A spiral/disk galaxy's mass is proportional to the square of the radius:
Mg = C1 * Rg * Rg
where C1 depends only on shape and is basically the same across all the spiral/disk galaxies.
Orbital speed of stars in the disk is proportional to the square root of the galaxy's mass (the observed absence of the other otherwise must-have orbital velocity equation component - ie. 1/SQRT(r) - is what causes crack pot theories like dark matter) :
Vdisk = C2 * SQRT(Mg) = C2 * SQRT(C1) * Rg
where C2 also dependents only on shape and is basically the same across all the spiral/disk galaxies.
Thus Vdisk = C * Rg where the C is pretty close to being the same across all the spiral/disk galaxies.
Angular speed of a star in the disk at the distance "r" from center is
Vdisk / (2pi * r) = (C * Rg) / (2pi * r)
which at the edge of the galaxy, ie. where r = Rg, becomes
(C * Rg) / (2pi * Rg) = C / 2pi
ie. the same constant across all the spiral/disk galaxies.
The end.
Mg = C1 * Rg * Rg
where C1 depends only on shape and is basically the same across all the spiral/disk galaxies.
Orbital speed of stars in the disk is proportional to the square root of the galaxy's mass (the observed absence of the other otherwise must-have orbital velocity equation component - ie. 1/SQRT(r) - is what causes crack pot theories like dark matter) :
Vdisk = C2 * SQRT(Mg) = C2 * SQRT(C1) * Rg
where C2 also dependents only on shape and is basically the same across all the spiral/disk galaxies.
Thus Vdisk = C * Rg where the C is pretty close to being the same across all the spiral/disk galaxies.
Angular speed of a star in the disk at the distance "r" from center is
Vdisk / (2pi * r) = (C * Rg) / (2pi * r)
which at the edge of the galaxy, ie. where r = Rg, becomes
(C * Rg) / (2pi * Rg) = C / 2pi
ie. the same constant across all the spiral/disk galaxies. The end.