Why Does Tension Vary on Different Sides of an Accelerating Pulley?

AI Thread Summary
Tension in a rope can vary on different sides of an accelerating pulley due to the effects of rotational inertia. For a massless, frictionless pulley, the tension remains uniform because no net torque is needed for rotational acceleration. However, if the pulley has mass or friction, different tensions can arise to create the necessary torque. Additionally, an off-center axis can lead to different tensions even if torques are equal. Understanding these principles is crucial for analyzing pulley systems in physics.
johnschmidt
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Sometimes when I see pulley and rope questions people will say "for a non-extensible rope the tension is uniform throughout the rope". But I am now learning pulleys and rotational inertia and it seems to be necessary to consider the rope on either side of a pulley to have _different_ tension if the pulley is being accelerated rotationally.

Why would this different tension not apply to a frictionless massless pulley that is being accelerated rotationally?

For example, here we see the rope have different tension on each side of the pulley:

 
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johnschmidt said:
Why would this different tension not apply to a frictionless massless pulley that is being accelerated rotationally?
The key word is massless. A massless pulley requires no net torque to rotationally accelerate, thus the tension must be the same on each side. (Actually, frictionless is important too! If there were friction, you'd need a net torque to overcome it.)
 
To be clear, the different torques are used when the pulley requires torque, but NOT simply because the pulley accelerates rotationally, correct?
 
johnschmidt said:
To be clear, the different torques are used when the pulley requires torque, but NOT simply because the pulley accelerates rotationally, correct?
Yes.
 
johnschmidt said:
To be clear, the different torques are used when the pulley requires torque, but NOT simply because the pulley accelerates rotationally, correct?

I meant different TENSIONS, of course, not different torques.

Thanks haruspex!
 
johnschmidt said:
I meant different TENSIONS, of course, not different torques.

Thanks haruspex!
Actually, it can happen that torques are the same but the tensions are different. The pulley's axis could be off-centre.
 
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