Moment of Inertia for connected, hinged panels

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Discussion Overview

The discussion revolves around calculating the moment of inertia (MOI) for a solar panel array consisting of three connected panels that are hinged and will be deployed in space. The focus is on understanding the dynamics of the panels as they are released from a folded position and how this affects their angular momentum.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster (OP) attempts to calculate the MOI for each panel based on their configuration and mass, using the formula I=1/3*M*a^2, but expresses uncertainty about the approach due to the interconnected nature of the panels.
  • Some participants suggest that a sketch of the deployment mechanism might clarify the situation, questioning whether the panels are in a "rolled" or "concertina" pattern.
  • One participant emphasizes that the answer depends on the control of the panels' motion and the specifics of the deployment mechanism, indicating that understanding how the panels are released is crucial.
  • The OP clarifies that the panels will be released simultaneously when a chord holding them in place breaks, which may influence the calculation of the MOI.
  • A link to an external image is provided to illustrate how the panels are connected, suggesting that visual context may aid in understanding the problem.

Areas of Agreement / Disagreement

There is no consensus on the correct approach to calculating the MOI due to differing views on the deployment mechanism and the interconnected dynamics of the panels. Participants express uncertainty and seek clarification on specific aspects of the problem.

Contextual Notes

The discussion highlights potential limitations in the OP's assumptions about the motion of the panels and the need for a clearer understanding of the deployment mechanism, which remains unresolved.

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Homework Statement


[/B]
There is a solar panel array of 3 panels connected to a spacecraft . The panels in the array are connected linearly (in a row: panel1 + panel2 + panel3 + spacecraft ) with hinges. They are all 0.2 meters by 0.3 meters and connected along the 0.3 meter side using 2 hinges for each panel. I'm looking for the MOI so that I can calculate the angular momentum of all 3 panels when they are released from their folded position once the craft is in orbit. They are folded together on the hinged sides and all 3 are in a "pile" before being released.

Homework Equations

[/B]
I=1/3*M*a^2 'a' being the length of the shorter side in this case 0.2

The Attempt at a Solution


[/B]
Innermost panel has to swing outward with the mass of the other 2 attached to it: I=1/3*(M*3)*a^2
Middle panel has to swing outward with the mass of itself plus outer panel attached to it:
I = 1/3*(M*2)*a^2
outermost panel: I = 1/3*M*a^2

Since the panels are connected and moving simultaneously when released, I'm not sure this is the way to do this and I can't find any similar examples which makes me think I'm really missing something.
Any help would be greatly appreciated!
 
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I doubt I will be able to help but I think sketch might help. Are the panel's "rolled" or "consterina" pattern?
 
Answer you are looking for depends on how the motion of the panels is being controlled . You really need to know how the deployment mechanism works .
 
CWatters said:
I doubt I will be able to help but I think sketch might help. Are the panel's "rolled" or "consterina" pattern?
Concertina pattern.
 
Nidum said:
Answer you are looking for depends on how the motion of the panels is being controlled . You really need to know how the deployment mechanism works .
The panels will be released all at once - a chord holding them "pinned down" in their folded position will break and the entire solar panel array comes free at once.
 

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