All of the questions on this exam concern a space station, consisting of a long
ID: 1392006 • Letter: A
Question
All of the questions on this exam concern a space station, consisting of a long thin uniform rod of mass 1.0 x 106 kg and length 971 meters, with two identical uniform hollow spheres, each of mass 2.7 x 106 kg and radius 354 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 0.09 rad/s, which is just what
Explanation / Answer
a) consider the rod + spheres as system
net force on system is zero
but net torque = 2FR = MOMENT OF INERTIA OF SYSTEM * ang acc.
where R = l/2 + r =839.5 m
so 2 FR = 4365.4 * 106 = (ML2 /12 + 2.2/3 Mr2 ) ang acc.
so ang acc = 78570 * 106 + 451137 .6 * 106 / 4365.4 * 106
= 121.34 rad/s2
apply eqn of motion w) final = w )initial + 121.34 t
so t = 0.00074 sec