As the title indicates, I was wondering if we can use different coordinate systems for different objects. Specifically in the classic inclined pulley problem:
For m_1 I usually choose my x-axis to be running parallel to the inclined plane and my y-axis perpendicular to the plane. However, then I'm not sure what coordinate system to use for m_2. I have seen books where they choose their x-axis as the actual rope, and the y-axis running perpendicular to that rope.
I was wondering if I could set up, in this case, two different coordinate systems for m_1 and m_2. Here's what I mean by that: for m_1 the x-axis would be parallel to the inclined plane and the y-axis perpendicular to it; for m_2, the y-axis would be running straight down, parallel to the rope and the x-axis would be then running parallel the ground. Can this work?
Also, do you have any tips on choosing a coordinate system?