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Centripetal force

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

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,
r - radius of curvature.

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 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. Derived formulas for each parameter can be found below the calculator.

PLANETCALC, Centripetal force

Centripetal force

Force
 
Mass
 
Speed
 
Radius
 
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}}

Radius of curvature

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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Creative Commons Attribution/Share-Alike License 3.0 (Unported) PLANETCALC, Centripetal force

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