A non-rigid object (such as a beam, rod, blade, etc.) experiences elongation due to the (fictitious) centrifugal force when rotated (as opposed to rigid bodies and simple mass points). This elongation can be easily viewed in the inertial frame of reference and in the rotating frame of reference. There are sources which claim that the centripetal force and the centrifugal force, which act on a mass element of length dx at any position along the longitudinal axis of the object, are the same in magnitude and opposite in direction. In force equilibrium, how is it possible that the length of a non-rigid object becomes greater as a result of rotation? To my understanding, a resultant force is required so that any deformation of the non-rigid object can occur.
Please correct me if any of my above statements are wrong. I would appreciate and be thankful if someone explained the matter to me by using formulas, please.