All of the questions concern a space station, consisting of a long thin uniform
ID: 1519159 • Letter: A
Question
All of the questions concern a space station, consisting of a long thin uniform rod of mass 4.9 x 106 kg and length 378 meters, with two identical uniform hollow spheres, each of mass 2.8 x 106 kg and radius 186 meters, attached at the ends of the rod, as shown below. Note that none of the diagrams shown is drawn to scale!
(c) Now, another feature of this station is that the rod-shaped section can change its length (kind of like an old-fashioned telescope), without changing its overall mass and remaining uniform in its density. Suppose that, however it was accomplished, the station is now rotating at a constant angular velocity of 0.13 rad/s. If the length of the rod is reduced to 232 meters, what will be the new angular velocity of the space station? Answer: __________.___ rad/s
Explanation / Answer
I = 4.9*10^6*378^2/12 + 4*2.8*10^6*186^2/5 + 2*2.8*10^6*(378/2)^2 = 3.3587*10^11
I' = 4.9*10^6*232^2/12 + 4*2.8*10^6*186^2/5 + 2*2.8*10^6*(232/2)^2 = 1.748*10^11
I*0.13 = I'w
w = 0.249 rad / s { from conservation of angular momemntum}