In other words, you don't know what balanced means.
it means there is the same mass on both sides of the pivot. So both sides of the pivot will experience the same acceleration. The only reason the vane responds to transients is because of the higher drag of the vane side will, appropriately, "weather vane" away from the induced relative wind caused by the transient.
And you won't present any math because I will always pick it apart piece by piece instead of just ignoring it like most do.
it means there is the same mass on both sides of the pivot. So both sides of the pivot will experience the same acceleration. The only reason the vane responds to transients is because of the higher drag of the vane side will, appropriately, "weather vane" away from the induced relative wind caused by the transient.
And you won't present any math because I will always pick it apart piece by piece instead of just ignoring it like most do.