How can we determine the location of the centroid?

International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter8: Centroids And Distributed Loads
Section: Chapter Questions
Problem 8.50P
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How can we determine the location of the centroid?

Expert Solution
Step 1

It’s the average of all the points of an object, this is the position where an object can be balanced.

Step 2

Mechanical Engineering homework question answer, step 2, image 1

Let us consider a surface as shown in figure. Small area ΔA at point A, and C is the point centroid

From equilibrium of the surface we can write

Mechanical Engineering homework question answer, step 2, image 2

Therefore for centroid at X coordinate we can write

Mechanical Engineering homework question answer, step 2, image 3

Therefore for centroid at Y coordinate we can write

Mechanical Engineering homework question answer, step 2, image 4

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