Whakaoti i te {l}{v=romega}{V=v/2pir}{s=r{(2piv)}}{t=s}{text{Solvefor}utext{where}}{u=t}

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

Whakaoti mō v, r, ω, V, s, t, u (complex solution)

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

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

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

Whakaoti mō v, r, ω, V, s, t, u

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

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

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

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

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