Final answer:
Ron and Roff are related such that their torques are equal and opposite, ensuring the sum of torques is zero for rotational equilibrium; this complements the condition that net external force must also be zero for equilibrium.
Step-by-step explanation:
Under equilibrium, Ron is related to Roff in that the sum of the torques (denoted by T for each individual torque) in the system must be zero. When considering rotational equilibrium, the torque produced by one force (Ron, for instance) must be balanced by the torque produced by another force (Roff), following the equation T2 = -T1, where T1 is the torque caused by Ron and T2 is the torque caused by Roff. This is derived from the second condition for equilibrium which states that the sum of the torques, taking into account the direction indicated by positive and negative signs for counterclockwise and clockwise directions respectively, must be equal to zero.
The relationship between Ron and Roff ensures that no net external torque acts on the system, thus maintaining its state of equilibrium. This principle applies to both forces and torques in a given system, meaning that the net force must be zero (net F = 0) as well as the net torque being zero. Additionally, this concept is independent of the choice of the axis of rotation due to the fundamental principle of rotational dynamics.