We have a random 2D distribution of many particles (a cloud) within distance "R" from the origin (forming a disk shape of points with the origin in the middle). Total mass of the system is “M”.
QUESTION: Considering that the total mass of the system is distributed evenly throughout this volume, what is the linear orbital speed of a particle "P", with mass “m”, at distance “r” from the origin?
Assume r < R
Newtonian gravity only please (F=GmM/rr), though using calculus fine.
If possible, please show how you derived your answer.