The "war on centrifugal force" is pedagogical. If you sit in an inertial frame, all forces you intend to teach are due to interactions between objects. This lets teachers introduce the interactions one at a time in a way that presents minimal opportunity for the "no, that equation doesn't work here for XYZ reasons which you won't understand until after you've taken vector calculus" problem.
If you allow rotating reference frames then you've got to talk about transformation rules in gory detail. Everyone understands centrifugal force, but what about the coriolis and euler forces? Our intuition doesn't tell us when they apply and when they don't, so we have to be systematic about it, and that means "gory details". And guess what "being systematic about it" involves? Moving to an inertial frame of reference and taking derivatives!
You can't be intuitively correct or systematic about rotating frames without thoroughly understanding inertial frames, so that's what you learn first, along with strongly worded advice to stay away from non-inertial frames (e.g. defining frame-dependent forces as "fictitious").
Anyone doing general relativity is comfortable enough with coordinate transformations that they can understand the caveats that come with frame-dependent forces and even take advantage of them to simplify calculations or definitions (the process of going from a "global" to a "local" coordinate system is highly nontrivial in GR).
That's why the Coriolis, Euler, and Centrifugal forces are called "fictitious" while gravity isn't.
This is what I love about HN - an anti-troll comment. Like most of us I think a generalist knowledge confers the right to an opinion and expressing that opinion.
Comments like this point out just how much I do not know, they sweep their arms across a horizon of maths and hard won understanding and say "only express that opinion after you know what that means"
Anti-trolling.
It's what keeps us honest about our own limitations, and reluctant to spout off crap.
love it. Now going to look up inertial frames and start translating.
If you allow rotating reference frames then you've got to talk about transformation rules in gory detail. Everyone understands centrifugal force, but what about the coriolis and euler forces? Our intuition doesn't tell us when they apply and when they don't, so we have to be systematic about it, and that means "gory details". And guess what "being systematic about it" involves? Moving to an inertial frame of reference and taking derivatives!
You can't be intuitively correct or systematic about rotating frames without thoroughly understanding inertial frames, so that's what you learn first, along with strongly worded advice to stay away from non-inertial frames (e.g. defining frame-dependent forces as "fictitious").
Anyone doing general relativity is comfortable enough with coordinate transformations that they can understand the caveats that come with frame-dependent forces and even take advantage of them to simplify calculations or definitions (the process of going from a "global" to a "local" coordinate system is highly nontrivial in GR).
That's why the Coriolis, Euler, and Centrifugal forces are called "fictitious" while gravity isn't.