Question: Could a mechanical experiment be performed in a given reference frame which would reveal the information about the acceleration of that frame relative to an inertial one?

My Guess: I have assumed that the observer in accelerating frame has no contact with any observer in inertial frame. Because if he did, both the observers may simply measure the acceleration of some accelerating object with respect to their frames and conclude that the measured values of accelerations are unequal.

Assuming the isolation of the observer in accelerating frame, now, Newton's laws of motion cannot be applied in an accelerating frame (I know they can be applied provided we introduce fictitious forces but suppose the observer does not do so in his calculations).

So I think one of the experiments can be: we measure the net momenta of two masses before and after a head-on collision. If the two net momenta happen to be equal, the frame is inertial otherwise it is accelerating

Does this reasoning make sense?