Inertial Reference Frame Locally

Why can we not CHOOSE a reference frame locally and treat everything inside of it as an inertial reference frame. For example in a classroom, the classroom is moving with the earth and so is a ball rolling down the class. Because they are both equally moving due to the earth's rotation, why can't we just ignore that? Simply treat that class room as a inertial reference frame For THIS REASON..

(I know we can treat it as an inertial reference frame because the acceleration of the earth for that short time and distance is negligible, but that's another reason, i would like to know why my reasoning is wrong, such that if they weren't negligible we could still ignore them.)

Thank you!

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How many legs does a horse have if you call a tail a leg?

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Why can we not CHOOSE a reference frame locally and treat everything inside of it as an inertial reference frame. For example in a classroom, the classroom is moving with the earth and so is a ball rolling down the class. Because they are both equally moving due to the earth's rotation, why can't we just ignore that? Simply treat that class room as a inertial reference frame For THIS REASON..

(I know we can treat it as an inertial reference frame because the acceleration of the earth for that short time and distance is negligible, but that's another reason, i would like to know why my reasoning is wrong, such that if they weren't negligible we could still ignore them.)
Non-inertial frames have fictitious forces. If those forces are not negligible then you cannot ignore them.

Khashishi