How Does Tension Direction Affect Torque in a Pulley System?

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In a pulley system with two blocks of different masses, the acceleration of the blocks can be calculated based on their motion. The tensions T1 and T2 were found to be 4.5 N and 4.87 N, respectively, while the angular velocity was determined to be 1.2 rad/s². The net torque acting on the pulley is given by the equation r(T2 - T1), where T1 is considered negative because it acts in the opposite direction to T2. This directional difference in tension influences the overall torque and angular acceleration of the pulley. Understanding these relationships is crucial for analyzing the dynamics of the system.
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Block 1 has mass m1 = 460g, block 2 has mass m2 = 500g, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R = 5.00cm. When released from rest, block 2 falls 75.0 cm in 5.00 s without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tension T2 and (c) tension T2? (d) What is the magnitude of the pulley's angular acceleration? (e) What is its rotational inertia?

I have solved most of the problem, but I just have one question about e. Solving the previous questions we get that angular velocity is 1.2 rad/s^2, T1=4.5 N and T2=4.87 N. I know that I=torque/angular velocity. The book says that the net torque in this case is r(T2-T1).. Here is my question. Why is T1 negative?

Thanks!
 
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because T1 will tend to rotate the pulley in opposite direction as compared to T2

also you can use cross product rule to find that direction of the two torques in opposite
 

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