
Concept explainers
Determine by direct integration the moments of inertia of the shaded area with respect to the x and y axes.
Fig. P9.185

Find the moment of inertia of the shaded area with respect to x and y axes.
Answer to Problem 9.185RP
The moment of inertia of the shaded area with respect to x axes is
The moment of inertia of the shaded area with respect to y axes is
Explanation of Solution
Given information:
The curve Equation is
Calculation:
Sketch the shaded portion with vertical strip as shown in Figure 1.
Refer to Figure 1.
Write the curve Equation as shown below:
Determine the moment of inertia
Substitute
Integrate Equation (3) with respect to x.
Thus, the moment of inertia of the shaded area with respect to x axes is
Determine the area of the strip element
Determine the moment of inertia
Integrate Equation (4) with respect to y.
Thus, the moment of inertia of the shaded area with respect to y axes is
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Chapter 9 Solutions
Vector Mechanics for Engineers: Statics
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