Let's say a body $a$ applies a force $\vec F_b,_a=\vec F$ as shown in the figure. so according to the third law the body $b$ also applies $\vec F_a,_b = - \vec F$
so the bodies start rotating about their COM with increasing velocities.So mechanical energy is increasing with time but there is no work being done on the system from outside. what am I getting wrong here. Please explain.
