Bismillahirrahmanirrahim.
Excuse me ... .
Consider a rigid straight rod $OP$ which be rotated which the rotary axis through $O$ and prependicular to $OP$ with constant angular frequency $\omega$ ... . Length of $OP$ is $R$ ... . In non-relativistic classical mechanics, the linear speed of $P$ is $v=\omega{R}$ constant ... . But if $R>c/\omega$, where $c:=299792458\,\textrm{m/s}$ is speed of light in vacuum, then $v>c$ ... . How can it ... ?
Is it valid to regard that its linear speed is $v=c\tanh(\omega{R}/c)$, so that its maximum linear speed is $c$ ... ?
The non-relativistic limit ($c\to\infty$) is
$\displaystyle\lim_{c\to\infty}v=\lim_{\epsilon\to0}\frac{\tanh(\epsilon\,\omega{R})}{\epsilon}=\omega{R}$ ... .
Is the approximation of this conjecture valid ... ?
Thank you ... .
http://www.thescienceforum.com/physics/34511-circular-motion.html#post406032Gloria in excelsis Deo.
