3 ( 9,81 ) = 6,67 ( 10 ^ { - 11 } ) ( \frac { m } { r ^ { 2 } } ) - ( w ^ { 2 } ) r
Solve for m
m=\frac{100000000000r^{2}\left(100rw^{2}+2943\right)}{667}
r\neq 0
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3\times 9,81r^{2}=6,67\times 10^{-11}m-w^{2}rr^{2}
Multiply both sides of the equation by r^{2}.
3\times 9,81r^{2}=6,67\times 10^{-11}m-w^{2}r^{3}
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
29,43r^{2}=6,67\times 10^{-11}m-w^{2}r^{3}
Multiply 3 and 9,81 to get 29,43.
29,43r^{2}=6,67\times \frac{1}{100000000000}m-w^{2}r^{3}
Calculate 10 to the power of -11 and get \frac{1}{100000000000}.
29,43r^{2}=\frac{667}{10000000000000}m-w^{2}r^{3}
Multiply 6,67 and \frac{1}{100000000000} to get \frac{667}{10000000000000}.
\frac{667}{10000000000000}m-w^{2}r^{3}=29,43r^{2}
Swap sides so that all variable terms are on the left hand side.
\frac{667}{10000000000000}m=29,43r^{2}+w^{2}r^{3}
Add w^{2}r^{3} to both sides.
\frac{667}{10000000000000}m=w^{2}r^{3}+\frac{2943r^{2}}{100}
The equation is in standard form.
\frac{\frac{667}{10000000000000}m}{\frac{667}{10000000000000}}=\frac{r^{2}\left(rw^{2}+29,43\right)}{\frac{667}{10000000000000}}
Divide both sides of the equation by \frac{667}{10000000000000}, which is the same as multiplying both sides by the reciprocal of the fraction.
m=\frac{r^{2}\left(rw^{2}+29,43\right)}{\frac{667}{10000000000000}}
Dividing by \frac{667}{10000000000000} undoes the multiplication by \frac{667}{10000000000000}.
m=\frac{10000000000000r^{2}\left(rw^{2}+29,43\right)}{667}
Divide r^{2}\left(29,43+w^{2}r\right) by \frac{667}{10000000000000} by multiplying r^{2}\left(29,43+w^{2}r\right) by the reciprocal of \frac{667}{10000000000000}.
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