Two rockets rotating attached by rod

In summary, the conversation discusses the calculation of the moment of inertia for a rod rotating about a given pivot. The parallel axis theorem is mentioned as a method for calculating the moment of inertia, and the conversation also includes a discussion on the correct way to derive the formula for the moment of inertia of a rod. There is also a brief mention of the CoM moving through space and its effect on the calculation.
  • #1
Esoremada
52
0

Homework Statement



http://puu.sh/5nKxl.png [Broken]

Homework Equations



α = ω/t
τ = I*α

The Attempt at a Solution



CM = [232200*99 + 99/2*12500] / (107100 + 232200 + 12500)
= 67.102 m


τ = 43320*67.102 + 43320*(99 - 67.102)
= 4288680 N

α = ω/t
τ = I*α
τ = I*(ω/t)

ω = τ/I * t
= 4288680 / [107100*67.1022 + 1250*(67.102 - 99/2)2 + 232200*(99-67.102)2] * 28.3
= 0.1688
 
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  • #2
Your answer would have been correct if the CoM had been fixed in space on an axle. What will happen instead?
 
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  • #3
haruspex said:
Your answer would have been correct if the CoM had been fixed in space on an axle. What will happen instead?

The CoM moves through space, but how can that affect this question when the distance from the centre of mass to the ships remains the same regardless of orientation and speed relative to space.
 
  • #4
Yes, thinking about this again I believe your method is correct, but in the calculation you treated the tunnel as a point mass at its centre. That slightly underestimates the moment of inertia of the system. I get 0.166. Is that error enough to explain your answer's rejection?
 
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  • #5
haruspex said:
Yes, thinking about this again I believe your method is correct, but in the calculation you treated the tunnel as a point mass at its centre. That slightly underestimates the moment of inertia of the system. I get 0.166. Is that error enough to explain your answer's rejection?

That was correct! So what is the correct way to calculate the moment of a inertia of a rod about a given pivot? I only know that it is 1/12*ML^2 and 1/3*ML^2 for pivots about the centre or end.
 
  • #6
Esoremada said:
That was correct! So what is the correct way to calculate the moment of a inertia of a rod about a given pivot? I only know that it is 1/12*ML^2 and 1/3*ML^2 for pivots about the centre or end.
Use the parallel axis theorem. The MoI about one end is simply a special case of that.
 
  • #7
Oh cool I never even noticed that. I get how to derive 1/3*ML^2 now but I try doing it in this problem and get it wrong

1250*(67.102 - 99/2)^2 + 1/12*1250*99^2

That's the moment of the rod rotating about its centre plus the moment of the rod's centre of mass rotating about the systems centre of mass. What am I doing wrong?
 
  • #8
Esoremada said:
Oh cool I never even noticed that. I get how to derive 1/3*ML^2 now but I try doing it in this problem and get it wrong

1250*(67.102 - 99/2)^2 + 1/12*1250*99^2

That's the moment of the rod rotating about its centre plus the moment of the rod's centre of mass rotating about the systems centre of mass. What am I doing wrong?
Isn't it 12500?
 
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  • #9
...I need more sleep. Thanks again :P
 
  • #10
What about treating the rod as two rods rotating about one end, where that commen one end is the center of mass?
 
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1. How do two rockets rotating attached by rod work?

The two rockets rotating attached by rod concept involves two rockets that are connected by a rod and rotate around a central axis. The rockets are powered by engines that create thrust and cause them to rotate around the rod. This rotation creates a gyroscopic effect, which helps stabilize the rockets in flight. The rockets can also adjust their orientation by changing the direction of their thrust, allowing them to maneuver in different directions.

2. What is the purpose of using two rockets rotating attached by rod?

The purpose of using two rockets rotating attached by rod is to provide stability and control during flight. The gyroscopic effect created by the rotation of the rockets helps to stabilize the flight and allows for more precise control of the rockets' direction. This can be useful in applications such as space exploration, where precise control and stability are crucial for successful missions.

3. How is the rotation of the rockets controlled?

The rotation of the rockets is controlled by the engines on each rocket. By adjusting the direction and intensity of the thrust, the rockets can change their orientation and control their rotation. Additionally, the length and angle of the rod connecting the rockets can also affect the rotation and stability of the system.

4. What are the advantages of using two rockets rotating attached by rod?

One of the main advantages of using two rockets rotating attached by rod is the increased stability and control during flight. This can be beneficial in various applications, such as space exploration or missile guidance systems. Additionally, the use of two rockets allows for redundant systems, increasing the overall reliability of the system.

5. Are there any limitations to the two rockets rotating attached by rod concept?

One limitation of this concept is the complexity of the system. The use of two rockets and a connecting rod adds additional components and mechanisms that can potentially fail. This can make the system more difficult and expensive to maintain. Additionally, the gyroscopic effect created by the rotation of the rockets can also make it challenging to predict and control the system's movements accurately.

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