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 (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).