​Laminas

​​In a nutshell

A lamina is a flat object with negligible thickness. The mass of a lamina is spread evenly over the whole surface.

Moments in laminae

For a uniform lamina in a regular shape, the centre of mass can be found at the point where the lines of symmetry meet; in other words, its middle. For a rectangular lamina, the centre of mass can also be found where the diagonals meet. When considering the distance from the centre of mass to the pivot, use distances that are perpendicular to the direction of the weight.

Example 1

A sign, with a height of $$3m$$, a width of $$1m$$ and a weight of $$20N$$, is held up by two strings. The sign is modelled as a lamina, suspended at points $$A$$ and $$B$$. If the string at point $$A$$ snaps, how much force must be applied at point $$C$$ to keep the sign in equilibrium?

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If the string snaps at point $$A$$, the point $$B$$ becomes a pivot. At this point, the moment of the weight of the sign becomes an anticlockwise moment. The force at point $$C$$ is a clockwise moment.

Therefore, since $$\frac{AB}{2}=0.5$$ and $$BC=3$$​:

$$\begin{aligned}0.5\times 20&=F_C\times 3\\10&=3F_C\\\dfrac{10}{3}&=F_C = 3.33\end{aligned}$$​​

The force at point $$C$$ must be $$\underline{3.33N}$$ to keep the sign in equilibrium.