A space station, consisting of a long thin uniform rod of mass 2.9 x 10^6 kg and

Question

A space station, consisting of a long thin uniform rod of mass 2.9 x 10^6 kg and length 157 meters, with two identical uniform hollow spheres, each of mass 2.2 x 10^6 kg and radius 41 meters, attached at the ends of the rod, as shown below. Note that none of the diagrams shown is drawn to scale!

Let’s start again with the station not rotating, and back to its original size, with the rod again at 157 meters long. This time, we would like to get the station rotating at a rate of 0.25 rad/s, but now about an axis that passes straight down the length of the rod. We will accomplish this by placing a pair of rocket engines as shown, each again with a thrust of 3.3 x 10^6 N, on one of the spherical end modules. How long must these engines fire in order to get the station’s angular velocity up to 0.25 rad/s? Answer: __________.___ minutes

Explanation / Answer

Here,

for moment of inertia

I = 2 * 2/3 * m * r^2

I = 4/3 * 2.2 *10^6 * 41^2

I = 4.93 *10^9 Kg.m^2

let the time taken is t

using law of motion

3.3 10^6* 2 * 41 * time = 0.25 * 4.93 *10^9

solving for time

t = 4.55 s = 0.075 min

the time taken is 0.075 min

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