Moment of inertia of a stiff wire bent into a wheel with spokes

AI Thread Summary
The discussion revolves around calculating the moment of inertia of a wheel made from a stiff wire, which includes a rim and four spokes. The user is trying to determine the mass of the spokes and the rim based on the total mass and length of the wire. They propose formulas for the moment of inertia of the rim and spokes but are struggling with the correct mass ratios and the final expression. The user expresses confusion about their calculations and seeks clarification on the correct approach to submit. The conversation highlights the complexities involved in deriving the moment of inertia for this specific geometric configuration.
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Homework Statement



A stiff uniform wire of mass M0 and length L0 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.

What is the moment of inertia of this wheel about an axle through its center perpendicular to the plane of the wheel? Express your answer in terms of the given quantities.

Homework Equations



Irim = MR2
Ispoke = 1/3ML2
Itotal = Irim + 4*Ispoke

The Attempt at a Solution



The length of one spoke, which should also be the radius of the rim, should be L0/(2\pi+4)

I am unsure of the mass of one spoke, as well as the mass of the rim. Would the mass of one spoke be the same ratio? (Mspoke = M0/(2\pi+4)) ?
If so, then what would be the mass of the rim? I thought Mrim = M0 - 4*Mspoke
therefore Mrim = (M0*(1-4/(2\pi+4))
but I am not getting it right when I submit it.
 
Physics news on Phys.org
What, exactly, are you submitting?
 
This is what I have: I = (1-4/(2\pi+4))*M0*(L0/(2\pi+4))2+4*M0/(2\pi+4)*(L0/(2\pi+4))2

It seems very messy/cumbersome. Am I going about this wrong?
 

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