Why the coil keeps turning
In the simple motor too, what happens is that a magnetic field exerts a force on a conductor when a current flows along it.
Because the conductor here is a coil, two forces in opposite directions act on it, on its two sides (picture 6) — that is, a couple — and the coil turns.
Figure to be added
A couple
Two equal forces in opposite directions acting along different lines make a couple. A couple does not move an object along; it turns it.
The insulation is removed from only one half of each end of the wire to stop a current flowing during the next half turn, after the coil has turned through half a turn. Otherwise, as picture 7 shows, in the second half of the turn the couple would act the opposite way and push the coil to turn back. With the current stopped, the coil keeps turning the same way through the remaining half on the angular momentum it gained at first.
Why the push would reverse
Follow one side of the coil. In the first half turn it is, say, on the left, with the current going away from you, and the left-hand rule pushes it up. Half a turn later that same side is on the right. The field has not changed, and if the current in the wire had not changed either, the force on it would still be up — but on the right side, up turns the coil the other way. Something has to change every half turn to keep the turning one way. The simple motor's answer is crude: switch the current off for half the time. A real motor does better with a commutator, which reverses the current instead, so the coil is pushed all the way round.
A couple turns the coil
Opposite forces on the two sides make a couple. Cutting the current for the second half turn stops the couple pushing it back.