Place the x and y reference axes in the lower left corner of the object. What is the bar of x in inches? Place the x and y reference axes in the lower left corner of the object. What is the bar of y in inches?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Place the x and y reference axes in the lower left corner of the object. What is the bar of x in inches?

Place the x and y reference axes in the lower left corner of the object. What is the bar of y in inches?

COMPUTE THE MOMENTS OF INERTIA AND RADII OF GYRATION WITH RESPECT TO BOTH CENTROIDAL AXES OF THE
COMPOSITE AREA. UNLESS OTHERWISE SPECIFIED UNITS ARE IN INCHES.
14"
9"
5"
Ø3" HOLE
6"
5"
5"
Xref
4"
Y ref
Transcribed Image Text:COMPUTE THE MOMENTS OF INERTIA AND RADII OF GYRATION WITH RESPECT TO BOTH CENTROIDAL AXES OF THE COMPOSITE AREA. UNLESS OTHERWISE SPECIFIED UNITS ARE IN INCHES. 14" 9" 5" Ø3" HOLE 6" 5" 5" Xref 4" Y ref
Expert Solution
Step 1

The centroid of the rectangle having the lower-left corner at the origin can be drawn as below,

Mechanical Engineering homework question answer, step 1, image 1

The centroid of the above area in the horizontal direction is given by half of its horizontal length,

x1=23 in2=11.5 in

The centroid of the above area in the vertical direction is given by half of its vertical length,

y1=16 in2=8 in

Step 2

The centroid of the circular hole can be represented as below,

Mechanical Engineering homework question answer, step 2, image 1

The centroid of the above area in the horizontal direction is at its center,

x2=4 in

The centroid of the above area in the vertical direction is at its center,

y2=5 in

Step 3

The centroid of the triangular area can be represented as below,

Mechanical Engineering homework question answer, step 3, image 1

The centroid of the above area in the horizontal direction is given by,

x3=14 in+9 in-9 in3=20 in

The centroid of the above area in the vertical direction is given by,

y3=5 in+6 in-6 in3=9 in

Step 4

The centroid of the smaller rectangular area can be marked as below,

Mechanical Engineering homework question answer, step 4, image 1

The centroid of the above area in the horizontal direction is,

x4=14 in+9 in2=18.5 in

The centroid of the above area in the vertical direction is,

y4=11 in+5 in2=13.5 in

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