Motors and generators are basically the same thing. They are spiral of wires around a spinning magnet.
If you apply current to the wires you create a magnetic field and that will cause the magnet to spin.
If you spin the magnet instead, the flip flopping of poles of the magnet will create a flow of electrons in the wire thru induction.
If you spun your electric motor via your dremel and connected to the positive and negative terminals you could possibly have enough current to power a light or something. (I say possibly because most electrical devices have diodes to keep current flowing one direction. ) Using a motor as a generator isn’t very efficient. Motor windings are designed to take electricity and create desired torque. Likewise generators are design to generate the most amount of current with the least amount of input torque.
It would generate electricity, yes. Often motors are designed to operate as generators. The spinning of the motor does create an electric field that resists the rotation of the motor. This is known as “generator action” and it’s a known thing in electrical engineering.
In fact, a lot of electric vehicles turn this bug into a feature called “dynamic” or “regenerative braking.” As the motor spins while coasting, it creates electricity. You can harness that electricity by removing the power source and attaching a load to it and use it to charge the vehicle’s batteries. This impedes the motor and slows it down. I’ve worked on trains that have massive [braking resistors](https://www.mdresistor.com/wp-content/uploads/2020/12/Resistances-de-traction-fixee-sur-une-rame-min-1.jpg) on the roof. If the train can’t recycle the electricity generated by braking, it turns it into waste heat by running it through that massive resistor.
So yes, you could generate a current by spinning a motor by using an electric drill. This will be far less efficient and generate a much lower current than what comes out of the wall, because of thermodynamics
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