The Satellite Derotator
NAVAL ACADEMY ANNAPOLIS MD DEPT OF PHYSICS
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When introducing linear collision problems, physics texts contrast the elastic and inelastic cases. This distinction is useful because, for an interaction between two bodies in one dimension, equality of the kinetic energies and linear momenta enables one to solve for the final velocities from the initial velocities and masses. A number of important problems are approximately elastic, including collisions between aircarts having spring bumpers, gravity boosting of space probes around planets, billiard-ball and superball bounces, and atomic collisions in the absence of electronic or nuclear excitations. In contrast, with the exception of planetary orbits, there are no standard examples of elastic angular collisions. The figure skater pulling in her arms, spinning disks that stick together, a bike wheel manipulated on a turntable, the revolving ball on a string whose length can be varied, people walking or jumping onto a merry-go-round - all of these are inelastic. However, there is an elastic rotational demonstration apparatus dating back to at least the 1960s, and more recently popularized by its inclusion in The Video Encyclopedia of Physics Demonstrations under the name of the satellite derotator. Although presented as an example of conservation of angular momentum, it is instructive to instead view it as a mechanism for transferring rotational kinetic energy from one object to another without loss. In particular, while intended solely as a means of halting the rotations of a satellite, one could imagine modifying the apparatus to controllably adjust its angular orientation or velocity, storing up mechanical energy for later use.
- Operations Research