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Solved: A wagon wheel is constructed as shown in Fig.
Chapter 9, Problem 35E(choose chapter or problem)
A wagon wheel is constructed as shown in Fig. E9.35. The radius of the wheel is \(0.300 \mathrm{~m}\), and the rim has mass \(1.40 \mathrm{~kg}\). Each of the eight spokes that lie along a diameter and are \(0.300 \mathrm{~m}\) long has mass \(0.280 \mathrm{~kg}\). What is the moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel? (Use the formulas given in Table 9.2.)
Equation Transcription:
Text Transcription:
0.300 m
1.40 kg
0.300 m
0.280 kg
0.600 m
Questions & Answers
QUESTION:
A wagon wheel is constructed as shown in Fig. E9.35. The radius of the wheel is \(0.300 \mathrm{~m}\), and the rim has mass \(1.40 \mathrm{~kg}\). Each of the eight spokes that lie along a diameter and are \(0.300 \mathrm{~m}\) long has mass \(0.280 \mathrm{~kg}\). What is the moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel? (Use the formulas given in Table 9.2.)
Equation Transcription:
Text Transcription:
0.300 m
1.40 kg
0.300 m
0.280 kg
0.600 m
ANSWER:
Solution 35E
Introduction
We have to calculate the moment of inertia of the wheel and then the moment of inertia of each spoke. Then, the total moment of inertia will be the sum of the above two quantity.
Step 1
First calculate the moment of inertia of the ring of the wheel. The moment of inertia of ring is given by
