Find centre of mass of a lamina.

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SUMMARY

The discussion focuses on calculating the center of mass (c.o.m) of a lamina formed by a rectangular card ABCD measuring 10 cm by 12 cm, with a circle of radius 3 cm cut out. The center of the circle is positioned 7 cm from side AB and 4 cm from side AD. To determine the c.o.m, participants suggest using integration or the principle of moments, and inquire about the implications of placing the circle on top of the rectangle instead of cutting it out.

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  • Basic principles of moments in mechanics
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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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