This effect is not due to the motor's inductance, which generates a voltage in opposition to a changing current via Faraday's law, but a separate phenomenon.
That is, the back-EMF is also due to inductance and Faraday's law, but occurs even when the motor current is not changing, and arises from the geometric considerations of an armature spinning in a magnetic field.
[6] To observe the effect of back-EMF of a motor, one can perform this simple exercise: with an incandescent light on, cause a large motor such as a drill press, saw, air conditioner compressor, or vacuum cleaner to start.
When the armature is not turning (called locked rotor) there is no back-EMF and the motor's current draw is quite high.
If the motor's starting current is high enough, it will pull the line voltage down enough to cause noticeable dimming of the light.