Whakaoti i te I=mgsqrt{1+(r/h)^2}

$$I = m g \sqrt { 1 + ( \frac { r } { h } ) ^ { 2 } }$$

Whakaoti mō g

$$\left\{\begin{matrix}g=\frac{I|h|}{m\sqrt{r^{2}+h^{2}}}\text{, }&h\neq 0\text{ and }m\neq 0\\g\in \mathrm{R}\text{, }&I=0\text{ and }m=0\text{ and }h\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Kia whakarewa i te \frac{r}{h} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$I=mg\sqrt{1+\frac{r^{2}}{h^{2}}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{h^{2}}{h^{2}}.

$$I=mg\sqrt{\frac{h^{2}}{h^{2}}+\frac{r^{2}}{h^{2}}}$$

Tā te mea he rite te tauraro o \frac{h^{2}}{h^{2}} me \frac{r^{2}}{h^{2}}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$I=mg\sqrt{\frac{h^{2}+r^{2}}{h^{2}}}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$mg\sqrt{\frac{h^{2}+r^{2}}{h^{2}}}=I$$

He hanga arowhānui tō te whārite.

$$\sqrt{\frac{r^{2}+h^{2}}{h^{2}}}mg=I$$

Whakawehea ngā taha e rua ki te m\sqrt{\left(h^{2}+r^{2}\right)h^{-2}}.

$$\frac{\sqrt{\frac{r^{2}+h^{2}}{h^{2}}}mg}{\sqrt{\frac{r^{2}+h^{2}}{h^{2}}}m}=\frac{I}{\sqrt{\frac{r^{2}+h^{2}}{h^{2}}}m}$$

Mā te whakawehe ki te m\sqrt{\left(h^{2}+r^{2}\right)h^{-2}} ka wetekia te whakareanga ki te m\sqrt{\left(h^{2}+r^{2}\right)h^{-2}}.

$$g=\frac{I}{\sqrt{\frac{r^{2}+h^{2}}{h^{2}}}m}$$

Whakawehe I ki te m\sqrt{\left(h^{2}+r^{2}\right)h^{-2}}.

$$g=\frac{I|h|}{m\sqrt{r^{2}+h^{2}}}$$

Whakaoti mō I

$$I=\frac{gm\sqrt{r^{2}+h^{2}}}{|h|}$$

$$h\neq 0$$