hammy:
We need a lot more information - a little motor you mount on a breadboard or a house sized motor ?
Doesn't really matter. The Arduino can send data to a motor controller to control the motor. It can't directly power and control any motor. With a suitable motor controller, the size of the motor doesn't matter. Nor do the voltage or current requirements.
another little question with an arduino is it possible to adjust the speed of live rotation from his phone
The Arduino doesn't have a phone, so it can't use his phone to do anything.
The Arduino is not a phone, so you can't call it do anything.
The Arduino COULD wear a bluetooth low energy shield, which could be controlled by a phone, with suitable software installed on the phone and a suitable sketch on the Arduino.