the wheels of a wagon can be the wheels of a wagon can be the wheels of a wagon

Question

the wheels of a wagon can be the wheels of a wagon can be the wheels of a wagon can be the wheels of a wagon can be The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius h0.421 m and mass 4.32 kg, and two thin crossed rods of mass 9.09 kg each. You would like to replace the wheels with uniform disks that are 0.0651 m thick, made out of a material with a density of 7370 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? Number 0017

Explanation / Answer

moment of inertia of the hoop is

I=MR2 = 4.32*0.4212 = 0.76568 kg-m2

The Moment of inertia of a rod through its center is

I=(1/12)ML2 = (1/12)(9.09 kg)(2*0.421)2 = 0.53704 kg-m2

Total moment of inertia is

Itot =0.76568+ 2*0.53704= 1.83976 kg-m2

the volume of the disk is

V=pir2t

and its mass is

m=p*pir2t

Since the moment of inertia of a disk is

Itot=(1/2)Mr2

(1/2)(p*pir2t)(r2) = Itot  

(1/2)(7370)*(pi*r4*0.0651)=1.83976

r=0.2223 m

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