Calculating Tension in Atwood Machine

[Kalibasa]

Homework Statement

I'm looking at how to calculate the tension in the ropes in an Atwood machine (two masses hanging on either side of a pulley, with mass 2 on the right side). We were told, for connected objects, that it was easiest to treat the two objects as a system and use a curved coordinate axis; then we were supposed to use this overall acceleration to find individual internal forces in a second step.

Homework Equations

The first step is ay= (m2-m1)g/(m1+m2)

But then in the second step he's suddenly giving us either of these equations to use:
Fnet2y= T-m2g= m2 (-ay)
Fnet1y= T-m1g=m1 (+ay)

The Attempt at a Solution

ay is negative for T2 and positive for T1. Does this mean that we're no longer using the curved axis in the second step?

 

[indr0008]

i'm not really familiar with this 'curved axis' thing, but actually ur first equation is derived from the latter two