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

AI Thread Summary
The discussion focuses on calculating the moment of inertia of a circular wheel made from a stiff uniform wire, which is cut and bent into a wheel with four spokes. The mass of each spoke is derived as M_0 divided by (2π + 4), and the length of each spoke is L_0 divided by (2π + 4). Participants seek clarification on the steps involved in calculating the moment of inertia for both the spokes and the circular section of the wheel. The conversation highlights discrepancies in the calculations presented, prompting requests for detailed work to resolve differences. Overall, the thread emphasizes the importance of precise calculations in determining the moment of inertia for the given structure.
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 \frac{1}{2\pi + 4}*M_0

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

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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