Consider a non$-$rotating space station in the shape of a long thin uniform rod of mass $1\mathrm{.}65$ x $10\mathrm{⁶}$ kg and length $1022$ meters. Rocket motors on both ends of the rod are ignited, applying a constant force of

 F $=2\mathrm{.}26$ x $10\mathrm{⁵}$ N to each end of the rod as shown in the diagram, causing the station to rotate about its center. If the motors are left running for $1$ minutes and $20$ seconds before shutting off, then how fast will the station be rotating when the engines stop?