Rotational Motion — Easy Practice (Set 2)

Quick Recap — Moments of Inertia & Theorems

• More standard results: solid cylinder about its axis $\tfrac12 MR^2$; rod about its centre $\tfrac{1}{12}ML^2$; rod about one end $\tfrac13 ML^2$.
• Parallel axis theorem: $I = I_{cm} + Md^2$.
• Perpendicular axis theorem (planar bodies only): $I_z = I_x + I_y$.
• Rolling without slipping: $v_{cm} = \omega R$; total KE $= \tfrac12 mv^2 + \tfrac12 I\omega^2$.
• Conservation of angular momentum: with no external torque, $I\omega =$ constant — pulling mass inward lowers $I$ and raises $\omega$.