Concept explainers
Determine the moment of inertia of the shaded area about the x axis.
The moment of inertia for the shaded area about the
Answer to Problem 1FP
The moment of inertia for the shaded area about the
Explanation of Solution
Given:
The height of the shaded area is
The width of the shaded area is
Show the area of the differential element parallel to the
From Figure 1,
Compute the area of the differential element parallel to the
Here, the area of the differential element is
Express the moment of inertia of the differential element parallel to the
Here, the first integral of the moment of inertia of the area about the centroidal axis is
Substitute
Substitute
Conclusion:
Express the moment of inertia for the shaded area about the
Substitute
Hence, the moment of inertia for the shaded area about the
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