Source of deformation on Spinning oblect

[quantumfoam]

Homework Statement

Hello guys! Now this is not a homework question, but it may sound like one. If a uniform sized and massed sphere was spinning in space away from any source of forces that could affect it, wouldn't the only forces that act on it are the centripetal and centrifugal? And if this sphere had elasticity, wouldn't the force that is stretching the sphere be either centripetal of centrifugal force? Now I am not including its gravitational force on purpose. Its gravitational field can be negligible. I also know that the centrifugal force is not a real force, but it is useful for explaining some phenomena. I'm using classical mechanics. The sphere will not be spinning at relativistic speeds.

Homework Equations

Well, mathematically, I figured that if the centripetal and centrifugal forces are the sources of deformation of stretching of the sphere, then by using Hooke's Law we find that
mωv=-kx
where mωv is the centripetal or centrifugal force magnitude and -kx is Hooke's Law. Is this right? Or am I forgetting something? I would really appreciate anyone's help. My extremely inferior mind is not sure of itself.

The Attempt at a Solution

 

[quantumfoam]

Can anyone help me?