A centrifugal fan has a power input of \(25 \mathrm{~kW}\), an inner radius of \(R_{1}=0.5 \mathrm{~m}\), an outer radius of \(R_{2}=1.0 \mathrm{~m}\), and delivers \(100 \mathrm{~kg} / \mathrm{s}\) of air. There are no friction losses, the air inlet absolute velocity has no tangential component, and the outlet absolute velocity has a tangential component equal to the blade velocity at the outer radius \(R_{2}\). The rotor depth (i.e., blade height) is \(1.0 \mathrm{~m}\). What is the required rotational speed of the rotor?