"Strictly speaking, Newton’s laws of motion are valid only in a coordinate system at rest with respe

"Strictly speaking, Newton’s laws of motion are valid only in a coordinate system at rest with respect to the 'fixed' stars. Such a system is known as a Newtonian, or inertial reference frame. The laws are also valid in any set of rigid axes moving with constant velocity and without rotation relative to the inertial frame; this concept is known as the principle of Newtonian or Galilean relativity."
Why should the inertial frame of reference not spin?
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Nollothwnfcm
From a Newtonian perspective, the earth and sun are not inertial frames since the earth orbits the sun (accelerates) and the sun orbits the galactic centre (accelerates) and the galaxy ...However they are "close enough" for most calculations
The standard statements of Newtons Laws are now more than 300 years old and they carry implicit assumptions that are not at all obvious (e.g. existence of a common time). An inertial frame is one where $F=ma$ where $F$ is the resultant force calculated from our knowledge of engineering. In an non-inertial frame "mysterious" forces appear (e.g. centrifugal force).
If $x$ is an inertial frame coordinate system, and $y$ is moving a constant velocity relative to $x$, then y=x+v.t. $y=x+v.t$. Differentiating ${a}_{Y}={a}_{X}$ so $F=ma$ in both coordinate systems. I.e. $y$ is an inertial frame coordinate system too. If $y=f\left(x\right)$ rotates with respect to $x$, the $y$ would not be a inertial frame coordinate system since $F=ma$ would no longer hold.