Swings use a physics principal known as Centripetal Acceleration. Acceleration is either a change in direction or speed. A swing traveling in a circular motion is constantly changing direction; it is always accelerating. According to Newton, all accelerations are created by forces that act upon the object. This holds true for centripetal accelerations; they are created by forces acting in toward the center of the circle formed by the circular path. These forces are known as Centripetal Forces.
The magnitude of the centripetal acceleration (a) of an object traveling in a circle of radius (r) and traveling at a velocity (v) is given by a=v^2/r.
The force required to create this acceleration (according to Newton’s Second Law) is given by mv^2/r. The m stands for the mass of the object.
The Centripetal Force Factor is the centripetal force divided by the weight of the object. This indicates what fraction of the weight of the object is required to cause the object to move in a circle.
In the example of the circular moving swing, the formula would be
(mv^2/r)/mg = v^2/rg
v= velocity of the turn
r= radius of the turn
g= gravity force
m= mass of the swing (or moving object)
Another real-life example:
A ball on string is attached to the end of a stick. The ball is swung overhead until the string is stretched parallel to the ground.
The tension in the string provides not only the force required for circular motion, but also the force to support the ball's weight.
Centripetal Force Factor = Force/mg = Tan 
Tan = Centripetal Force /mg
or
Centripetal Force = mg (Tan )
In plain words:
The centripetal force factor of any object in circular motion is equal to the tangent of the angle at which the swinging object hangs.
The angle that an object will hang as it swings can be determined using the inverse tangent.