حل {l}{v=romega}{V=v/2pir}{s=r{(2piv)}}{t=s}{u=t}{text{Solvefor}wtext{where}}{w=u}

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

حل مسائل v، r، ω، V، s، t، u، w (complex solution)

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

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

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

حل مسائل v، r، ω، V، s، t، u، w

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

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

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

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

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