The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh = 0.156 m and mass 5.65 kg, and two thin crossed rods of mass 8.23 kg each. Imagine replacing the wagon wheels with uniform disks that are ta = 4.62 cm thick, made out of a material with a density of 8290 kg/m³. 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? O ta H rd = 0.2043 Incorrect m
The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh = 0.156 m and mass 5.65 kg, and two thin crossed rods of mass 8.23 kg each. Imagine replacing the wagon wheels with uniform disks that are ta = 4.62 cm thick, made out of a material with a density of 8290 kg/m³. 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? O ta H rd = 0.2043 Incorrect m
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Transcribed Image Text:The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius \( r_h = 0.156 \, \text{m} \) and mass \( 5.65 \, \text{kg} \), and two thin crossed rods of mass \( 8.23 \, \text{kg} \) each. Imagine replacing the wagon wheels with uniform disks that are \( t_d = 4.62 \, \text{cm} \) thick, made out of a material with a density of \( 8290 \, \text{kg/m}^3 \). 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?
**Diagram Explanation:**
There are two main illustrations:
1. **Wagon Wheel Representation**:
- Shows a circular wheel with a thin outer hoop.
- Radius labeled as \( r_h \).
- Crossed rods are visibly depicted within the hoop.
2. **Disk Replacement Representation**:
- Shows a solid, uniform disk with thickness labeled \( t_d \).
- The radius of the disk is labeled \( r_d \).
In the input box next to the diagram for \( r_d \), the value \( 0.2043 \, \text{m} \) is entered, and it is marked as "Incorrect".
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