Cue Column:

• When to use parallel axis?
• Perpendicular axis limitation?
• Common mistake?

Notes: Parallel Axis Theorem: I = $I_{cm}$ + $Md^2$. Use when the rotation axis is parallel to the centre-of-mass axis but shifted by distance d. Works for ANY rigid body (3D or 2D).

Perpendicular Axis Theorem: $I_z$ = $I_x$ + $I_y$. ONLY for planar $\frac{laminar}{2D}$ bodies. The z-axis is perpendicular to the plane, and x, y are in the plane, all intersecting at the same point.

Common Mistake: Applying perpendicular axis theorem to 3D bodies (sphere, cylinder along their length). This gives wrong answers. It only works for flat objects like discs, rings, and rectangular plates.

Summary: Parallel axis shifts the axis (adds $Md^2$). Perpendicular axis splits MOI into two in-plane components (2D bodies only).