How do I transpose the formula F=mv²/r to make v the subject ?

The concept to remember is that you can multiply both sides of the equation by the same amount and the equation remains true. You can also divide both sides by the same amount, or add or subtract the same amount, or raise both sides to the same power, and it remains true. Here the object is to get 'v' by itself. You could proceed like this:

Starting with
F = \frac {mv^2} r


We need to get rid of the factors 'm' and 'r' on the right hand side. So first let's multiply both sides by 'r', and see how that allows us to eliminate the 'r' factor on the right hand side::


[math]F \times r = \frac {mv^2} r \times r = \frac {mv^2} {\cancel r} \times \cancel r =mv^2\\
Fr = mv^2


Now divide both sides by m:

\frac {Fr} m = \frac {mv^2} m = \frac {\cancel m v^2} {\cancel m} = v^2\\
\frac {Fr} m = v^2


Finally we need to eleminate the power of 2 on the right hand side. We can do tgis by taking the square root of both sides:


\frac {Fr} m = v^2 \\
\sqrt {\frac {Fr} m} = \sqrt {v^2} = v


So the conclusion is:


v = \sqrt { \frac {Fr} m}


Hope this helps.