PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
Two satellites, A and B, orbit the same planet in initially separate circular paths. Satellite A has mass m and orbits at radius 2R. Satellite B has mass 2m and orbits at radius R. At a certain instant satellite B receives a brief, purely tangential impulse that places it into a new circular orbit of radius 2R. External influences on the system are negligible except during the impulse.
(a) Determine the magnitude of the angular momentum of each satellite about the planet’s center before the impulse.
(b) Compute the ratio LBLA of their angular momenta before the impulse.
(c) Immediately after the impulse, but before gravitational forces have altered the motion, find the angular momentum of satellite B in terms of known quantities.
(d) Compare the angular momentum found in part (c) with LA, and discuss how any difference must ultimately be accounted for once gravitational forces resume control of the motion.