COMPARISON OF TRANSLATIONAL MOTION AND ROTATIONAL MOTION

1          Linear displacement                      → d                    Angular displacement                 θ

2          Linear velocity                              → v                    Angular velocity                          ω

3          Linear acceleration                       → a = Dv / Dt     Angular acceleration                  α = ω / t

4          Mass                                           → m                    Moment of inertia                     I

5          Linear momentum                         → p = m v          Angular momentum                  L = Iω

6          Force                                           → F = m a          Torque                                    t = I α

7          Newton’s Second Law of motion  → F = DP / Dt    Result similar to Newton’s       t = DL / Dt

Second Law

8          Translational kinetic energy           → k = ½ mv²     Rotational kinetic energy           K = ½ Iω²

9          Work                                           → W = F d        Work                                       W = t θ

10        Power                                          → P = F v          Power                                      P = t ω

11        Equations of linear motion             → v = v₀ + at     Equations of rotational              ω = ω_i + αt

with constant linear                     S = v₀t + ½ at²      motion with constant                θ = ω_i t + ½αt²

            acceleration                                     2aS = v_f ² + v_i ² angular acceleration               2αθ = ω_f² - ω_i²