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A Circle of Diameter 1.5 M is Cut from a Composite Plate.Determine the Centroid of the Remaining Area of Plate. - Engineering Mechanics

Answer in Brief

A circle of diameter 1.5 m is cut from a composite plate.Determine the centroid of the remaining area of plate.

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Solution

PART AREA( in m2) X co-ordinate of centroid(m) Y co-ordinate of centroid(m) Ax(m3) Ay(m3)
Rectangle 3 x 4
=12
3 + `3/2` = 4.5 2 54 24
Triangle 0.5 x 3 x 4
=6
3 - `3/3` = 2 `4/3` = 1.3333 12 8
Semicircle 0.5 x 22 x 𝝅
=6.2832
6+`(4 xx 2)/(3π)`
=6.8488
2 43.0324 12.5664
Circle
(To be removed)
-𝝅r2 =-0.752 x 𝝅 =-1.7671 6 2 -10.6029 -3.5343
Total 22.5161     98.4295

 

41.0321

X co-ordinate of centroid ( 𝑥̅ ) = `(ΣAx)/(ΣA) = (98.4295)/(22.5161) = 4.3715 m`
Y co-ordinate of centroid(𝑦̅) = `(ΣAy)/(ΣA) = (41.0321)/(22.5161) = 1.8223 m`

Centroid is at (4.3715,1.8223)m

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