When the net external torque acting on a system is zero, the total angular momentum of the system is a constant.  Since angular momentum is a vector quantity, this is stated as

    Ltot(before) = Ltot(after)

In the special case of rotations about a fixed axis, taken to be the z axis, the equation becomes

    Ltot(before)_z = Ltot(after)_z.

where Ltot_z = L1_z + L2_z + … gives contributions of all bodies that constitute the system.