Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 4 / 11C / c / ii

At time $t$, the remaining water has angular momentumDuring $dt$, the ejected mass is $-dm$, and its signed tangential speed in the inertial frame is $R\omega +u$. Conservation of angular momentum gives, to first order,After simplification, the angular rocket equation isHere $u$ is signed relative to the direction of rotation; reversing the spray changes its sign.