Why are tensions in the pulley different when the pulley has a mass or moment of inertia?

When two blocks are connected by a string passing over a pulley whose moment of inertia is given (means pulley is not massless) then why does the string not have same tensions? What will be the direction of friction while rotation, if any? (between string and pulley)

Problems that depict situations where the tensions are same on ropes on both sides of the pulley are ideal situations.It is stated so in order to minimize any complexities that may arise if the pulley was to rotate.Now, if the tensions were not equal on both sides, the pulley would experience a net non-zero torque and hence a net angular acceleration and eventually rotate.Also,these are cases where pulleys have friction between its rim and the rope..if there were no friction on the rope-rim interface the pulley would not turn and its mass would become irrelevant . Because the pulley possesses mass, you need to apply a non-zero net torque to it to increase its angular acceleration (assuming that is the goal here). If the tensions were the same on both sides of the contact point between the string and the pulley, there would be no angular acceleration.

• Even if the tensions are equal there ,would be net torque as the tensions ( equal in magnitude) have opposite direction wrt centre of pulley which would lead to a net non-zero torque . – Tripti Khulbe Jul 31 '15 at 13:23
• It's possible that they could exert a net force on the pulley, thus causing linear acceleration, but if the torques applied are equal in magnitude, there should be no rotational acceleration. – Rations Jul 31 '15 at 13:33
• I think you are saying the opposite. If the tensions are equal in magnitude and opposite in direction the net force will be zero but net torque depends on the origin chosen and in this case the net torque about the origin, which is the centre of pulley, is not zero if tensions are equal. – Tripti Khulbe Jul 31 '15 at 13:49
• If they are completely opposite (i.e., form an 180-degree angle), then they will exert no net force or net torque. If not, they will exert a net force. Take, for example, the left drawing in the currently accepted answer. Even though the tensions are equal in magnitude, they still exert a downwards net force on the pulley. – Rations Jul 31 '15 at 14:03
• You may be confusing yourself over how the direction of torque is defined. In this case, torques are either clockwise or counterclockwise. If the sum of the torques in the clockwise direction is equal to the sum of the torques in the counterclockwise direction, the net torque is zero. – Rations Jul 31 '15 at 14:06

It can be understood as follows that the tensions in the strings at both ends are different because of friction between the strings and pulley which is enabling the pulley to rotate along with the string. Moreover if the tensions were same no net torque would act and sysem wil remain stationary... (Tensions in both the strings will be same if there were no friction and the string would have simply slipped without any rotation in the pulley and would have no relevation with mass of the pulley or its moment if inertia .) .

protected by Qmechanic♦Sep 1 '16 at 14:30

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