Consider a unit circle.
Define:
- angular displacement: $\phi=\theta_1-\theta_2$;
- angular position: $0\leq\theta<2\pi\;$ s.t. $\;\phi\equiv_{2\pi}\theta$;
- minor arc length: $m= \begin{cases} \theta, &\text{ for } 0<\theta<\pi,\\ 2\pi-\theta, &\text{ for } \pi<\theta<2\pi. \end{cases}$
To my mind:
- the angular analogue of linear displacement is $m$;
- the angular analogue of linear distance is $\phi$.
So why is $\phi$, as defined here, called angular displacement rather than angular distance?
