Composite Laminas - Rectangles

Introduction to Laminas

A lamina is a plane figure (two-dimensional shape) with mass but with negligible thickness, made of solid, uniform material.
Composite laminas are figures made up of simpler shapes like triangles, rectangles, circles etc., we are focusing on composite rectangles in this section.
It is important to find the centre of mass in laminas, which we learned about in the previous section.

For a single, regular (uniform distribution of mass) rectangle, the centre of mass is simply at the intersection of the diagonals- the geometric centre.
The position of this centre of mass does not change regardless of the mass or the size of the rectangle, as long as the rectangle remains uniform and flat.

For composite laminas made up of rectangles, the response is somewhat different and needs calculations.
To find the centre of mass of a composite rectangular lamina, perform the following steps:

1. Find the centre of mass for each individual rectangle separately. It is simply the geometric centre.

2. Find the moment of each rectangle about a chosen axis by multiplying the mass of the rectangle by the distance of the centre of mass from the axis.

3. Sum all the moments to get the total moment of the lamina about the axis.

4. Sum all the masses to get the total mass of the lamina.

5. Divide the total moment by the total mass to find the location of the centre of mass of the composite lamina.

Knowing the centre of mass of a composite rectangular lamina is important in engineering and design, where balance and weight distribution are critical for structural stability and functionality.