electromagntic induction

You need to keep on pushing the coil in order to maintain it rotating at constant speed.

This is just the principle of a dynamo (electricity generator). The simplest explanation is because of conservation of energy. The coil is rotating in a magnetic field, an induced emf is produced. A current would flow if an external circuit is connected, thus producing electrical energy. A mechanical work done therefore must be input into the dynamo. The requirement of such mechanical work is why a force is needed to rotate the coil continuously.

If looking at the problem from another angle (the force angle), a coil rotating at constant speed in a magnetic field should have not net force acting on it. Since the induced current flowing in the coil would, under the interaction of the magnetic field, produces a force opposing the rotation of the coil, an external applied force must be present, to counternalance the magnetic force, in order to maintain a "zero net force" condition.