Increasing shaft speed with DC motor

[yellowcoconut]

Hi all,

First timer here

I would like to understand how to work out how torque is involved when increasing shaft speed using DC motors.
Say if a shaft is rotating at X rpm with an applied torque of T [N.m] and a DC motor is connected through a 1:1 gearing to connect the rotating shaft and motor output shaft.

If the motor is off both shafts would spin at X rpm. However what would happen if the motor was turned?
Would it simply be to add the motor shaft speed to the current shaft speed X? Where is the torque involved in this? Is it dependent on mass of the gear rings used and distance from motor because that's the only equation for torque i can relate T = F*D

thanks

edit for missing info

 

[Valkarie]

:Yes, the motor would increase the speed of the shaft from X rpm to (X + motor speed). The torque involved would depend on the amount of torque the motor is able to generate. If the motor is capable of generating a torque of T [N.m], then the total torque on the shaft would be T [N.m] + the existing torque on the shaft.