# Motion Equations

The motion equations for classical physics below are also in a pdf here. Circular/harmonic motion equations are in a pdf here.

 Parallel Equations of Motion RA Gillmann, 2023-03-09 Displacement + Time Dischronment + Stance Angle & Arc Length Angle & Arc Duration Stance / DistanceTime / Distime Displacement: sTime | distime: t Dischronment: tStance | distance: s Angle length: θ = s/rArc length: s Angle duration: φ = t/qArc duration: t Radius | Period Length radiusr = S/(2π) = qv Duration radiusq = T/(2π) = rw Angular velocityω = φ/t = κ/u = 2πf = 2π/T= dθ/dt = dt/dφ = v⊥/r = 1/q Wavenumber (angular lenticity)κ = θ/s = ω/v = 2πh = 2π/λ= dθ/ds = ds/dφ = w⊥/q = 1/r Velocity | Lenticity | Wavenumber Cross/Tangential velocityv⊥ = ds/dt = r×ω = r/q = S/T Cross/Tangential lenticityw⊥ = dt/ds = q×κ = q/r = T/S Acceleration | Relentation Radial accelerationa∥ = v2/r = rω2 = v/q = r/q² Radial relentationb∥ = w2/q = qκ2 = w/r = q/r² Angular accelerationα = dω/dt = aT/r Angular relentationβ = dκ/ds = bT/q Tangential accelerationa⊥ = ω×v = Tdv/dt = rα Tangential relentationb⊥ = Tdw/ds = qβ Wavelength | Period λ = S = 2πr = 2πvq T = 2πq = 2πwr λ = S = 2π/κ = 1/h T = 2π/ω = 1/f Revolutions | RepetitionsFrequency | Circuncy RevolutionsN = θ/(2π) RepetitionsZ = φ/(2π) Period frequencyf = ω/(2π) = 1/T Length frequency (circuncy)h = κ/(2π) = 1/λ Displacement | Dischronment s = s0 + vt t = t0 + wx θ = θ0 + ωt φ = φ0 + κs First Equation of Motion v = v0 + at w = w0 + bs ω = ω0 + αt κ = κ0 + βs Second Equation of Motion s = s0 + v0t + ½at² t = t0 + w0s + ½bs² θ = θ0 + ω0t + ½αt2 φ = φ0 + κ0t + ½βs2 Third Equation of Motion v² = v0² + 2a∙(s – s0) w² = w0² + 2b∙(t – t0) ω² = ω0² + 2α∙(θ – θ0) κ² = κ0² + 2β∙(φ – φ0) Inertia | Facilia Mass – linear inertia: m = 1/n Vass-linear facilia: n = 1/m Angular inertia: I = mr2 Angular facilia: J = nq2 Momentum | Levamentum Momentum: p = mv Levamentum: q = nw Angular momentum: L = Iω Angular Levamentum: Γ = Jκ Kinetic Energy and Lethargy Kinetic energy: EK = ½mv2 Kinetic lethargy: LK = ½nw2 Angular energy EA = ½Iω2 Angular lethargy LA = ½Jκ2 Newton’s Second Law Force: F = ma = dp/dt Release: R = nb = dq/ds Torque: τ = Iα = s × F Strophence: σ = Jβ = t × R Work | Repose Linear work: W = F ∙ s Linear repose: Y = R ∙ t Angular work: W = τ ∙ θ Angular repose: Y = σ ∙ φ Power | Placidity Linear power: P = F ∙ v Linear placidity: Z = R ∙ w Angular power: P = τ ∙ ω Angular placidity: Z = σ ∙ κ