Critical Traps to Avoid

Perpendicular axis theorem is ONLY for 2D (planar) bodies — never for spheres or cylinders
In rolling, friction is static (not kinetic) and does zero work
Tension is NOT equal on both sides of a massive pulley
Mass and radius do NOT affect rolling acceleration — only the shape ( $k^2$ / $R^2$ ) matters
The contact point in rolling has zero velocity (not the centre of mass)
Angular momentum conservation does NOT mean energy conservation
Apply the rolling constraint v = R*omega only when the problem specifies "rolls without slipping"
$I_{cm}$ is always the minimum MOI among all parallel axes