Find centre of mass of a lamina.

AI Thread Summary
To find the center of mass of a lamina with a rectangular shape and a circular cutout, one can use the principle of moments or integration. The rectangle measures 10 cm by 12 cm, with a circle of radius 3 cm removed, positioned 7 cm from one edge and 4 cm from another. The center of mass can be determined by calculating the centroid of the rectangle and subtracting the area of the circle's centroid, adjusted for its position. If the circle were added on top of the rectangle instead of being cut out, the approach would involve recalculating the combined center of mass considering both shapes. Understanding these principles allows for accurate determination of the lamina's center of mass.
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A lamina comprises a uniform rectangular card ABCD where AB = 10 cm and BC = 12 cm
with a circle of radius 3 cm cut out. The centre of the circle is 7 cm from AB and 4 cm from AD.

How would I find the centre of mass for this lamina? I know to find the centre of mass for a uniform lamina we can integrate or simple find the centre of the shape's diagonals. Also, how would I find it if the circle was added on top instead? I'm sorry I don't have much of an idea how to do these.
 
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You can use the principle of moments to calculate the c.o.m. of the lamina.
 

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