When I first learned Newtonian mechanics, I found it much easier to solve certain problems thinking in terms of centrifugal force, rather than centripetal force

When I first learned Newtonian mechanics, I found it much easier to solve certain problems thinking in terms of centrifugal force, rather than centripetal force, and thinking so did me none the worse, as long as I kept in mind the caveats required for this approach. E.g., the classic problem of determining at what point you will fall off when skiing straight down a giant frictionless spherical snow ball. For me this is much easier to analyze by asking yourself at what point the centrifugal force pushing you off of the snowball will counteract the vector of gravity that is pushing you onto the snowball's tangent. The so-called "right" way of thinking about this problem is at what point the centripetal vector of gravity is no longer sufficient to constrain your movement to a circle. That's much harder to visualize for me. And would be even more so for non-spherical shapes. The real right way to think about this, is to think about it both ways and then to convince yourself that they are equivalent. Not to pretend that there is no such thing as centrifugal force.