Centripetal Acceleration defines the distance that is covered and the direction of the movement. Since the velocity vector (the direction) of a body changes when moved in a circle - there is an acceleration.

a = v^{2 }/ r r = v^{2} / a v = (ar)^{1/2}

Where:

a = Centripetal acceleration and is directed perpendicular to v (m/s^{2}, in/s^{2})
v = Tangential velocity or instantaneous velocity (m/s, ft/s)
r = Radius of the circle (m, ft)
m = meters
ft = feet
s = seconds

Centripetal Force Equations

F = m a
F = m v^{2} / r

Where:

F = centripetal force (N, lb_{f})
a = Centripetal acceleration and is directed perpendicular to v (m/s^{2}, in/s^{2})
m = Mass (kg, slugs)
s = seconds