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Last week I posted in General Physics some questions about what happens in a collapsing gas cloud, and I was advised that total angular momentum is conserved. I thought of asking for extra clarification here, as that seems really amazing -- I apologize for asking the same thing twice. I use a galaxy to ask the question. Our galaxy has a huge momentum today, and in the past it was just a huge gas cloud. So, what astronomers believe is closest approximation to the formation of our galaxy?
(a) The original gas cloud and our galaxy have about the same mass and total angular momentum
(b) The original gas cloud and our galaxy have significantly different total mass and total angular momentum
If (a) is true, then why these equations fail to explain that; say a particle just on the outskirts of a circular gas cloud, and it is collapsing with the gas cloud, and after it collapses it remains at the outskirts of the galaxy; then, for the particle:
Force gravity = Centripetal force
G.M.m/r^2 = m.v^2/r = m.w^2.r
w = GM/r^3
L = I.w = mr^2.w = G.M.m/r
M = mass of the gas cloud, which per (a) is the same, but r has decreased, so the angular momentum of the particle on the outskirts of the gas cloud increases, therefore angular momentum of one particle cannot be the same, and (a) is impossible... the only way for L to be preserved is by decreasing M...
Where is the equation wrong?
(a) The original gas cloud and our galaxy have about the same mass and total angular momentum
(b) The original gas cloud and our galaxy have significantly different total mass and total angular momentum
If (a) is true, then why these equations fail to explain that; say a particle just on the outskirts of a circular gas cloud, and it is collapsing with the gas cloud, and after it collapses it remains at the outskirts of the galaxy; then, for the particle:
Force gravity = Centripetal force
G.M.m/r^2 = m.v^2/r = m.w^2.r
w = GM/r^3
L = I.w = mr^2.w = G.M.m/r
M = mass of the gas cloud, which per (a) is the same, but r has decreased, so the angular momentum of the particle on the outskirts of the gas cloud increases, therefore angular momentum of one particle cannot be the same, and (a) is impossible... the only way for L to be preserved is by decreasing M...
Where is the equation wrong?