The outline below is also in pdf form *here*.

Angular speed (velocity) and angular pace (legerity)

- Speed,
*v*= Δ*s*/Δ*t*, Pace,*u*= Δ*t*/Δ*s*so*u*= 1/*v*and*v*= 1/*u*except if*u*or*v*are zero- Zero speed: no motion but time changes because time is independent
- Zero pace: no motion but length changes because length is independent

Circular motion in space and time

distance, *x*; distime, *t*; radius *r* (or *a* or R or A); period radius *q*; circumference S = 2π*r* = wavelength *λ*; period T = 2π*q* = wavetime *μ*; angular velocity, *v*; angular legerity, *u*; arc length, *s*; arc time, *w*

- Circle in space
- space angle
*θ*, arc length*s*, radius*r* - angle in space:
*θ*≡*s*/*r; r*=*s*/*θ*;*s*=*rθ;*1/*θ*=*r*/*s*; 1/*r*=*θ*/*s* - angular time rate:
*ω*≡*θ*/*t; t*=*θ*/*ω*;*θ*=*ωt*; 1/*ω*=*t*/*θ*; 1/*t*=*ω*/*θ*

- space angle
- Circle in time
- time angle
*φ*, arc time*w*, period radius*q* - angle in time,
*φ*≡*w*/*q*;*q*=*w*/*φ*;*w*=*qφ*; 1/*φ*=*q*/*w*; 1/*q*=*φ*/*w* - angular space rate:
*ψ*≡*φ*/*x*;*x*=*φ*/*ψ*;*φ*=*ψx*; 1/*ψ*=*x*/*φ*; 1/*x*=*ψ*/*φ*

- time angle