Calculating Moment of Inertia for a Soldered Wire Wheel

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Homework Help Overview

The problem involves calculating the moment of inertia for a circular wheel constructed from a uniform wire, which includes spokes extending from the center. The original poster presents the problem statement and attempts a calculation based on the moment of inertia of a rod.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the total moment of inertia using a formula for a rod but questions the correctness of their approach. Other participants suggest considering the structure as a hoop with spokes and emphasize the need to determine the radius of the wheel in relation to the original wire length.

Discussion Status

Participants are exploring different interpretations of the wheel's structure and the implications for calculating the moment of inertia. Some guidance has been offered regarding the assumptions about the hoop's properties, but no consensus has been reached on the correct approach or final calculation.

Contextual Notes

There is a focus on the relationship between the wire length and the radius of the wheel, which may not be fully defined in the problem statement. The discussion also highlights the need to clarify assumptions about the mass distribution and geometry of the wheel.

Quincy
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The problem 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?


Homework Equations


I (from end of rod) = mL^2/3


The Attempt at a Solution


Itotal = 4 * ((M0/4)(L0/4)^2)/3 =

M0L0^2/48 -- What am I doing wrong?
 
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If it forms a circular wheel, it would form a hoop with 4 rods in it. You will need to get the radius of that circle which will also be the length of a rod in terms of L0
 
rock.freak667 said:
If it forms a circular wheel, it would form a hoop with 4 rods in it. You will need to get the radius of that circle which will also be the length of a rod in terms of L0

Should I assume that the hoop is a thin circular hoop whose moment of inertia is mr^2 when the axis of rotation is perpendicular?
 
Quincy said:
Should I assume that the hoop is a thin circular hoop whose moment of inertia is mr^2 when the axis of rotation is perpendicular?

I think that would be fine.
 

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