Ofcourse, when the axle of the motor rotates, produces current.
As the motor starts to turn, the interaction of the magnetic fields inside it causes it to generate a voltage internally. This "back voltage" or EMF electromagnetic force opposes the applied voltage and the current that flows is governed by the difference between the two. So, as the motor speeds up, the internally generated voltage rises, the EMF falls and less current is forced through the motor.The motor naturally stops accelerating.
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