Say that the ball was traveling due west at 10 fps right at the instant that the glue let loose. What direction and what velocity would the ball be going a second later? Still due west and 10 fps (though it would now be 10ft away from the disk). The ball did not accelerate or change direction, so there was no force acting on it, only inertia.
Ah, but is that the case? A simple test: Take any object on a string and spin it in a circle and let's see what you have. There's the object being subjected to all this abuse, and if we look at things we see it acted on by 3 things, primarily: the froce trying to spin it in the circle, and the string, which becomes centripetal force as it is holding/pulling the object toward the center. This creates a lateral acceleration toward the circle vs. the kinetic tendency to continue straight on a tangent with the circle. That acceleration creates a centrifugal force that pushes out from the center, extending the string.
I know you already disagree with that because in the minds of degreed engineers, the force extending the string is the centripetal. But we're getting to the good part.
Now that you have it spinning, your position on this is that if the centripetal force is abruptly terminated, the object will continue in a straight line in the direction it's going at the time. So which direction is it going? If I am spinning this setup over my head and facing 12:00 o'clock with 3:00 being at my right, and spinning it counterclockwise, then at the moment it reaches 12:00, the object is going where? Well, it's going in a circle, of course, and not straight in any direction. But according to what you've said, if it were not for the centripetal force accelerating it toward the center (thereby making it turn), it would continue forward from wherever and not move toward the center. So if, at this point, I terminate the centripetal force by releasing the string, the centrifugal force should also be eliminated and the object will fly straight to 9:00 on my left because that's where it was going when I let go of it.
Why then does it instead fly to about 11:30 when released at 12:00, hmm? Because at the instant I released the string the centripetal force was cut off immediately while the centrifugal force built up in the unit's mass had not been relieved yet. That force then accelerated it outward away from the center.