Why do rotating pulleys have different tensions on either side?

[ximath]

Dear All,

Suppose there is a a pulley with mass and a massless cord around it, if pulley is rotating then I have learned that there are different tensions on either side of the pulley. I am having some trouble visualizing it. Moreover, if there are two different tensions on the cords, where exactly they are separated from each other ?

I have searched a little bit and read that thread several times :
https://www.physicsforums.com/showthread.php?p=1958707

There is a statement on that thread which is;

but a string touching anything (like a pulley) with friction will have different tension on either side, even if the string is massless.

Could you please explain this further ? Why and how it can have different tension on either side, if a string is touching somewhere and where these tensions are separated ?

 

[tiny-tim]

Could you please explain this further ? Why and how it can have different tension on either side, if a string is touching somewhere and where these tensions are separated ?

but a string touching anything (like a pulley) with friction will have different tension on either side, even if the string is massless.

oooh, that's me!

the reason the tension is usually the same on either side of a point on a string is that Newton's third law requires that the tensions are equal and opposite

but if you have an outside force … in this case, friction … then Newton's third law is irrelevant (to be precise, it just says that the string exerts a force on the pulley ), and the friction acts in the same direction on each side of the string

and so on one side it acts with the tension, and on the other it acts against the tension

 

[astrokreng]

I can explain the concept of tension at rotating pulleys. When a pulley is rotating, it is subjected to two different forces: the weight of the pulley and the tension in the cord. The tension in the cord is caused by the weight of the object attached to it, which pulls on the cord. This tension is transmitted through the cord to the pulley.

Now, when the pulley is rotating, the tension in the cord on either side of the pulley is not equal. This is because the pulley is not a frictionless surface. As the cord rubs against the pulley, there is some friction present which creates a force that acts against the direction of motion. This force reduces the tension on one side of the pulley, while increasing it on the other side. This is why there are different tensions on either side of the pulley.

To better understand this concept, imagine a pulley with a massless cord around it. On one side of the pulley, there is an object with a weight of 10 N attached to the cord. This creates a tension of 10 N in the cord. As the pulley rotates, the cord rubs against the surface of the pulley, creating a friction force. This friction force is equal to the tension in the cord, which means that the tension on one side of the pulley is now only 5 N (10 N - 5 N). On the other side of the pulley, the tension remains at 10 N.

In terms of where these tensions are separated, it is important to note that the tension in the cord is constant throughout its length. However, as the cord wraps around the pulley, the direction of the tension force changes, resulting in different tensions on either side of the pulley.

I hope this explanation helps to clarify the concept of tension at rotating pulleys. It is important to understand that friction plays a crucial role in creating different tensions on either side of the pulley. If you have any further questions, please do not hesitate to ask.