Translational vs Rotational Motion TRANSLATIONAL Mass: m [kg] Velocity: v [m/s] Force: F = ma [N] Momentum: p=mv KE = ½$mv^{2}$ Work: W = Fd Power: P = Fv ROTATIONAL Moment: I [kg·$m^{2}$] Ang. vel: ω [rad/s] Torque: τ = Iα [N·m] Ang. mom: L = Iω KE = ½Iω^{2} Work: W = τθ Power: P = τω ↔ ↔ ↔ ↔ ↔ ↔ ↔ Conservation: F_net=0 → p=const | τ_net=0 → L=const

Key takeaway: Every linear equation in mechanics has a rotational version. Replace $m \to I$, $v \to \omega$, $F \to \tau$, $p \to L$.