1. The problem statement, all variables and given/known data
I am after finding general geometric expressions for a quarter-circle that is split into two segments along either its domain or range (they are equal). I.e. Taking the circle shown in Figure 1 and concentrating on the upper right quadrant, I am after expressions for the individual areas (top and bottom) and their respective centroids x1, y1 and x2, y2 (Figure 2) when cut at "c".
Figure 1:
Figure 2:
2. Relevant equations
Area of circle = ∏r[itex]^{2}[/itex]
Equation of quarter circle: y(x) = √(x[itex]^{2}[/itex]-r[itex]^{2}[/itex])
3. The attempt at a solution
Apart from stating the obvious equations (above) I’m stuck on this problem.
I have searched my textbooks/google (using general key words) for expressions of this particular case with no luck.
I have never been strong with deriving expressions from first principals and would appreciate any ideas/push in the right direction. This is a problem directed at self-study, not homework.
I am after finding general geometric expressions for a quarter-circle that is split into two segments along either its domain or range (they are equal). I.e. Taking the circle shown in Figure 1 and concentrating on the upper right quadrant, I am after expressions for the individual areas (top and bottom) and their respective centroids x1, y1 and x2, y2 (Figure 2) when cut at "c".
Figure 1:
Figure 2:
2. Relevant equations
Area of circle = ∏r[itex]^{2}[/itex]
Equation of quarter circle: y(x) = √(x[itex]^{2}[/itex]-r[itex]^{2}[/itex])
3. The attempt at a solution
Apart from stating the obvious equations (above) I’m stuck on this problem.
I have searched my textbooks/google (using general key words) for expressions of this particular case with no luck.
I have never been strong with deriving expressions from first principals and would appreciate any ideas/push in the right direction. This is a problem directed at self-study, not homework.
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