Center of Mass of Uniform Circular Arc

Theorem

Let $\WW$ be a wire of uniform density.

Let $\WW$ be bent into the shape of the arc of a circle $\CC$ of radius $r$ subtending an angle of $2 \alpha$ from the center of $\CC$.

Then the center of mass of $\PP$ is the point $\dfrac {r \sin \alpha} \alpha$ from the center of $\CC$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Appendix: Table $4$ Centres of mass The position of the centre of mass of certain uniform bodies.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $4$ Centres of mass The position of the centre of mass of certain uniform bodies.