Centripetal Force

on . Posted in Classical Mechanics

centripetal force 1Centripetal force, abbreviated as \( F_c \) or \( F_{cp} \), is the force that makes an object follow a curved path.  It is a force generated when an object keeps traveling along a axis of rotation.  An example of of centripetal force is when driving around a corner.  The centripetal force is the reactionary force equal to the centrifugal force felt.  When centripetal force is greater than the centrifugal force, the vehicle will lose traction and slide. 

Centripetal Force Index

The most common example of centripetal force is when a body moves with uniform speed along a circular path.  The centripetal force is directed at right angles to the motion and points to the center or the curve.   The equations below and their associated calculator shows two different ways of calculating centripetal force.

 

centripetal force formula

\(\large{ F_c =  m \; a_c }\)     (Centripetal Force)

\(\large{ m =  \frac{F_c}{a_c} }\) 

\(\large{ a_c =  \frac{F_c}{m} }\) 

Solve for Fc

mass, m
centripetal acceleration, ac

Solve for m

centripetal force, Fc
centripetal acceleration, ac

Solve for ac

centripetal force, Fc
mass, m

 Symbol English Metric
\(\large{ F_c }\) = centripetal force \(\large{lbf}\) \(\large{N}\) 
\(\large{ a_c }\) = centripetal acceleration \(\large{\frac{ft}{sec^2}}\) \(\large{\frac{m}{s^2}}\)
\(\large{ m }\) = mass \(\large{lbm}\) \(\large{kg}\)

 

centripetal force formula

\(\large{ F_c = \frac { m \; v^2 }{ r } }\) 
 Symbol English Metric
\(\large{ F_c }\) = centripetal force \(\large{lbf}\) \(\large{N}\) 
\(\large{ m }\) = mass \(\large{lbm}\) \(\large{kg}\)
\(\large{ r }\) = radius of circular path \(\large{ft}\) \(\large{m}\)
\(\large{ v }\) = velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{sec}}\)

 

centripetal force formula

\(\large{ F_c =  m \; \omega^2 \; r  }\) 
 Symbol English Metric
\(\large{ F_c }\) = centripetal force \(\large{lbf}\) \(\large{N}\) 
\(\large{ \omega }\)   (Greek symbol omega) = angular velocity \(\large{\frac{deg}{sec}}\) \(\large{\frac{rad}{s}}\)
\(\large{ m }\) = mass \(\large{lbm}\) \(\large{kg}\)
\(\large{ r }\) = radius of circular path \(\large{ft}\) \(\large{m}\)

 

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Tags: Force Inertia