How Does Friction Affect Torque in an Atwood Machine?

[AnotherStuden]

Homework Statement

Two masses are suspended from a pulley of mass m supported by an axle (Atwood machine).
What is the net torque acting on the pulley wheel in terms of T1 and T2?

There is friction between pulley and rope.
Ropes are massless and pulley can rotate without friction about its own wheel.

Homework Equations

τ = I*α

The Attempt at a Solution

This is what I got so far:
http://img685.imageshack.us/img685/4333/24667502.th.png

Others get τnet = (T1-T2)r
Why??

Thanks in advance!

 

[AnotherStuden]

Wait nevermind, I just realized that both tensions should be pointing downward.

So, (T1-T2)=r is correct.

Thanks anyways!

 

[kerimek]

Firstly, it is important to note that the net torque acting on the pulley wheel will be equal to the sum of the individual torques acting on it. In this case, there are two forces acting on the pulley wheel - the tension forces T1 and T2 from the masses, and the friction force F between the pulley and the rope.

Using the equations of motion for rotational motion, we can write the net torque as:

τnet = τT1 + τT2 + τF

Where τT1 and τT2 represent the torques due to the tension forces T1 and T2, and τF represents the torque due to the friction force F.

Let's break down each of these torques:

τT1 = T1r (since the force is acting at a distance r from the center of rotation)
τT2 = -T2r (since the force is acting in the opposite direction)
τF = -Fr (since the friction force is acting in the opposite direction to the motion)

Therefore, the net torque can be written as:

τnet = T1r - T2r - Fr

Simplifying this, we get:

τnet = (T1 - T2)r - Fr

So, the net torque on the pulley wheel is indeed equal to (T1 - T2)r, as others have calculated. As for why the friction force is not included in the net torque calculation, it is because it acts in the opposite direction to the motion and therefore does not contribute to the rotation of the pulley wheel.