Final answer:
The condition not required for a system to be in equilibrium is that the system is at rest. The necessary conditions for equilibrium are that both the net external force and torque must be zero.
Step-by-step explanation:
The condition that is not required for a system to be in equilibrium is that the system is at rest. For a state of equilibrium, two conditions must be satisfied: the net external force on the system must be zero (net F = 0) and the net external torque on the system must also be zero (net T = 0). A system can be in equilibrium even if it is moving, as long as it's moving with constant velocity and not accelerating (this would still satisfy net F = 0 and net T = 0). Therefore, being at rest is not a necessary condition for equilibrium.