A and B move at speed v (v << c) in a circle of radius r, at diametrically opposite points. They both see their clocks ticking at the same rate. Show this in three ways. Work in:
(a) The lab frame (the inertial frame whose origin is the center of the circle).
(b) The frame whose origin is B and whose axes remain parallel to an inertial set of axes.
(c) The rotating frame that is centered at the origin and rotates with the same frequency as A and B.