Understanding the centrifugal force
I'm learning about mechanics in noninertial frames and I'd like to clarify the apparent centrifugal force.
To set things straight,
Centrifugal force = Fcf = m(Ω×r)×Ω
where Ω×r is the instaneous velocity at a point on the outside of a circle (or other rotating path) and Ω is the angular velocity?
By looking at a picture, this would have the centrifugal force pointing out radially from the rotating path (which makes sense when imagining a centrifuge for example).
Is this force called "fictitious" because there is actually no force (as observed from a rotating frame of reference, or an inertial frame?) that is causing an object to accelerate in this radial direction? What is the force exactly?
For example - Imagine you are spinning a ball on a string around in circles and the string breaks, causing the ball to fly outward perpandicular to the direction of motion. Is the centrifugal force responsible for this?
How does this force relate to observations seen from a noninterial or inertial frame?