Centre of Mass for Laminas and Solids (AQA A-Level Further Maths): Flashcards

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Centre of Mass for Laminas and Solids
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Symbol for centre of mass

GG

Centre of mass of uniform rectangular lamina

Intersection of diagonals

Triangle centroid position from vertex along median

23\frac{2}{3} of distance from vertex

Circular arc centre of mass formula

OG=rsinααOG = \frac{r\sin\alpha}{\alpha}

Sector centre of mass formula

OG=2rsinα3αOG = \frac{2r\sin\alpha}{3\alpha}

Units for α\alpha in arc/sector formulas

Radians

Moment equation to find xˉ\bar{x}

Total mass ×xˉ=\times \bar{x} = \sum(mass ×\times x-coord)

Solid cone centre of mass from base (hh = height)

14h\frac{1}{4}h

Solid hemisphere centre of mass from centre (rr = radius)

3r8\frac{3r}{8}

Hemispherical shell centre of mass from centre

r2\frac{r}{2}

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