Rotation
Start with the model and its assumptions. These relationships use SI units unless you convert every quantity consistently.
Rotation
| Relationship | Formula | When it applies |
|---|---|---|
| Circular motion | v = rω; aᶜ = v²/r = rω² | v denotes speed and ω angular-speed magnitude; centripetal acceleration points toward the centre. |
| Torque & inertia | τ = r × F; I = Σmᵢrᵢ²; Στ = Iα | rᵢ is perpendicular distance from the axis; use torque components about a stationary pivot or the centre of mass, with constant I. |
| Angular momentum & energy | L = Iω; Krot = ½Iω² | L = Iω applies about a principal or fixed symmetry axis. |
| Rolling | vCM = Rω; K = ½mvCM² + ½Iω² | Rolling without slipping. |
Find definitions and the original reference tables in the glossary →