a space station, consisting of a long thin uniform rod of mass 3.5 x 106 kg and
ID: 1408123 • Letter: A
Question
a space station, consisting of a long thin uniform rod of mass 3.5 x 106 kg and length 372 meters, with two identical uniform hollow spheres, each of mass 2.0 x 106 kg and radius 119 meters, attached at the ends of the rod, as shown below. Note that none of the diagrams shown is drawn to scale!
(a) Suppose that the station starts out at rest (not rotating). What we want is to get it spinning about an axis passing through its center of mass, at an angular velocity of 0.15 rad/s, which is just what’s needed to produce 1-g of artificial gravity at the end points. To achieve this, we use rocket motors to apply a constant force F = 2.2 x 106N to each sphere as shown, directed toward the centers of the spheres. How long must the motors fire in order to bring the station from rest up to an angular velocity of 0.15 rad/s? answer in minutes
Explanation / Answer
Torque provided T = 2*F*(372/2 + 119) = 2*2.2*10^6*(186+119)
= 1342000000 Nm
Moment of inertia I = 3.5*10^6*372^2/12 + 2*(2/3*2*10^6*119^2 + 2*10^6*(119+186)^2)
= 450224666667 Kgm^2
angular acc. a= T/I = 1342000000/450224666667= 0.00298 rad/s^2
t = w/a = 0.15/0.00298 = 50.33 s
=0.84 minutes
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