Yes, the equilibrium condition depends upon the number of forces and, thereby, sources of torque on either side of the fulcrum.
An object must not be accelerating in order for it to be in equilibrium. This dictates that the object's net force and torque must both be zero.
This first condition is expressed as an equation, which reads:
Fnet=0
The forces operating along each axis of motion must aggregate to zero in order to accomplish this condition. For instance, the usual x- and y-axes have zero net external forces. This appears as
net Fx = 0
net Fy = 0
Both static equilibrium, where the item is traveling at zero velocity, and dynamic equilibrium, where the object is moving at a constant velocity, require that the condition Fnet=0 hold.
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