Equation for the Origin of Spiral Galactic Formation and Rotation

Already formed galactic arms existed in sets of two or more orbiting each other due to the Big Bang. As the orbits of the arms decayed due to gravitational attraction they attached in their fore sections tangentially accreting forming spiral galaxies which began to rotate due to the transformation of the orbital motion of the pre-galactic arms into the rotational motion of the newly formed spiral galaxy. If $I_1\omega_1$, $I_2\omega_2$, and $I_n\omega_n$ are the angular momentums of the pre-galactic arms, and $(I\omega)_{galaxy}$ is the angular momentum of the newly formed spiral galaxy, the equation for the formation and origin of spiral galaxy rotation is $I_1\omega_1 + I_2\omega_2 +...+ I_n\omega_n = (I\omega_{galaxy})$.