Concept explainers
(a)
Find the polar moment of inertia of the area with respect to point O.
(a)
Answer to Problem 9.48P
The polar moment of inertia of the area with respect to point O is
Explanation of Solution
Calculation:
Sketch the cross section as shown in Figure 1.
Refer to Figure1.
It is divided into 4 parts as shown above.
Find the area of section 1 ellipsoid using the relation:
Substitute
Find the area of section 2 ellipsoid using the relation:
Here,
Substitute
Find the area of section 3 ellipsoid using the relation:
Substitute
Find the area of section 4 ellipsoid using the relation:
Substitute
Find the total are of section (A) as shown below:
Substitute
Find the centroid
Find the centroid
Find the centroid
Find the centroid
Find the centroid
Substitute
Find the polar moment of inertia
Substitute
Find the polar moment of inertia
Substitute
Find the polar moment of inertia
Substitute
Find the polar moment of inertia
Substitute
Find the total moment of inertia
Substitute
Thus, the polar moment of inertia of the area with respect to point O is
(b)
Find the centroid of area.
(b)
Answer to Problem 9.48P
The centroid of area is
Explanation of Solution
Calculation:
Find the centroid of area using the relation:
Substitute
Thus, the centroid of area is
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Chapter 9 Solutions
Vector Mechanics for Engineers: Statics
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