# Confused about pulleys and tension

1. Nov 5, 2013

### 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:

Last edited by a moderator: Sep 25, 2014
2. Nov 5, 2013

### Staff: Mentor

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.)

3. Nov 5, 2013

### johnschmidt

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

4. Nov 5, 2013

Yes.

5. Nov 8, 2013

### johnschmidt

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

Thanks haruspex!

6. Nov 8, 2013

### haruspex

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