My beard trimmer has a very weak motor, so I want to upgrade it with this DC motor.
I want to run it with 5V.
What is an adequate power supply for this? Do I need a DC motor starter? What kind of starter do I need?
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At 6 V the initial startup ('stall') current is specified at 24 A. Therefore according to Ohm's law the resistance should be 6/24 = 0.25 ohms, and the startup current at 5 V would be 5/0.25 = 20 A.
Power supplies that can do 20 A at 5 V are available, but they are generally large and expensive. One cheap option might be an ATX-12V PSU from an old PC.
Next problem is that the motor will spin at over 12,000 rpm with much more torque than the original motor. Your trimmer may not be able to withstand this power for long.