iSoul In the beginning is reality

# More equations of motion

Expanding on a previous post here, this is a summary of the equations of motion for space-time and time-space. See also a pdf version in the Time-space Glossary option above.

s = displacement magnitude, t = time magnitude, v = velocity, v0 = initial velocity, a = acceleration, u = tempo, u0 = initial tempo, b = expedience, ω = angular velocity, ω0 = initial angular velocity, ψ = angular tempo, ψ0 = initial angular tempo, θ = spatial angle, ψ = temporal angle, S = circumference, T = period, Rs = spatial radius, and Rt = temporal radius.

 Linear w/3D space Linear w/3D time Angular w/3D space Angular w/3D time Average Rate v =  Δs/Δt u = Δt/Δs ω = Δθ/Δt ψ = Δϑ/Δs Average 2nd Rate a = Δv/Δt b = Δu/Δs α = Δω/Δt β = Δψ/Δs Instantaneous Rate Velocity v = ds/dt Tempo u = dt/ds Angular velocity ω = dθ/dt = dt/dϑ Angular tempo ψ = dϑ/ds = ds/dθ Instantaneous 2nd Rate Acceleration a = dv/dt Expedience b = du/ds Tangential acceleration α = dω/dt Tangential expedience β = dψ/ds Centripetal/Radial 2nd Rate Centripetal acceleration acen = v2/Rs Centripetal expedience bcen = 1/(u2Rs) Radial acceleration arad = Rs ω2 Radial expedience brad = Rt ψ2 Uniform Tangential Rate vtan = 2πRs/T utan = T/(2πRt) vtan = Rs ω ℓtan = Rt ψ Circumference/Arc Length Spatial circumference S = 2πRs Temporal circumference T = 2πRt Spatial arc length θ = s/Rs Temporal arc length ϑ = t/Rt Period T = 2πRs/v T = 2πRtu T = 2π/ω T = 2π/ψ Radius Spatial radius Rs = S/(2πv) Temporal radius Rt = T/(2πu) Spatial radius Rs = ds/dθ = s/θ = v/ω Temporal radius Rt = dt/dϑ = t/ϑ = ℓ/ψ Position s t On a circle: s = Rs θ On a cycle: t = Rt ϑ Displacement s = s0 + vt t = t0 + us θ = θ0 + ωt ϑ = ϑ0 + ψs Second Equation of Motion s = s0 + v0t + ½at² t = t0 + u0s + ½bs² θ = θ0 + ω0t + ½αt2 ϑ = ϑ0 + ψ0t + ½βs2 First Equation of Motion v = v0 + at u = u0 + bs ω = ω­ + αt ψ = ψ0 + βs Third Equation of Motion v² = v0² + 2a(s – s0) u² = u0² + 2b(t – t0) ω² = ω0² + 2α(θ – θ0) ψ² = ψ0² + 2β(ϑ – ϑ0)