Solve F=(2pir)^2/T/r*m

$$F = \frac { \frac { ( 2 \pi r ) ^ { 2 } } { T } } { r } \cdot m$$

Solve for T

$$\left\{\begin{matrix}T=\frac{4\pi ^{2}mr}{F}\text{, }&r\neq 0\text{ and }m\neq 0\text{ and }F\neq 0\\T\neq 0\text{, }&F=0\text{ and }m=0\text{ and }r\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r.

$$Fr=\frac{\left(2\pi r\right)^{2}}{T}m$$

Expand \left(2\pi r\right)^{2}.

$$Fr=\frac{2^{2}\pi ^{2}r^{2}}{T}m$$

Calculate 2 to the power of 2 and get 4.

$$Fr=\frac{4\pi ^{2}r^{2}}{T}m$$

Express \frac{4\pi ^{2}r^{2}}{T}m as a single fraction.

$$Fr=\frac{4\pi ^{2}r^{2}m}{T}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{4\pi ^{2}r^{2}m}{T}=Fr$$

Variable T cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by T.

$$4\pi ^{2}r^{2}m=FrT$$

Swap sides so that all variable terms are on the left hand side.

$$FrT=4\pi ^{2}r^{2}m$$

The equation is in standard form.

$$FrT=4\pi ^{2}mr^{2}$$

Divide both sides by Fr.

$$\frac{FrT}{Fr}=\frac{4\pi ^{2}mr^{2}}{Fr}$$

Dividing by Fr undoes the multiplication by Fr.

$$T=\frac{4\pi ^{2}mr^{2}}{Fr}$$

Divide 4\pi ^{2}r^{2}m by Fr.

$$T=\frac{4\pi ^{2}mr}{F}$$

Variable T cannot be equal to 0.

$$T=\frac{4\pi ^{2}mr}{F}\text{, }T\neq 0$$

Solve for F

$$F=\frac{4\pi ^{2}mr}{T}$$

$$T\neq 0\text{ and }r\neq 0$$