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Find the moment of inertia and radius of gyration of the shaded area with respect to y axis by using direct integration.

Answer to Problem 9.18P
The moment of inertia of the shaded area with respect to y axis by using direct integration is
The radius of gyration of the shaded area with respect to y axis by using direct integration is
Explanation of Solution
Given information:
The curve equation is
Calculation:
Sketch the vertical strip shaded portion as shown in Figure 1.
Write the curve Equation as follows:
Modify Equation (1).
Determine the area of the strip element
Determine the moment of inertia
Substitute
Consider
Differentiate both sides of the Equation.
Find the moment of inertia of the shaded area with respect to y axis by using direct integration.
Substitute
Thus, the moment of inertia of the shaded area with respect to y axis by using direct integration is
Find the area of shaded portion (A) as shown below:
Substitute
Substitute
Find the radius of gyration of the shaded area with respect to y axis by using direct integration.
Here, A is are of shaded portion and
Substitute
Thus, the radius of gyration of the shaded area with respect to y axis by using direct integration is
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Chapter 9 Solutions
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