Consider a non - rotating space station in the shape of a long thin uniform rod of mass 1 . 1 2 1 .

Consider a non$-$rotating space station in the shape of a long thin uniform rod of mass $1\mathrm{.}12$ x $10^6$ kg and length $626$ meters. Rocket motors on both ends of the rod are ignited, applying a constant force of F $=2\mathrm{.}79$ x $10^5$ 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 $28$ seconds before shutting off, then how fast will the station be rotating when the engines stop?

a$.4\mathrm{.}01$ rpm

b$.1\mathrm{.}60$ rpm

c$\mathrm{.}5\mathrm{.}61$ rpm

d$\mathrm{.}6\mathrm{.}73$ rpm

F axis F