The wheels of a wagon can be approximated as the combination of a thin outer hoo
ID: 1974653 • Letter: T
Question
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius rh = 0.580 m and mass 4.89 kg, and two thin crossed rods of mass 9.52 kg each. You would like to replace the wheels with uniform disks that are 5.88 cm thick, made out of a material with a density of 7860 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?
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius rh = 0.580 m and mass 4.89 kg, and two thin crossed rods of mass 9.52 kg each. You would like to replace the wheels with uniform disks that are 5.88 cm thick, made out of a material with a density of 7860 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?Explanation / Answer
net moment inertia of first wheel = Mr2 + 2Xm(2r)2 /12
= 4.89 X 0.5802 + 2X 9.52 X 1.162 /12
= 1.645+ 2.135 = 3.78 kg-m2
mass of second wheel = volume X density = r2 h X 7860 = 1452.94r2 kg
moment of inertia of disk = mr2 /2 = 1452.94r2 X r2 /2
both are equal, so
725.97r4 = 3.78
r = 0.2686 m or 26.86 cm
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