Why do I feel centrifugal acceleration when standing on a revolving ball?

[Like Tony Stark]

Homework Statement

Let's suppose that I have a ball attached with a string, and I'm making it spin.

Relevant Equations

Newton's equations

If a "stand" on the ball, I would feel a centrifugal force, which would be pulling me out of the circle. But in the equation of centrifugal force we have $\vec r$, which is the vector that goes from the centre of the non inertial frame to the body in motion. But if I'm on the ball, my system is the ball, and the distance from the system (the ball) to the particle (the ball) is zero, so why do I feel centrifugal acceleration?
Then, if I want to consider the centrifugal force of a body falling from a skyscrapper, which would be the direction of $\vec r$ that I should consider? From the body to the centre of the Earth, or from the centre of the Earth to the body?

 

[tnich]

You feel acceleration because your velocity (in the inertial frame) is changing. The direction of the acceleration vector in that frame is toward the center of the circle. The acceleration is applied to your feet by the ball, and feels like the normal force on your feet when you stand on the earth. Even if you think of yourself as stationary in the non-inertial frame of the revolving ball, you still feel the force of the ball on your feet. You can't tell the difference between that and the normal force of earth. So it "seems like" there is an equal and opposite gravity-like force that balances the normal force on your feet and holds you stationary. That imaginary centrifugal force is directed away from the center.