The sum of anti-clockwise torques must equal what?

In rotational dynamics, one of the fundamental principles is the equilibrium condition regarding torques. When an object is in rotational equilibrium, the sum of the anti-clockwise torques acting on it must equal the sum of the clockwise torques. This is derived from Newton's second law for rotation, which states that if an object is not rotating or is in a steady rotation, there's no net torque acting on it.

When considering torques, we take into account both the magnitude of the force applied and the distance from the pivot point at which the force is applied, considering the angle at which the force is acting. In equilibrium, the forces and torques balance each other out, leading to the conclusion that the torques in one direction must match those in the opposite direction to prevent any angular acceleration.

Thus, stating that the sum of anti-clockwise torques must equal the sum of clockwise torques is essential for maintaining equilibrium in a system. This principle helps in analyzing situations such as levers, seesaws, and various mechanical systems where rotational movement occurs.