In galilean relativity, is an observer assumed to be at rest only to simplify calculations, or is there a physical reason for this assumption?

Question

I am a beginner in Physics and my teacher taught us "Relative Motion" yesterday. He said that the "Observer is assumed at rest." Is the observer assumed to be at rest only to simplify calculations, or is there some physical basis for this assumption?

For example, observer A is moving with an acceleration of 2 $\frac{m}{s^2}$, observer B is at rest, and A sees B accerating at $-2 \frac{m}{s^2}$. But we know that acceleration comes from Force (Newton's Second Law). So for B to be accelerating, they should have some net Force. But in reality, we know that B does not have any net force acting on it?

Answer 1

Is the observer assumed to be at rest only to simplify calculations, or is there some physical basis for this assumption?

As you guessed, the purpose is to simplify calculations. I don’t think I would call it a physical basis, but rather a mathematical basis.

What we are trying to do is to express our physical scenario as a mathematical equation, and then solve that equation to tell how the physical scenario will behave. But we can always use algebra to change it to a different mathematical equation that has the same solution. That will still tell us how the physical scenario will behave.

Now, in the scenario you gave above, it may not seem to make much sense to change to the accelerating frame. But suppose that you are trying to calculate a mission for a rocket. You may find it much easier to solve the equations in coordinates where the moon is stationary rather than rotating around the earth.

Choosing good coordinates is somewhat of an art. But it can make the difference between getting an analytical solution, a numerical solution, or no solution at all.

Answer 2

All physics is equal in inertial systems, i.e. in systems which are not accelerating. As soon as we are looking at the world from the perspective of a non-inertial system, we will be seeing fictitious forces that SEEM to accelerate objects that are actually moving on inertial trajectories. It sounds like that is the lesson that your teacher is trying to teach here. Another way of saying this is that "the world looks the most simple from the viewpoint of an inertial observer", because such an observer does not have to deal with fictitious forces.