Two identical uniform disks are initially rotating with the same constant angular velocity \(\omega_i\) about a vertical frictionless axle through their centers. Two separate scenarios are established:

System 1: The disk is on a free-spinning axle. A small block of mass \(m\) is dropped vertically onto the disk at a distance \(r\) from the center and sticks to it.

System 2: The disk is attached to a motor that maintains the constant angular velocity \(\omega_i\) throughout the process. An identical small block is dropped vertically onto the disk at the same distance \(r\) and sticks to it.

Which of the following correctly describes the change in the angular momentum \(L\) and the angular velocity \(\omega\) for each disk-block system immediately after the block sticks?