Rotational Equilibrium and Balanced Torques

Torque depends on both force and distance from the pivot: torque = force times the lever arm. That's why a small child can balance a heavy adult on a seesaw. The adult's weight is bigger, but if the child sits far enough from the pivot, the child's smaller weight times a bigger distance produces the same torque. Equal torques pulling in opposite rotational directions cancel out, so the seesaw doesn't rotate.

To solve a balance problem, set the sum of torques equal to zero: torque clockwise equals torque counterclockwise. Write each torque as weight times distance from the pivot, then solve for the unknown distance or weight. This turns a geometry problem into one line of algebra, the rotational twin of setting sum of forces equal to zero in translational equilibrium.

Rotational equilibrium only requires zero net torque, nothing about speed. A wheel spinning at a constant 50 rad/s has zero net torque, so it is in rotational equilibrium, even though it is obviously not at rest and never stops turning. This mirrors Newton's first law: zero net force means constant velocity, not zero velocity. An object can satisfy rotational equilibrium while spinning steadily forever. If you also want the object to stay in one place, not just spin at constant rate, you need translational equilibrium too: the net force must also be zero. Both conditions together, zero net torque and zero net force, describe a rigid body that is completely static or moving/rotating at constant rate with no change in either.