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Galilean relativity principle states that two frames moving with uniform linear motion cannot be distinguished. But is it always possible to realize to be in a non-inertial frame?

In a rotating frame it is surely possible for the observer to realize that because of Coriolis force, which cannot be explained, even supposing the presence of a source of force somewhere.

But in a frame moving linearly, for istance, with acceleration $A$? Coriolis term is not present, so what is the way for the observer in the frame to realize that he is in a non-inertial frame?

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    $\begingroup$ Newton's laws don't apply in non-inertial frames. If you let go of a ball and it falls to the floor or drifts to the ceiling, there is a non-inertial acceleration term that wouldn't be there if you were in an inertial system. $\endgroup$
    – CuriousOne
    Commented Apr 6, 2016 at 21:36
  • $\begingroup$ @CuriousOne: this should be an answer, because it is. $\endgroup$
    – user107153
    Commented Apr 6, 2016 at 23:50
  • $\begingroup$ The most easiest: watch whether all bodies, small or large, are having same acceleration. $\endgroup$
    – user36790
    Commented Apr 7, 2016 at 10:03

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It is possible as soon as one is sure to be very distant from every body (gravitational source) in the universe. This is because all inertial forces behave as gravitational forces. If one is confined to stay in a closed room and observes the motion of bodies therein, he/she cannot decide whether the observed accelerated motion is due to a gravitational field or to fictitious inertial forces. However if he/she is allowed to check the distribution of masses outside the room he/she can decide which of the two options is the correct one.

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In a non-inertial frame, observers will see fictitious forces with no reaction pair. For example, in a frame accelerating linearly forward, there appears to be a force acting backwards, and one cannot find the reaction (or source) of this force.

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