How Do Tensions on Either Side of a Rotating Pulley Compare?

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SUMMARY

The discussion centers on the analysis of tensions in a pulley system with a 10-cm-diameter, 2.0 kg pulley rotating on frictionless bearings. The key conclusion is that the tensions T_L (left side) and T_R (right side) are equal due to the constant angular acceleration indicated by the linear increase in angular velocity. The relevant equation for torque, T = mr²α, is highlighted as essential for understanding the relationship between the tensions and the pulley’s motion.

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  • Knowledge of Newton's second law for rotation
  • Basic skills in interpreting graphs of motion
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Homework Statement



A rope passes over a 10-cm-diameter, 2.0 kg pulley that rotates on frictionless bearings. A graph shows the pulley's angular velocity as a function of time. The graph increases from (0,0) up to (3,120) linearly. Basically, there is a pulley with a rope thrown over it such that there are two sides to the rope, and two separate tensions, T_L (on the left side of the pulley), and T_R (on the right)

a) Is the tension T_L in the left rope larger, smaller, or equal to the tension in the right rope? Explain.

b) If you answered "equal" in part a, what is the magnitude of the tension T_L? If you answered "larger" or "smaller" in part a, what is the difference abs(T_L - T_R) between the two tensions?


Homework Equations



T = mr^2*alpha

The Attempt at a Solution



I thought that the tension in the left rope was larger, but this turned out to be wrong. I thought it must be, because omega was positive and constantly increasing, meaning the pulley was rotating counter clockwise. Also, just from the angular velocity/acceleration, I'm not sure how to relate T_L to T_R.

Please, I could really use some help!
 
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is it possible for you to have the diagram? I, personally, like to have a strong grasp on understanding the problem. By the way, your equation isn't correct for torque. Torque is basically the cross product of a Force vector and the Radius (displacement vector).

P.S. you don't HAVE to show a diagram. But I don't really understand the problem. sorry :(
 

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