When are torques positive or negative? 
hi, i'm having a little trouble with this problem. the correct answer is D, but i got B because i'm confused about the signs of T2 and T1. it makes sense to me that T2 is positive in the equation, because it's a negative quantity, and the pulley will rotate clockwise, and it avoids a double negative. but why is T1 being subtracted? it's a positive quantity, so subtracting that will just make the net torque even more negative, which i don't see making sense in the context of the problem. i feel like it should be added.
 A: The interpretation which you were expected to use of the two forces is shown in the diagram below with the mass $m_2$ accelerating downwards and the pulley wheel having a clockwise angular acceleration.

$T_1,\, T_2$ and $\alpha$ will come out to be positive quantities.  
If $\hat y$ is a unit vector into the screen then you have
$(T_2\,R \,\hat y + T_1\, R\,(-\hat y ))=T_2\,R \,\hat y - T_1\, R\,\hat y = I\, \alpha \,\hat y \Rightarrow (T_2-T_1)R= I\alpha$
A: Strictly speaking, torque is a vector and will have a magnitude and direction but not really a sign.  
In the above problem, however, it seems the clockwise rotation of the pully is defined to be positive and counterclockwise rotation negative.  In this case, the sign is simply a result of whatever direction we decide to define as positive and indicates whether the angular rotation is clockwise or counterclockwise.
As to which answer is correct, please note that the two forces acting on the pully ($T_1$ and $T_2$) are acting in opposite directions (at least with respect to the rotational direction of the pully).  Therefore, we know that the magnitude of the torque must have the form $\pm(T_2 - T_1)R$, where the sign will be determined by whether we define counterclockwise to be positive or negative.
I hope this helps.
