Is my understanding of inertial frames correct?

Question

My teacher taught us the concept of inertial frames in a manner not usually presented in books. So I wish to confirm if his approach to the concept is valid. Firstly he makes some points clear :

1. Acceleration has two causes, one being Force and other being the reference frame itself. He defines force outside atomic nucleus as mass-mass interaction and charge charge interaction mathematically represented by the equations for Gravitational Force and Electromagnetic forces which are frame independent. An inertial reference frame is a frame of reference in which the only cause for acceleration of a body is a net Force.
2. To find an Inertial reference frame, find a body in the universe whose net Force is 0 by using the equations of above forces. Then find a reference frame in which the body is at rest or moving with constant velocity. (Or attach your reference frame to the body itself). Then such a frame is called an inertial reference frame because the only cause for acceleration is Force.
3. Newton's first law is an assertion that an inertial frame exists.

After this he gives a justification of why and when can we assume Earth to be an inertial reference frame, when rotation of Earth can be ignored.

Assume you are observing the Earth from an inertial reference frame. We can apply Newton's second law for Earth $\sum \mathbf{F}_{Earth}= {m}_ {Earth}\mathbf{a}_{Earth}.$

Assume there exists a particle on Earth with mass m. Write It's Net form as a vector sum of Forces applied by the Earth and bodies which are not Earth.

$\sum \mathbf{F}_{Not Earth} + \sum\mathbf{F}_{By Earth} = {m}\mathbf{a} $

Since most forces are applied over long distances almost all Interactions will be gravitational and hence of the form $\mathbf{F} = Gm_1m_2/r^2 $

Thus dividing the above equations by masses of Earth and particle we get $\sum \mathbf{F}_{Not Earth}/m = \sum \mathbf{F}_{Earth}/{m_{Earth}} $ From this we get $\mathbf{a} - \mathbf{a_{Earth}} = \sum \mathbf{F_{ByEarth}}/m $

$ m\mathbf{a_{fromEarth}} = \sum \mathbf{F_{ByEarth}}$

I find this explanation much more satisfying than the usual explanations I have found in books but I wish to know if this can be extended to the scenario Earth's rotation is to be considered and can we justify the neglecting of Electromagnetic Forces without Newton's Laws.

Answer 1

I like the philosophy of your professor (to associate Newton's First Law to inertial frames, rather than the standard "an object in motion stays in motion unless acted on by a force", which seems to be already taken care of by Newton II). If we want Newton's Laws to be a set of axioms for mechanics then it should not repeat the content of the Second Law and it must account for this issue of what is a valid frame (in which to apply Newton II).

I tell my students that Newton's First Law is: (1) the definition of an inertial frame (a frame in which an object experiencing no net force moves with a constant velocity), and (2) a statement that the other laws should only be applied in an inertial frame. The first part also acts as a test of whether your laboratory is an inertial frame: put a ball on the floor and make sure it does not have any unexplained accelerations (like it would if your lab is on the back of a truck that's starting and stopping).

I could not follow your discussion starting at "Thus dividing the above equations..." nor how it proves that the Earth can be treated as an inertial frame. For performing mechanics experiments, the Earth is close enough to inertial. But for understanding the weather, it is not at all inertial (the "fictious" Coriolis force is essential to describe the atmospheric motion).