Why Does the Solution Use (T2 - T1) * R for Net Torque?

[RoboNerd]

Homework Statement

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https://web.njit.edu/~gary/111/assets/HW10_SOL.pdf

The problem is on page 3 of the document along with relevant solutions.

Homework Equations

F=ma, and Sigma Torques = (moment of inertia) * angular acceleration

The Attempt at a Solution

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I have been killing this problem for three hours now.

I was wondering why do they have in the solutions the net torque being (T2 - T1) * R.

Torque going in the counter clockwise direction should be positive and vice versa, so this seems wrong to me.
T2 is going in the clockwise direction of the pulley, so it should be negative, in my opinion.

Could anyone please weigh in why they have the order being T2 - T1, and not T1 - T2 [which is what I did]?

Thanks!

 

[TSny]

They are just taking the positive direction of motion of the system to correspond to the block on the incline moving down the incline. When the the block on the incline is moving in the positive direction, the pulley rotates clockwise. So, in this problem, they are taking clockwise as the positive direction for rotation so that ##\alpha## will be positive when ##a## is positive.

 

[RoboNerd]

Thanks! That does make sense!