For
an extended object, several torques may be applied. If the system has no
angular acceleration, it is said to be in rotational equilibrium. In this
case the sum of the torque vectors applied to the system must add to zero.
This is called the second condition of equilibrium; the first being the
requirement that the net force must be zero on a system in equilibrium.
(Note that is often true that one condition of equilibrium is satisfied, while the other is not.)
If the sum of the torques is zero and the system is not rotating, then no particular axis of rotation (center of rotation in two dimensions) is required by the physical system. You are then free to choose any convenient axis of rotation and calculate all the torques with respect to that axis. Moreover, in this case, you can repeat the calculation of the torque sum with a second axis and (often) extract new information about the system.