# Centripetal Force Solver

The Centripetal Force Calculator is a tool for students, designed to help calculate the unknown parameters in the centripetal force formula.

The formula states that the force required to maintain an object moving in a circular path is equal to the mass of the object multiplied by the square of its velocity, divided by the radius of the circular path.
$F_{c}=ma_{c}=m{\frac {v^{2}}{r}}=m\omega ^{2}r$,

where
ac — centripetal acceleration,
m — mass,
v — speed,
ω — angular speed,

The calculator allows users to input any three known parameters and calculate the unknown parameter, making it an excellent tool for solving physics homework problems.

It can be used to calculate the force required to maintain an object in circular motion, the mass of an object moving in a circular path, the radius of a circular path required to maintain an object in motion at a certain speed, and the velocity required to maintain an object in a circular path of a certain radius. Here is an example of such problem: A 500-gram ball, attached to the end of a cord, is revolved in a horizontal circle with an angular speed of 5 rad/s. If the cord’s length is 50 cm, what is the centripetal force?

While the formula is not very hard, you can easily make errors by using wrong units, for example, revolutions per second instead of radians per second, centimeters instead of meters, and so on. The calculator allows users to easily convert between different units of measurement, making it a versatile tool. You can find formulas for each parameter below the calculator.

#### Centripetal force

Force

Mass

Speed

Angular speed

Digits after the decimal point: 3

### Derivation of formulas for unknown parameters from centripetal force formula

#### Force

$F_{c}=m{\frac {v^{2}}{r}}=m\omega ^{2}r$

#### Mass

$m={\frac {F_{c} r}{v^{2}}}={\frac {F_{c}}{\omega^{2} r}}$

$r={\frac {m v^{2}}{F_{c}}}={\frac {F_{c}}{m \omega^{2}}}$

#### Speed

$v=\sqrt{ \frac{F_{c} r}{m} }$

#### Angular speed

$\omega=\sqrt{ \frac{F_{c}}{m r} }$

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