  In this paper we deal analytically with a version of the so called clock
paradox in which the moving clock performs a circular motion of constant
radius. The rest clock is denoted as (1), the rotating clock is (2), the
inertial frame in which (1) is at rest and (2) moves is I and, finally, the
accelerated frame in which (2) is at rest and (1) rotates is A. By using the
General Theory of Relativity in order to describe the motion of (1) as seen in
A we will show the following features. I) A differential aging between (1) and
(2) occurs at their reunion and it has an absolute character, i.e. the proper
time interval measured by a given clock is the same both in I and in A. II)
  From a quantitative point of view, the magnitude of the differential aging
between (1) and (2) does depend on the kind of rotational motion performed by
A. Indeed, if it is uniform there is no any tangential force in the direction
of motion of (2) but only normal to it. In this case, the proper time interval
reckoned by (2) does depend only on its constant velocity v=romega. On the
contrary, if the rotational motion is uniformly accelerated, i.e. a constant
force acts tangentially along the direction of motion, the proper time
intervals $do depend$ on the angular acceleration alpha. III) Finally, in
regard to the sign of the aging, the moving clock (2) measures always a
$shorter$ interval of proper time with respect to (1).
