# Relative motion between two points on a rotating disc

Consider two children A and B sitting on diametrically opposite points of a merry go round rotating about its centre. Suppose A and B are facing each other. As seen from A, B never seems to move and neither rotates about him. However, if we calculate the relative velocity of B w.r.t. A by usual formula ( http://emweb.unl.edu/NEGAHBAN/EM373/note15/note.htm ) or by subtraction of velocities, it comes out to be 2Rω.

Where am I going wrong? This question has bugged me for a long.time and I have not found suitable explanation to this dilemma. Someone please clarify from a practical and mathematical standpoint.

The radius of this circumference will be the distance of the two guys ($$2R$$). At the same time, the period for one complete revolution will be the same of the time for one complete rotation (the period $$T$$), so also the angular speed will be the same. Since the tangential velocity of the circular motion is given by $$\omega R$$, and the radius of the circle described by the second child around the first one is $$2R$$, you have the final velocity $$2R\omega$$.