Map da Sapling Learning The wheels of a wagon can be approximated as the combina
ID: 1646209 • Letter: M
Question
Map da Sapling Learning The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius h 0.421 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 0.0525 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 of the disk be? Number 0.0525 m O Previous PreviousCheck Answer Next Exit check Answer 0 Next ExitExplanation / Answer
According to the given problem,
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[4.89 kg + (2/3)(9.52 kg)]
I = 1.9916 kg-m²
New disc wheel:
I = (1/2)(md)(rd)²
(md) = (d)()(h)(rd)²
(md) = (8290 kg/m³)()(0.0525 m)(rd)²
(md) = (1367.3 kg/m²)(rd)²
1.9916 kg-m² = (1/2)(1367.3 kg/m²)(rd)^4
(rd) = 0.2323 m