An object is said to be in rotational equilibrium if the net torque acting on it is zero that means ΣT = 0. The torque sum may be taken about any single point on the object or out of it. It is usually taken about a point at which the calculation of perpendicular distances is convenient.

What does it mean if torque is zero?

If Torque = 0 ; that means either Force(perpendicular) = 0 , or Radius = 0; Case I : If Force(perpendicular) = 0; that means Acceleration(perpendicular) will be equal to 0; therefore Velocity(perpendicular) won't change . This implies Angular Momentum (L=mvr) won't change. Angular Momentum remains constant.

Under what conditions is the torque zero?

That is, when line of action of forces passes through the axis of rotation, torque is zero.