I have an Atwood Machine. I have an aluminium Pulley of radius 4 inch. A gym cable running over it. Not sure coefficient of friction but smooth movement. One end of rope, I attach wt. of 0.5 kg. I had to attach weight of 1 kg for acceleration to start. If I attach 2 kg, I had to attach 3.1 kg, for the system to start acceleration. If I attach 4 kg, I had to attach 6.1 kg to other end. Now if I take 2 pulleys and run rope over them and repeat experiment, I need even more weight differential for system to accelerate. Thus there are some forces acting which need to overcome to start system acceleration. I think apart from inertia of pulley and static frictional force, probably some x and y directional force components are coming into play. All Atwood problems talk about equation for acceleration but not able to find equation for "weight differential" required for the system to start accelerating. Also any suggestions on ways to reduce this weight differential to start system acceleration shall help.