Question

Docking bay: A space station consists of a large circular ringof mass m_r and radius R, connected by thin spokes (ofnegligible mass) to a tiny (negligible size) but dense (notnegligible mass) central hub of mass m_h. Initially, thestation is at rest, neither translating nor rotating. An unpoweredspace pod of mass m_p (much smaller than m_r )drifts through space with speed v_p, approaching a spacestation on a path exactly tangential to the ring. As the podtouches the ring, the station's docking mechanism suddenly grabs itand holds it in place at that point on the ring.

a.) What is the station's moment of inertia about its hub beforethe pod docks?

b.) As the pod approaches the station, what is its angularmomentum relative to the station's hub?

c.) After the pod docks, at what rate (in radians/sec) does thestation rotate?

For the remainder of this problem, use "ω" as the station'sangular velocity after docking no matter what answer you found forpart (c).

d.) What apparent weight would a person in the pod feel becauseof this rotation?

e.) The station has rotational thrusters: jets located aroundthe outside of the ring, pointed tangentially to control therotation of the station. How much work must these jets do on thestation in order to stop the rotation?

f.) If the station has four jets, located 90^o apartaround the ring and each capable of exerting a tangential force Fon the station, what total torque can they apply?

g.) How much time will the jets require to stop therotation?