- #1

Tina20

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## Homework Statement

Far out in space, a mass1=146500.0 kg rocket and a mass2= 209500.0 kg rocket are docked at opposite ends of a motionless 70.0 m long connecting tunnel. The tunnel is rigid and has a mass of 10500.0 kg.

The rockets start their engines simultaneously, each generating 59200.0 N of thrust in opposite directions. What is the structure's angular velocity after 33.0 s?

## Homework Equations

center of mass = (m1x1 + m2x2 + m3x3)/m1 + m2 + m3

where m1 = mass of rocket 1, m2 = mass of tunnel, m3 = mass of rocket 3

x(number) = distance to the origin (in this case, rocket one used as origin (set at 0)

Moment of Inertia = m1r1^2 + m2r2^2 (m=mass, r= distance to center of mass)

Moment of inertia of thin, long rod about center = 1/12 ML^2 (M=mass, L=length of rod)

Torque = lengthxForce

angular acceleration = Torque/inertia

angular velocity = angular acceleration x time

## The Attempt at a Solution

So, I found the center of mass, and I know it's correct because the previous question asked for it and was found to be correct. It was 41m.

Now, I think I may be calculating my moment of inertia wrong?

I = m1r1^2 + m3r3^2 + 1/12 ML^2

I = 447 938 063.8 kg*m^2

Am is supposed to include the moment of inertia of the tunnel (rod) in this scenario? Obviously I use the mass and their relative distances to the center of mass for the rockets to find their moment of inertia...but do I just add on the moment of inertia of the rod?

My answer was incorrect, so I am trying to figure out what is wrong about my process. I am assuming my moment of inertia is incorrect.

The torque is 70m x 59200N = 4144000 N*m

Please help :)