Calculating Moment of Inertia for a Soldered Wire Wheel

[Quincy]

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

I_total = 4 * ((M₀/4)(L₀/4)^2)/3 =

M₀L₀^2/48 -- What am I doing wrong?

 

[rock.freak667]

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

 

[Quincy]

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?

 

[rock.freak667]

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.