Solve for r (m_1v^2)/r=m_2g

$\frac{m_{1} v^{2}}{r} = m_{2} g$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$r, 1$

The LCM of one and any expression is the expression.

$r$

Multiply each term in $\frac{m_{1} v^{2}}{r} = m_{2} g$ by $r$ to eliminate the fractions.

Multiply each term in $\frac{m_{1} v^{2}}{r} = m_{2} g$ by $r$ .

$\frac{m_{1} v^{2}}{r} r = m_{2} g r$

Simplify the left side.

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{m_{1} v^{2}}{r} r = m_{2} g r$

Rewrite the expression.

$m_{1} v^{2} = m_{2} g r$

Solve the equation.

Rewrite the equation as $m_{2} g r = m_{1} v^{2}$ .

$m_{2} g r = m_{1} v^{2}$

Divide each term in $m_{2} g r = m_{1} v^{2}$ by $m_{2} g$ and simplify.

Divide each term in $m_{2} g r = m_{1} v^{2}$ by $m_{2} g$ .

$\frac{m_{2} g r}{m_{2} g} = \frac{m_{1} v^{2}}{m_{2} g}$

Simplify the left side.

Cancel the common factor of $m_{2}$ .

Cancel the common factor.

$\frac{m_{2} g r}{m_{2} g} = \frac{m_{1} v^{2}}{m_{2} g}$

Rewrite the expression.

$\frac{g r}{g} = \frac{m_{1} v^{2}}{m_{2} g}$

Cancel the common factor of $g$ .

Cancel the common factor.

$\frac{g r}{g} = \frac{m_{1} v^{2}}{m_{2} g}$

Divide $r$ by $1$ .

$r = \frac{m_{1} v^{2}}{m_{2} g}$