Abstarct: In recent years it has been shown that in relativistic heavy ion collisions at the Large Hadron Collider LHC and RHIC quark-gluon plasma (QGP) is produced by the strong coupling constant. Since the coupling is strong, one can not use perturbation approach. A new method for studying QGP is to use the AdS / CFT correspondence. The thesis has used this method and the problem of acceleration of heavy quarks in the QGP quark gluon plasma and vacuum is reviewed. To study accelerated motion, circular motion of a heavy quark with constant speed is considered. From the AdS / CFT, the dual picture is a rotating string t in the bulk. We begin with an overview of the resources in question and find the differential equation of motion for the case of plasma and vacuum. The different ways to solve them are examined analytically and numerically. Analytical solutions only in the case of quarks in the vacuum can be obtained and shown in other cases numerical methods must be used. Also lost energy quarks are studied in various limits and it can be seen that as the rotational accelerations decreases the drag force and as the rotational accelerations increases the radiation is dominant. Then a new problem is considered which express that the rotating heavy quark in the vacuum is moving with a constant speed in the direction of the axis of rotation. The energy loss is calculated and is shown analytically that in this casethe energy loss is greater than when the quark energy loss has only rotational motion. Another problem is that the study of the motion of rotation quarks in non-relativistic space –time and just move in vacuum.