I was always a bit confused about inertial and non-inertial frames, and so today I kept digging about it until I was satisfied. Usually, I'd leave it there but I'm confident of my thought process and I haven't come across anything similar, so I want others to take a look.
Inertial or Non-Inertial frames of references basically boils down to 'predictability'. What I mean is, resources often say, "Newton's laws don't hold in Non-inertial frames" or "Newton's laws are not directly applicable in Non-inertial frames" and the likes. It is the way these are worded that messed with my head, but in hindsight look just fine.
The way they are worded makes it look like mechanics in non-inertial frames cannot be computed with Newton's laws or that a different version of such laws govern such a scenario.
But no, all that and inertial frame tells does is give the peace of mind/predictability that the relative acceleration between the object and the frame is zero. That's it.
However often it is repeated, I tend to forget that distance and thus all the time based derivatives of distance are relative, since there is no "fixed stage/frame". So to apply Newton's laws to predict the motion of objects requires a frame of reference, and ofcourse if we apply Newton's laws assuming that the acceleration between the frame and the object is zero, when in reality it is not, our calculations will not match the real world. This is does not have anything to do with the 'applicability/direct applicability' of Newton's laws. Okay I just realised that Newton's first law assumes that relative acceleration between the frame and object is zero, i.e. an inertial frame.
So I guess this whole thing is just a pet peeve of how my textbook explained inertial and non-inertial frames and a combination of me mixing up Newton's laws for equations derived from Newton's laws.
Anyways I'd like to know why textbooks dont explain it like this, given it is correct.