I have a 3V/50mA Motor on my hand which I want to power using Arduino's Pins. Of course I know that these give out 5V and therefore might damage my Motor, but after reading the documentation I discovered that Arduino can only deliver 40mA of current. My question now is: If I connect the motor to the digital Pin, will it damage the Arduino? I know that the motor won't be damaged, since the current is in it's specified range.
If the motor really takes 50mA at 3V (motor specifications are very unreliable/difficult to read) then it will take a lot more if you feed it 5V. So yes damage is pretty much inevitable.
50mA will be the no-load current I suspect, which isn't useful for any design calculations.
I suspect the motor can pull maybe 1A or so at stall, so you'll need to bear that in mind (you
can measure this with a meter).
Motors take far more current than any logic chip can provide, and generate large inductive kickback
voltages that will destroy semiconductors if not snubbed or handled with a free-wheel diode or diodes.
Motors always need a driver, which can be a transistor or MOSFET, or H-bridge (for driving in both
directions).
As for the voltage difference, you can select a PWM duty cycle to slow the motor down and extend
its life. But you shouldn't be thinking of sharing power between motors and logic circuitry in the
first place - separate power for motors is going to remove a lot of sources of problems.
Use a darlington transistor and power the motors directly from the 5V you will have about 1.4 volt drop across the transistor depending on choice. You can then use something in the 300 to 1K resistor in series with the base. Of course you realize a power supply the Arduino IS NOT!