An amusement park ride consists of a vertical hollow cylinder of radius \(R\) that rotates about a central vertical axis with a constant angular speed \(\omega\). A rider of mass \(m\) stands against the interior vertical wall, and when the floor drops away, the rider remains pinned to the wall without sliding downward. If a second rider of mass \(2m\) enters the same cylinder, which of the following statements correctly compares the minimum angular speed \(\omega_{\text{min}}\) required to prevent the second rider from sliding down to that of the first rider, and provides the correct physical justification?