Solving Torque on a Pulley: 0.5Nm, 4kg Block, 12cm Diameter

[cjavier]

The problem is: The two blocks in the figure are connected by a massless rope that passes over a pulley. The pulley is 12cm in diameter and has a mass of 2kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.5Nm. If the blocks are released from rest, how long does it take the 4 kg block to reach the floor?
Here is the picture:

My approach was as follows:
Ʃ_τ = τ_left-weight - τ_tension - τ_right-weight
Then, when I found total torque...
Ʃτ = I\alpha(\alpha is angular acceleration)
Then finally...
a_tangential = \alphar

When I found a, however, it was different than the answer on chegg. What am I doing wrong?

Thanks To Everyone on this site

 

[Doc Al]

My approach was as follows:
Ʃ_τ = τ_left-weight - τ_tension - τ_right-weight

What exerts the torque on the pulley is the tension in the ropes, not the weights of the hanging.

Of course, those tensions depend on the weights. You'll need additional equations for each mass to solve for the acceleration.