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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