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Explainer Video

Tutor: Labib

Summary

​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 3m3m3m, a width of 1m1m1m and a weight of 20N20N20N, is held up by two strings. The sign is modelled as a lamina, suspended at points AAA and BBB. If the string at point AAA snaps, how much force must be applied at point CCC to keep the sign in equilibrium?


Maths; Moments; KS5 Year 13; Laminas

​

If the string snaps at point AAA, the point BBB becomes a pivot. At this point, the moment of the weight of the sign becomes an anticlockwise moment. The force at point CCC is a clockwise moment.

Therefore, since AB2=0.5\frac{AB}{2}=0.52AB​=0.5 and BC=3BC=3BC=3​:


0.5×20=FC×310=3FC103=FC=3.33\begin{aligned}0.5\times 20&=F_C\times 3\\10&=3F_C\\\dfrac{10}{3}&=F_C = 3.33\end{aligned}0.5×2010310​​=FC​×3=3FC​=FC​=3.33​​​


The force at point CCC must be 3.33N‾\underline{3.33N}3.33N​ to keep the sign in equilibrium.



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FAQs - Frequently Asked Questions

Where is the centre of mass of a uniform lamina?

The centre of mass of a uniform lamina can be found at the point where the lines of symmetry meet.

How do you resolve moments with a lamina?

To resolve moments using laminae, you must find the centre of mass.

What is a lamina?

A lamina is a flat 2D object with negligible thickness.

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