Solve {l}{v=romega}{V=v/2pir}{s=r{(2piv)}}{text{Solvefor}ttext{where}}{t=s}

$$\left. \begin{array} { l } { v = r \omega }\\ { V = \frac{v}{2 \pi r} }\\ { s = r {(2 \pi v)} }\\ { \text{Solve for } t \text{ where} } \\ { t = s } \end{array} \right.$$

Solve for v, r, ω, V, s, t (complex solution)

$$r=\frac{\left(\pi \omega \right)^{-\frac{1}{2}}\sqrt{2t}}{2}\text{, }t\neq 0\text{, }s=t\text{, }v=r\omega \text{, }\omega \neq 0\text{, }V=\frac{\omega }{2\pi }$$

$$r=-\frac{\left(\pi \omega \right)^{-\frac{1}{2}}\sqrt{2t}}{2}\text{, }t\neq 0\text{, }s=t\text{, }v=r\omega \text{, }\omega \neq 0\text{, }V=\frac{\omega }{2\pi }$$

$$r\neq 0\text{, }t=0\text{, }s=0\text{, }v=0\text{, }\omega =0\text{, }V=0$$

Solve for v, r, ω, V, s, t

$$r=-\frac{\sqrt{\frac{2t}{\pi \omega }}}{2}\text{, }t>0\text{, }s=t\text{, }v=r\omega \text{, }\omega >0\text{, }V=\frac{\omega }{2\pi }$$

$$r=-\frac{\sqrt{\frac{2t}{\pi \omega }}}{2}\text{, }t<0\text{, }s=t\text{, }v=r\omega \text{, }\omega <0\text{, }V=\frac{\omega }{2\pi }$$

$$r=\frac{\sqrt{\frac{2t}{\pi \omega }}}{2}\text{, }t>0\text{, }s=t\text{, }v=r\omega \text{, }\omega >0\text{, }V=\frac{\omega }{2\pi }$$

$$r=\frac{\sqrt{\frac{2t}{\pi \omega }}}{2}\text{, }t<0\text{, }s=t\text{, }v=r\omega \text{, }\omega <0\text{, }V=\frac{\omega }{2\pi }$$

$$r\neq 0\text{, }t=0\text{, }s=0\text{, }v=0\text{, }\omega =0\text{, }V=0$$