(A) \(\hat{e}_r=\cos\theta\,\hat\imath+\sin\theta\,\hat\jmath\) and \(\hat{e}_\theta=-\sin\theta\,\hat\imath+\cos\theta\,\hat\jmath\) change direction with \(\theta\): \(\dot{\hat{e}}_r=\dot\theta\,\hat{e}_\theta\) and \(\dot{\hat{e}}_\theta=-\dot\theta\,\hat{e}_r\). True.
(B) \(F_1=m\ddot r\) and \(F_3=mr\ddot\theta\) are the “\(m\times\)acceleration” terms an observer co-rotating with the radius vector would measure directly. They are not fictitious. False.
(C) \(F_2=-mr\dot\theta^2\) and \(F_4=2m\dot r\dot\theta\) arise only from the rotation of the unit vectors. Seen from the rotating frame they appear as the centrifugal (\(mr\dot\theta^2\) outward) and Coriolis (\(-2m\dot r\dot\theta\)) pseudo-forces. True.
(D) In uniform circular motion \(\ddot r=0\), so \(F_1=0\), but \(F_2=-mr\dot\theta^2\neq0\) (the centripetal term). False.
\[
\boxed{\text{(A) and (C)}}
\]
Answer: (A), (C)
