Rotational Mechanics: Tension Difference in Pulley Due to Friction

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Tension differs on both sides of a pulley due to friction, which affects the net torque. The tension from one rope attempts to rotate the pulley in one direction, while the other rope's tension works in the opposite direction. For the pulley to rotate at a constant speed, the net torque must be zero, meaning the torque difference from the two tensions must counteract the frictional torque. Friction is applied at the pulley shaft, opposing its rotation, leading to a non-zero tension difference in the ropes. Understanding this relationship clarifies why tensions cannot be equal when friction is present.
shashank
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I can't get it why tension is different in both sides of pulley due to friction?
 
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The tension in the rope on one side of the pulley is trying to rotate the pulley in one direction, and the tension on the other side is trying to rotate the pulley in the opposite direction. If the pulley is rotating at a constant speed, then the net torque on the pulley has to be zero, which means that the difference between the torques from the two ropes has to exactly cancel the torque from friction. The frictional torque is non-zero, so the difference in the tension of the ropes has to be non-zero, which means that it can't be the same in both ropes.
 
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But I can't get that where is the friction being applied and in which direction?
 
Friction is being applied at the shaft of the pulley and opposes its rotation.
 
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Thanks a lot sir...
 

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