given a Yo-Yo that is rolling on the floor without slipping:
ive set the direction as followed:
X- direction of T
Y-towards the sky
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I've managed to understand the problem: the directions must be set according to the direction of rotation. therefore, if the rotation is in the direction of the tension (which is, in fact, the situation) then the z-axis (direction of omega) is going "inside" the page. thus binding the x-direction to be left and the y-direction is upwards.
Both the tension and the friction force are in the direction of rotation, so they add. If you were just considering forces, the tension and friction forces are in opposite directions, but you have a torque equation and the two torques are in the same direction.