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

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Centre of Mass for Laminas and Solids
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What symbol is used to represent the centre of mass?

GG

Where is the centre of mass of a uniform rectangular lamina located?

At intersection of diagonals

For a triangular lamina, what fraction along the median from vertex is the centre of mass?

23\frac{2}{3}

For a circular arc with radius rr and angle 2α2\alpha, what is OGOG?

rsinαα\frac{r\sin\alpha}{\alpha}

For a sector with radius rr and angle 2α2\alpha, what is OGOG?

2rsinα3α\frac{2r\sin\alpha}{3\alpha}

In what units must angles be for circular arc and sector formulas?

Radians

What equation finds xˉ\bar{x} for composite shapes using moments?

Total mass × xˉ\bar{x} = sum of parts

Where is the centre of mass of a uniform solid cone from its base?

14h\frac{1}{4}h

Where is the centre of mass of a hemispherical shell from the centre?

r2\frac{r}{2}

A solid hemisphere has centre of mass at what distance from its centre?

3r8\frac{3r}{8}

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