Concept explainers
PROBLEM 5.16
Determine the y coordinate of the centroid of the shaded area in terms of r1, r2, and α.
The y coordinate of the centroid of the shaded area in terms of
Answer to Problem 5.16P
The y-coordinate of the centroid of the plane area is
Explanation of Solution
Write the expression for the y-coordinate of the centroid of the sector with radius
Here
Write the expression for the area of the sector with radius
Write the expression for the y-coordinate of the centroid of the sector with radius
Here
Write the expression for the area of the sector with radius
Write the expression for
Substitute (I), (II), (III) and (IV) in the above equation to calculate
Write the expression for
Substitute (II) and (IV) in the above equation to calculate
Write the expression to calculate the y-coordinate of the centroid of the given area.
Conclusion:
Substitute (V) and (VI) in the above equation to calculate
Thus, the y-coordinate of the centroid of the plane area is
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Chapter 5 Solutions
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