# Moment of Inertia for a wheel

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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rock.freak667
Homework Helper
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

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
Homework Helper
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.