/32
• Remaining MOI: I = $MR^2$/2 - 3$MR^2$/32 = 13$MR^2$/32