I know that centrifugal is labeled a fictitious force only arising in a rotating reference frame, but I still struggle to understand the forces at play intuitively in tethered rotating bodies.
I've always been told that the reason a slingshot works is because the ball wants to go in a straight line. "Yeah cool", I've always just nodded my head but never been able to understand it really. Intuitively why wouldn't that straight line be in the direction of acceleration - which would be the tangent line at the arc segment at release point. The direction of acceleration is the same direction for the propagation of inertia usually!? The fact that its perpendicular really makes it look like its own force! It appears as if inertia in one direction is instantly translated to its perpendicular!
Also, (this might be two questions), if every force has an equal and opposite one, then why is centripetal force considered a legitimate force but its opposite (centrifugal) a fictitious force? Centripetal ALSO only occurs in a rotating reference frame right?
Everything I've read about these two "forces" over the years is always included the same old catch phrases, but for some reason I can't understand it intuitively. I've seen the pictures of the boy with the ball on the string and the arrows pointing inwards for centripetal and outwards for centrifugal but to me thats just labelling an observed effect that is occurring. It doesn't explain WHYYYYY :). I've parroted off the mechanics to people many times with zero intuitive understanding as to why its all happening.
Is the explanation related to inertial properties?