On the Angular Momentum of Rockets, Balloons, and Other Variable Mass Systems

Abstract

Variable mass systems are a classic example of open systems in classical mechanics. The reaction forces due to mass variation propel ships, balloons, and rockets. Unlike free constant mass systems, the angular momentum of these systems is not of constant magnitude due to the change in mass. In this paper, we show that the angular momentum vector for such a system has a fixed direction in space and, thus, is partially conserved for both rigid and flexible, torque-free, variable mass systems. A potential use of this result is that it provides a suitable stationary reference frame against which the orientation of variable mass system could be measured.