Any help appreciated, thanks. The wheels of a wagon can be approximated as the c

Question

Any help appreciated, thanks.

The wheels of a wagon can be approximated as the combination of athin outer hoop, of radius r_h = 0.421 m and mass 4.51 kg, and two thin crossed rods of mass 8.66 kg each. You would like to replace the wheels with uniform disks that are 0.0525 m thick, made out of a material with a density of 8750 kilograms per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? r_d =

Explanation / Answer

Find moment of inertia of current wheel.
I = (M)(rh)² + 2[(1/12)(m)(2 rh)²]
I = (M)(rh)² + (2/3)(m)(rh)²
I = (rh)²[M + (2/3)(m)]
I = (0.421 m)²[4.51 kg + (2/3)(8.66 kg)]
I = 1.83 kg-m²

New disc wheel:
I = (1/2)(md)(rd)²

(md) = (d)()(h)(rd)²
(md) = (8750 kg/m³)()(0.0525 m)(rd)²
(md) = (1443.2 kg/m²)(rd)²

1.83 kg-m² = (1/2)(1443.2 kg/m²)(rd)^4
(rd) =.224 m

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