Centripetal acceleration

In Kinematic of the not, the centripetal acceleration is the acceleration, directed towards the center, of a point in rotation around a fixed axis. If the point turns around the center at a distance r and with a angular Velocity $\ omega$ × sec^-1 then the size of its centripetal acceleration is

$a_c = \ omega^ 2 r = \ frac {v^2} {R}$

where $v$ is the speed of the point on the circle.

In vectorial terms one a:

$\ mathbf {has} _c = - \ frac {v^2} {R} \ hat {\ mathbf {R}} = - \ frac {v^2} {R} \ frac {\ mathbf {R}} {R} = - \ omega^2 \ mathbf {R}$

where $\ mathbf {R}$ is the vector connecting the center to the point in rotation, $\ hat {\ mathbf {R}} = \ mathbf {R} /r$ is a vector of the same unit direction than $\ mathbf {R}$ and $v$ is the speed of the point (the standard of the Flight Path Vector $\ mathbf {v}$ ).

The sign - indicates that acceleration is directed towards the center (contrary to the vector of position which is directed towards the point)

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The concept of Centrifugal force is related to centripetal acceleration.

See too

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