#### Centripetal Acceleration, Force Equations and Calculator

**Centripetal Acceleration and Force Equations**

**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

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