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

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Centre of Mass for Point Masses and Laminas
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What is the centre of mass of a system of point masses?

The weighted average position of masses

How do heavier masses influence the centre of mass location?

They pull it more strongly toward them

What is the formula for centre of mass in one dimension?

xˉ=miximi\bar{x} = \frac{\sum m_i x_i}{\sum m_i}

Which axis do you take moments about to find xˉ\bar{x} in 2D?

The y-axis

Three masses: 2 kg at x=1x=1, 3 kg at x=4x=4, 5 kg at x=7x=7. Find xˉ\bar{x}.

xˉ=5.1\bar{x} = 5.1

What happens to gg when finding centre of mass using moments?

It cancels from both sides

For a suspended body in equilibrium, what must be true?

Centre of mass directly below suspension

What happens if tension and weight are not vertically aligned?

They create a couple causing rotation

For a suspended framework, if xˉ=1.73\bar{x}=1.73 m and yˉ=1.31\bar{y}=1.31 m, find angle with vertical.

37.1°37.1°

What is the first step in the problem-solving strategy for centre of mass?

Draw a diagram with all information

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