How to find Centroid for a rectangular section inclined at an angle theta? Is there any general formula available?
Centroid for a rectangular section inclined at an angle theta
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geometry
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0What do you mean by a rectangular section? A section of what? – 2012-07-05
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0A rectangle only. – 2012-07-05
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0As you probably know, it's in the middle, where the diagonals meet. What else needs to be done? – 2012-07-05
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0Yes.I agree with ur point.If it is inclined then how will you calculate along with that inclination angle? – 2012-07-05
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0Take the midpoint of two opposite vertices. – 2012-07-05
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0The centroid is independent of rotations. – 2012-07-05
1 Answers
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The location of the centroid of a body doesn't change with rotation . If you are working in a coordinate system, then only the coordinates of the centroid change (not with respect to the body but with respect to axes). Thus,in a rectangle centroid $(x,y)$ is intersection of two diagonals and if the rectangle is rotated by $\theta$ then new coordinates$(x',y')$ are given by system of equations $$x'=x\cos\theta-y\sin\theta$$ and $$y'=x\sin\theta+y\cos\theta$$
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0Thank you Avatar.It's useful. – 2012-07-05