I followed the directions from similar problems listed (here on Chegg), and the

Question

I followed the directions from similar problems listed (here on Chegg), and the answers were wrong. Please help!

The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius rn = 0.580 m and mass 5.65 kg, and two thin crossed rods of mass 9.52 kg each. You would like to replace the wheels with uniform disks that are 0.0462 m thick, made out of a material with a density of 8290 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 cl the disk be?

Explanation / Answer

Moment of inertia of wagon wheel, I = I_hoop + I_rods

= M_hoop*r_hoop^2 + 2*m_rod*(2*rh)^2/12

= 5.65*0.58^2 + 2*9.52*(2*0.58)^2/12

= 4.036 kg.m^2

let rd is the required radius.

I = 0.5*M*rd^2

we know, Mass, M = density*Volume

= 8290*pi*rd^2*0.0462

so,

I = 0.5*8290*pi*rd^2*0.0462*rd^2

4.036 = 601.3*rd^3

rd = (4.036/601.3)^(1/3)

= 0.189 m <<<<<<<----------------Answer

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