Feedback to your questions

Great questions on sticky notes...let me address a few:

Where does the Atwood Machine equation come from?
It is the result of setting up simultaneous equations from the pictures you drew of the two masses hanging on the strings.  The two equations, when combined and solved algebraically (with letters instead of numbers) land us at this quantity:

a = [(m2-m1)/(m2+m1)]g
Where g = 9.8 m/s/s

Take a look at this whiteboard where a student group showed the solution (somewhat clearly...might take some thinking):

Stay tuned...more to come!