Law of inertia (inertial observer and inertial frames of reference)

[Vigorous]

I am trying to figure out what are inertial observer and inertial frames of reference. The law of inertia holds for inertial observers. Inertial observers are objects with zero net force acting on them, and move with constant velocity. Suppose we fix a set of coordinate axis in space, relative to that set of coordinate axis we can measure the particles location with time. Hence measure its velocity and know if it changes or not. But we still haven't tested the requirement that no forces are acting on the particle. so what I am trying to get at, is that an inertial observer is a particle analysed for the forces acting on it and if they sum to zero and the velocity is changing then the law of inertia does not hold. But why do we come to this conclusion and not say that the force analysis done on the particle is incomplete. Acceleration calls for a force.

 

[Dale]

This is somewhat difficult to do experimentally using Newtonian physics. However, with general relativity, or even with Cartan’s version of Newtonian physics, it becomes very straightforward:

An inertial object is one where an attached accelerometer (the 6 degree of freedom kind) reads 0.

An inertial frame is one where inertial objects have 0 coordinate acceleration.

 

[A.T.]

The law of inertia holds for inertial observers.

It doesn't make sense to apply just one of Newtons Laws. The only make sense together.

But why do we come to this conclusion and not say that the force analysis done on the particle is incomplete.

Newtons 3rd Law tells you what qualifies as real forces, and in Newtonian physics that includes Gravity.