# What are the variants of the centripetal force formula?

Like, how would you make Fc = mv2/r into m=... ?

### 3 Answers

- Steve4PhysicsLv 710 months agoBest Answer
F = mv²/r

Multiply both sides by r:

Fr = mv² (equation 1)

___________________

Divide both sides of equation 1 by v²:

Fr/v² = m

______________________

Divide both sides of equation 1 by F:

r = mv²/F

______________________

Divide both sides of equation 1 by m:

Fr/m = v²

The square root both sides:

√(Fr/m) = v

Make sure you can do this for yoursefl as rearranging formulae is an essential skill!

- Andrew SmithLv 710 months ago
F = mv^2/r

F = m w^2 R

F = 2 Ek / R

F = - U / R

There are so many variants that are used for different purposes.

However for the formula you quote there are four unknowns so that there are four variants with a single quantity as the subject.

But there are three more variants with two variables on each side of the equation.

And one with no variables on one side of the equation.

F = m v^2 / r

m = F.r / v^2

r = m v^2 / F

v = sqrt ( F.r/m)

F.r = m v^2

F/m = v^2 / r

F/ v^2 = m/r

F.r/(m v^2) = 1

But there are also many whole FAMILIES of centripetal force formulae

F= m w^2 R

F = 2Ek/ R

F = - U/ R

And still more that apply in other circumstances such as elliptical orbits.

You CANNOT attempt to remember every possible variant of a formula. There are way too many for that.