Centripetal Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

acceleration centripetal 2Centripetal acceleration ( \(a_c\) ) is acceleration towards the center that keeps an object in an elliptical orbit with the direction of the velocity vector constantly changing.

Centripetal Acceleration Formula

\(\large{ a_c = \frac { v^2 } { r }   }\)         

\(\large{ a_c = \frac {  \left( r  \omega \right) ^2 } { r }   }\)         

\(\large{ a_c = r \omega^2  }\)         

Where:

\(\large{ a_c }\) = centripetal acceleration

\(\large{ \omega }\)  (Greek symbol omega) = angular velocity

\(\large{ r }\) = radius

\(\large{ v }\) = velocity

Solve for:

\(\large{ v =   \sqrt { a r }   }\)

\(\large{ r = \frac { v^2 } { a }   }\)

 

Tags: Equations for Acceleration