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given a Yo-Yo that is rolling on the floor without slipping:

enter image description here why is the total torque equals to T*r+F_friction*R=I*w rather then

-Tr-F_frictionR=I*w

ive set the direction as followed:

X- direction of T

Y-towards the sky

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  • $\begingroup$ I assume you are asking about the torque measured about the center of the yo-yo. What angular direction have you set to be the positive direction? It is arbitrary. $\endgroup$ – Bill N Feb 27 at 18:31
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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.

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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.

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