The question is a bit unclear. Now for simplicity assume the armature (rectangular coil) is resting in the position shown in the diagram in link. The long sides have current flowing perpendicular to the field direction. So when you apply Flemming's left hand rule for both the wires, the left wire has a force going into the page and right wire has a force popping out. Try to visualize this. This creates a torque or rotational motion. So the coil turns. At this position, the other shorter sides have a force in the upper and lower directions on the plane of paper by Flemming's left hand rule so they cancel out.
Now when the coil has turned such that the coil's plane is perpendicular to magnetic field plane, the long wires do experience a downward and upward force but they cancel out. At the same position shorter wires experience inwards and inwards force ( But since they are facing each other they turn out opposite and cancel again) - no net force .
But a fan switched off still keeps rotating for a short while. This is due to inertia of motion. For this reason the coil is able to rotate once even when no force acts and comes back to the original position where it receives a force and rotates again and this cycle keeps on going as long as there is current.
But this results in non- uniform motion. So an extra coil is placed horizontally. I think this extra coil is the answer to your question.
This video is worth 1000 times my answer due to the visualizing power it gives :
https://www.youtube.com/watch?v=LAtPHANEfQo
Lastly, rather than learning the fleming's left hand rule, I suggest you to learn vector cross product (if u don't know it) and then learn the Lorenz force law. This might take a couple of hours but it is better than memorising that rule for years and you get an amazing insight with it. Make use of Khan academy.