\(\psi\) is circular It is wrapped around a circle of perimeter \(2\pi r\), where \(r\) is the radius from the particle center, travelling at light speed \(c\). On every cycle of period \(T=\frac{1}{f}\), it traveled once along the perimeter and has rotated by \(2\pi\) rad. It is then better to redefine light speed with consideration for the value of \(\pi\),
\(c=\pi*10^8\)
instead of
\(c=2.99792458*10^8\)
such that \(r\) is defined/measured without the uncertainty associated with the value of \(\pi\).
\(\pi\) at light speed will be quite a splat.
