Further Topics with Centres of Mass (AQA A-Level Further Maths): Flashcards

Thin, flat plate with uniform density

$\rho$

$(x, \frac{1}{2}y)$

$\frac{\int_a^b xy \, dx}{\int_a^b y \, dx}$

$\frac{\int_a^b \frac{1}{2}y^2 \, dx}{\int_a^b y \, dx}$

$\frac{\int_a^b xy^2 \, dx}{\int_a^b y^2 \, dx}$

$0$ by symmetry

$\delta m = \rho \pi y^2 \delta x$

Vertically below point of suspension

$\frac{4a}{3\pi}$