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

[johnschmidt]

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:

 

[Doc Al]

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.)

 

[johnschmidt]

To be clear, the different torques are used when the pulley requires torque, but NOT simply because the pulley accelerates rotationally, correct?

 

[haruspex]

To be clear, the different torques are used when the pulley requires torque, but NOT simply because the pulley accelerates rotationally, correct?

Yes.

 

[johnschmidt]

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!

 

[haruspex]

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.