Equation for the Origin of Rotation of Two Armed Spiral Galaxies

Pre-formed galactic arms were created in sets of two or more before galaxies were formed. These pre-formed galactic arms were orbiting each other. Over time, due to gravitational attraction, the orbits of the arms decayed with the set of two arms tangentially colliding in their fore sections and attaching there forming two armed spiral galaxies which began to rotate. The rotation of the two armed spiral galaxies was due to the conversion of the angular momenta of each of the arms adding together to form the total angular momentum of the newly formed two armed spiral galaxy. If $(I\omega)_{arm}$ is the angular momentum of each of the pre-formed galactic arms, and $(I\omega)_{galaxy}$ is the angular momentum of the newly formed two armed spiral galaxy, the equation for the origin of rotation of the galaxy is $ (I\omega)_{arm1} + (I\omega)_{arm2}= (I\omega)_{newly formed galaxy}$.