- #1

TimeRip496

- 254

- 5

_{1}, Q

_{2}, ... taken in order from P; the parts of the surface cut off by the cone at these points are S

_{1}, S

_{2}, ... and the outward-drawn normals are denoted n

_{1}, n

_{2}, ...

Now if P lies outside Σ (region of masses, each at points Q

_{1}, Q

_{2}, ...), the cone will cut S an even number of times, and the signs will be plus and minus alternately, so that the total normal force across S

_{1}, S

_{2}, ... will be zero. On the other hand, if P lies inside Σ, the cone will cut S an odd number of times, the sign being minus and plus alternately, so that the total normal forces across S

_{1}, S

_{2}, ... will be -mω."

Source: Spherical harmonic T.M.Macrobert

Help with this text! I don't understand the second paragraph as to why the cone will cut S an odd number of times, the sign being minus and plus alternately when P lies inside Σ vs when P lies outside Σ. I know the cone is just a mathematical object but I can't follow the author thought process here. How did he use the cone to cut the surface at Q

_{1}, Q

_{2}, ... ? Why will the normal force across S due to particle at P be zero when P is outside the mass but not inside the mass?