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In order to study quark and anti-quark interaction, one should consider alleffects of the medium in motion of the pair. Because the pair, is not producedat rest in QGP. So the velocity of the pair, has some effects on itsinteractions that should be taken into account. In this paper we apply someconformal transformations for a rotat- ing string dual to a rotating heavyquark in $AdS_3$ which construct an accelerating string dual to an acceleratingquark and anti-quark pair. So, we can have a comparison between when pair hasangular velocity or not. Then we can study effects of angular velocity on theaccelerating quark and anti-quark which are constructed by performing specialcon- formal transformations, conformal SO(2,2) transformation and particular$SL(2,R)_L$ and $SL(2,R)_R$ transformation. The accelerating quark andanti-quark show different behavior with increasing in angular velocity. Withuseful numerical solutions we show that quark and anti-quark can deccelerate toachieve each other or accelerate to get away from each other. We will seevariable behaviors of the pair in different transformations. There are variousbehavior like, permanent behavior, increase or decrese in acceleration or wewill consider uncertain behavior.

Conformal Transformations, Rotating String and Effects of angular velocity on Accelerating Quark-Antiquark pair in $AdS_3$