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Find the Co-ordinate of the Centroid of the Area as Shown in the Given Figure. - Engineering Mechanics

Answer in Brief

Find the co-ordinate of the centroid of the area as shown in the given figure.

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Solution

Figure Area(mm2) X co-ordinate of centroid (mm) Y co-ordinate of centroid (mm) Ax
(mm2)
Ay
(mm2)
Quarter circle 0.25 x π x R2
=0.25 x 202 x 𝝅
=314.1593
`(4R)/(3pi)=(4xx20)/(3pi)`
=8.4883
`(4R)/(3pi)=(4xx20)/(3pi)`
=8.4883
2666.6667 2666.6667
Semi-circle
(to be removed)
-0.5 x π x r2
= -157.0796
10 `(4R)/(3pi)=(4xx10)/(3pi)`
=4.2441
-1570.7963 -666.6667
Total 157.0796     1095.8704 2000

∴ X co-ordinate of centroid (x̅)= `(∑ Ax)/(∑A)=(1095.8704)/(157.0796)=6.9765 cm`

∴ Y co-ordinate of centroid (y)=`(∑ AY)/(∑A)=(2000)/(157.0796)=12.7324 cm`
Centroid = (6.9765,12.7324) cm

Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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