**Formula**

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

where 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. The speed in the formula is squared, so twice the speed needs four times the force. The inverse relationship with the radius of curvature shows that half the radial distance requires twice the force. This force is also sometimes written in terms of the angular velocity *ω* of the object about the center of the circle:

Expressed using the period for one revolution of the circle, *T*, the equation becomes:

Read more about this topic: Centripetal Force

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