Turning a Straight Wire into a wheel with spokes, solve for I

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Homework Help Overview

The problem involves calculating the moment of inertia of a circular wheel constructed from a uniform wire, which includes four spokes extending from the center. Participants are tasked with determining the moment of inertia based on the mass and length of the wire.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss various expressions for the moment of inertia, with one attempting to derive a formula while another questions the validity of the results. There are inquiries about the mass and length of the spokes and the circular section, as well as requests for detailed steps in the calculations.

Discussion Status

The discussion is active, with participants sharing their calculations and questioning each other's results. There is a focus on clarifying the contributions of the spokes and the circular section to the overall moment of inertia, indicating a collaborative exploration of the problem.

Contextual Notes

Participants are working under the constraint that no wire is wasted and that the mass of the solder can be neglected. There is an emphasis on ensuring that all components of the wire's structure are accounted for in the calculations.

gkinnish
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Homework Statement


A stiff uniform wire of mass M_0 and length L_0 is cut, bent, and the parts soldered together so that it forms a circular wheel having four identical spokes coming out from the center. None of the wire is wasted, and you can neglect the mass of the solder.
 
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Can you show your work?
 
solving for the moment of inertia i came up with 4/3(M/(L/(2pi+4))^2)
 
gkinnish said:
solving for the moment of inertia i came up with 4/3(M/(L/(2pi+4))^2)

can you show your steps... that's not what I'm getting... some things are similar... some things are different.

The mass of each spoke is [tex]\frac{1}{2\pi + 4}*M_0[/tex]

The length of each spoke is [tex]\frac{1}{2\pi + 4}*L_0[/tex]

What's the moment of inertia of each spoke?

What's the mass of the circular section? What's the moment of inertia of the circular section?
 

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