In the figure, block 1 has mass m1 = 0.460 kg, block 2 has mass m2 = 0.500 kg, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R = 0.0500 m. Tension T1, the tension force on block 1, is 4.54N. Tension T2, the tension force on block 2, is 4.87N. What is the net torque acting on the pulley? Please note that I know that the answer is to be that taunet = -T1R + T2R Why is tau1 = -T1R? Why is tau2 = T2R? Is the angle between R and the tension force in each case 90o? And so the formula tau = r F sin theta is simply tau = F r = T R here? What about the sign? Here is where I need help: I do not know how to determine the signs of the torques, that is, how to determine the direction of the rotation (clockwise or counterclockwise). Please explain what is the axis of rotation here, and how to determine the direction of the rotation (clockwise or counterclockwise) for this problem specifically and in general. I know that the convention is that if the direction of rotation is counterclockwise, then the torque is positive, and if the direction is clockwise, then the torque is negative. But how do you determine the direction of the rotation?

In the figure, block 1 has mass m₁ = 0.460 kg, block 2 has mass m₂ = 0.500 kg, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R = 0.0500 m. Tension T₁, the tension force on block 1, is 4.54N. Tension T₂, the tension force on block 2, is 4.87N. What is the net torque acting on the pulley?

Please note that I know that the answer is to be that  tau_net = -T₁R + T₂R

Why is tau₁ = -T₁R? Why is tau₂ = T₂R?  Is the angle between R and the tension force in each case 90^o? And so the formula tau = r F sin theta is simply tau = F r = T R  here? What about the sign?

Here is where I need help: I do not know how to determine the signs of the torques, that is, how to determine the direction of the rotation (clockwise or counterclockwise). Please explain what is the axis of rotation here, and how to determine the direction of the rotation (clockwise or counterclockwise) for this problem specifically and in general. I know that the convention is that if the direction of rotation is counterclockwise, then the torque is positive, and if the direction is clockwise, then the torque is negative. But how do you determine the direction of the rotation?