You have said:
If,for instance,the relative motion observed between two frames of reference is that of uniform acceleration, how can we determine which frame is the unaccelerated system? It is obviously not possible.
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Another part of this very question is also: How can we call the occupied frame of reference as being inertial regardless of whether other frames of reference are accelerating with respect to the occupied frame of reference?
Both these questions have been answered below.
Why would it not be possible? If you are in a reference frame which is accelerating at all, then you will experience pseudo-forces(forces whose source is not determined in that frame). That will tell you that your frame is accelerating. Moreover,if the relative motion between two frames is that of uniform acceleration,then both are accelerating! You do not have to determine WHICH is accelerating! The presence of acceleration(uniform or not) for any reference frame, guarantees that you will experience pseudo-force if you are in it.
for example, if you throw a ball from a height,it seems to hit the ground after travelling a path perpendicular to ground. but the actual trajectory is not so. as the ball falls it is deflected due to Coriolis force,which is a pseudo-force. so technically the earth is not an inertial frame of reference in any way since we can never point to a source who caused this Coriolis force!
You have said:
Resnick states that the frame of reference he occupies is an unaccelerated one. With respect to what? If accelerated motion were to be observed with respect to other frames of reference, how are we to determine that we occupy an inertial frame of reference at all?
According to Resnick he occupies an inertial frame that means, in his frame, Newton's first law holds true. obviously you need a reference object.
when we say a car travels at 75m/s then we actualy mean it travels 75m/s with respect to, say,a stationary tree. but it would travel at 50m/s with respect to another car travelling with 25m/s. so you need a reference object.
The pseudo force depends only on the acceleration of the observer frame (which is why if the acceleration of the observer is zero (in the inertial reference frame case) there is no pseudo force.)
Therefore, given that the acceleration of the observer is $A_2$ the pseudo force acting on any body (which has mass $m$) observed will be $-m \cdot A_2$.
No, we do not take the relative acceleration of the observer and the body observed but the acceleration of the observer as measured by any inertial frame.
Best Answer
Indeed you are correct, it is not necessary to refer to a second frame in order to determine if the first is inertial. You can simply use accelerometers. If the acceleration relative to the reference frame is not equal to the acceleration measured by the accelerometer (for all accelerometers) then the frame is non-inertial.
For example, say we are using a spinning space station as our reference frame. An accelerometer at rest on the space station is not accelerating relative to the reference frame, but the accelerometer measures centripetal acceleration. Therefore it is a non inertial frame. No comparisons to other frames are needed