A-Level Maths M2 Notes

Centres of mass (CoM) calculations

… Area is the equivalent of mass as the shapes are usually uniform laminae.

… Finding the centre of mass of a rectangular lamina with a triangular cut out, by subtracting the moment of a small triangle from the rectangle:
Moment of compound lamina = moment of rectangle – moment of triangle cut out.
Or more generally:
Moment of actual lamina = moment of the ‘uncut out’ shape – moment of ‘cut out’ shape

… The central of mass of a triangle is located 2/3 of its height from its vertex (or 1/3 of the height from the base)

… Where possible, use symmetry to find centres of mass.

… It’s useful to define x-y axes on the lamina (preferably with the lamina in the positive quadrants)

… To find the ‘angle of dangle’, i.e. the angle made by the object hanging from a pivot and the vertical, draw a straight line from the pivot through the CoM of the object. Then use the known geometry of the CoM to calculate the angle require using trigonometry.