My main question is why?
Is this going to be lcd, crt, or tv? If it is crt there could be issues with degaussing.
How much are you looking to adjust the angle? If this is a standard cab you will probably want a glass infront of the monitor so angle should be fixed. Instead of adjusting the monitor angle to probably suit player, just by a stool for short people.
But for your other question about motors, people have used them before to rotate a monitor from horizontal to vertical screen display.