A space station is approximately a ring of radius,R, and mass m,which rotates about its symmetry axis with angularvelocity,~ω=ω0ˆe3. A meteor is traveling with momentum,~p, that isparallel to the original ˆe3, and strikes the space station at apoint on the rim,transferring the entire momentum to the spacestation (an inelastic collision where the meteor sticks to thespace station). Further, though the meteor has significantmomentum,it is of very small mass so that the moment of inertiatensor elements are approximately the same before and after thecollision

a) What is the vector angular momentum of the space station withrespect to a coordinate system with origin at the center of thering and one axis along ˆe3 just before the collision?

b) What is the vector angular momentum of the space station inthe same coordinate system (and defining the ˆe2 axis as in thedirection from the origin to the point of impact on the edge of thering) just after the collision?

c) After the collision, there are no further torques acting onthe space station. Assume that the angular momentum of the spacestation after the collision differs by only a small (vector) amountfrom the initial angular momentum. Write down equations of motionthat describe how the components of~ωfor the space station evolvewith time.

d) Use these equations to describe how the rotational velocityvector of the space station evolves with time. If you predictsimple rotation about a new direction, say so and describe the newdirection. If you predict precessional motion, say so and predictthe precession frequency. If you think something else happens, sayso and describe the motion. In all cases, Explain: Back up yourprediction with reasoning and (possibly approximate) solutions ofthe equations from part (c).