A space station is constructed in the shape of a hollow ring of mass 4.65 104 kg

Question

A space station is constructed in the shape of a hollow ring of mass 4.65 104 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius 115 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g. (See figure below.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring.
(a) What angular momentum does the space station acquire?
1 kg · m2/s

(b) For what time interval must the rockets be fired if each exerts a thrust of 120 N?
2 s

Explanation / Answer

Mass of a hollow ring is M = 4.65 *10^4 kg

radius r = 115 m

r w^2   = g

w = g / r

    = 9.8 / 115 m

      = 0.29 rad /s

Moment of inertia is I = M r^2

                                     = 4.65 *10^4 kg * ( 115 m)^2

                                     = 6.14*10^8 kg m^2

a ) Angular momentum is   L = I w

                                               = 6.14 *10^8 kg m^2 * 0.29 rad / s

                                                 = 1.78 *10^8 kg m^2 /s

b ) torque = d L / dt

          dt   = L_f - L _i / 2 ( F ) ( r )

                = 1.78 *10^8 / 2 ( 120 N ) ( 115 m )

                = 6.44*10^3 s

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