1. Translational-Rotational Analogues
l Translational Rotational l
Displacement x θ
Velocity v ω
Acceleration a α
Force (Torque) F τ
Mass (Moment of Inertia) m I
Newton’s 2nd Law: ∑F = ma ∑τ = Iα
Kinetic Energy (KE) (½)mv2 (½)Iω2
Work (constant F, τ) Fx τθ
Momentum mv Iω
(Angular Momentum)

2. Translational-Rotational Connections
Velocity: v = rω
Acceleration: atan= rα
aR = (v2/r) = ω2r
Force & Torque: τ = rF
Mass (Moment of Inertia):
I = ∑(mr2) = cMR2
(c = a unitless number that depends on geometry)
Newton’s 2nd Law: ∑F = ma, ∑τ = Iα