Centripetal Force

Centripetal force (from Latin centrum "center" and petere "to seek") is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens. Isaac Newton's description was: "A centripetal force is that by which bodies are drawn or impelled, or in any way tend, towards a point as to a center."

Formulae

The magnitude of the centripetal force on an object of mass m moving at a speed v along a path with radius of curvature r is:^[5]

$F = ma_c = \frac{m v^2}{r}$

where

a c

is the centripetal acceleration. The direction of the force is toward the center of the circle in which the object is moving, or the osculating circle, the circle that best fits the local path of the object, if the path is not circular.^[6] This force is also sometimes written in terms of the angular velocity ω of the object about the center of the circle:

$F = m r \omega^2 \,$