Question

The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius rh = 0.315 m and mass 5.84 kg, and two thin crossed rods of mass 8.23 kg each. You would like to replace the wheels with uniform disks that are 0.0588 m thick, made out of a material with a density of 6910 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?

0.0588 m

Answer 1

First, Calculate the moment of inertia of the given wheel with two thin crossed rods [4 spokes]

-----(1)

Now, calculate the Moment of Inertia of a given disk

, but we need to calculate the mass using the density given

Mass

replace in M

Given bothe the Moment of Inertias are same equtate them and the radius