My question albeit trivial is something I wish to understand better. Given a system either say 3 masses, 2 masses and a pulley (with mass), and 2 masses attached via a string with mass $m$ (and uniform mass density $\lambda$).
In these cases do we have to consider 9 generalized coordinates (excluding constraints for now) since there are 3 mass-full objects and assuming we are in 3D-space.
Is this always true? Is it therefore a good practice when formulating Lagrangians to identify objects with mass and finding their respective kinetic and potential energies?
EDIT: Assume stationary lab frame of reference and no rotations (other than the pulley/disk)