Since you don't seem to like that definition I would be fascinated to know what word you, Silvertiger, would choose as your alternative. ;-)A centripetal force (from Latin centrum, "centre" and petere, "to seek") is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.
Edit:
It seems to me that your confusion arises because in your anxiety to draw attention to the centrifugal force you are trying to ignore the centripetal force.
Both forces act on a radius member. We have action and reaction to keep the elements of a rotating radius component in dynamic equilibrium.
We have the centripetal force pulling an element towards the centre and a centrifugal force pulling the element towards the circumference.
The physical manifestation of these two forces is of course the radial tensile strain in the element.
Both forces are real forces. You can't be a little bit pregnant and you can't have strains produced by unreal forces.