Centripetal force

This online calculator calculates unknown parameter in the centripetal force formula, whether force, mass, radius or speed.

Timur

Created: 2020-09-09 13:54:10, Last updated: 2021-02-25 07:04:40

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The calculator below can be used to verify solutions of centripetal force problems. If you have a problem with numeric data, you are supposed to use centripetal force formula:

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

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

The formula relates four parameters. Thus three parameters should be given in the problem statement, sometimes indirectly, and the fourth parameter should be calculated. 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. That's why the calculator allows different units for each parameter and takes care of converting them to SI units and back. You can find formulas derived 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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