Datrys 3(9.81)=6.67(10^-11)(m/r^2)-(w^2)r

$$3 ( 9.81 ) = 6.67 ( 10 ^ { - 11 } ) ( \frac { m } { r ^ { 2 } } ) - ( w ^ { 2 } ) r$$

Datrys ar gyfer m

$$m=\frac{100000000000r^{2}\left(100rw^{2}+2943\right)}{667}$$

$$r\neq 0$$

Camau ar gyfer Datrys Hafaliad Llinol

Lluoswch ddwy ochr yr hafaliad â r^{2}.

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}rr^{2}$$

Er mwyn lluosi pwerau sy’n rhannu’r un sail, adiwch eu esbonyddion. Adiwch 1 a 2 i gael 3.

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Lluosi 3 a 9.81 i gael 29.43.

$$29.43r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Cyfrifo 10 i bŵer -11 a chael \frac{1}{100000000000}.

$$29.43r^{2}=6.67\times \frac{1}{100000000000}m-w^{2}r^{3}$$

Lluosi 6.67 a \frac{1}{100000000000} i gael \frac{667}{10000000000000}.

$$29.43r^{2}=\frac{667}{10000000000000}m-w^{2}r^{3}$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$\frac{667}{10000000000000}m-w^{2}r^{3}=29.43r^{2}$$

Ychwanegu w^{2}r^{3} at y ddwy ochr.

$$\frac{667}{10000000000000}m=29.43r^{2}+w^{2}r^{3}$$

Mae'r hafaliad yn y ffurf safonol.

$$\frac{667}{10000000000000}m=w^{2}r^{3}+\frac{2943r^{2}}{100}$$

Rhannu dwy ochr hafaliad â \frac{667}{10000000000000}, sydd yr un peth â lluosi’r ddwy ochr â chilydd y ffracsiwn.

$$\frac{\frac{667}{10000000000000}m}{\frac{667}{10000000000000}}=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Mae rhannu â \frac{667}{10000000000000} yn dad-wneud lluosi â \frac{667}{10000000000000}.

$$m=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Rhannwch r^{2}\left(29.43+w^{2}r\right) â \frac{667}{10000000000000} drwy luosi r^{2}\left(29.43+w^{2}r\right) â chilydd \frac{667}{10000000000000}.

$$m=\frac{10000000000000r^{2}\left(rw^{2}+29.43\right)}{667}$$