Torque to rotate pulley with equal mass on each side.

[mrkevelev]

Lets say there is a pulley attached to the ceiling. Hanging on the pulley is a rope and on each end is a 1000 lb. weight. I believe that theoretically it wouldn't take any torque at all to rotate the pulley if it were frictionless (maybe inertia would play a role, but let's ignore that). However, in reality there will be a downward force on the pulley's shaft, causing friction. Let's say that a motor is connected to the pulley. I want to know if I turn the pulley, will the rope slip? My thoughts are that increasing weight will give better friction between the pulley and rope, and therefore, as long as the weights are equal, the torque required to rotate the pulley will be quite low, even though shaft friction increases as well with weight.

 

[anorlunda]

Everything in your question is related to friction. One kind of friction compared to another kind of friction.

There can be no answer without putting numbers on the friction values. You can make the answer come out either way, it slips or doen't slip, depending on the friction values.

 

[russ_watters]

...and speed/acceleration.

 

[jack action]

In your system, there is a torque required for each of these resistances:

• The friction between the shaft and bearing;
• The friction between the rope and pulley;
• The inertia of the weights, pulley and rope.

The first one will be there all the time, as soon as the pulley rotates. If you increase the weight, the friction increases and with it, the torque required.

The second one is present only if there is slipping between the rope and the pulley. If you increase the weight, the friction increases and this reduces the chance of slipping.

The third one is present only if there is an acceleration. This means inertia has no effect at constant speed. Of course, if you increase the weight, you increase inertia. In this case if you don't increase the extra torque (i.e. above the friction torque already discussed), it will only reduce the acceleration. So it is not a requirement for the system to work, unless you have a minimum acceleration to achieve.

That being said, if the torque input is high enough, it will break the shaft friction and the pulley will begin to rotate. If the pulley is accelerating, then some part of the torque is lost there too. If the resultant output torque creates a friction force that exceeds the maximum static friction force between the pulley and the rope, then slipping begins and you have to use the kinetic friction force instead, no matter how high the input torque is. This friction force (whether it is static or kinetic friction) will be the force that accelerates the rope and the weights.