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Physics LibreTexts

1.S: Centers of Mass (Summary)

SUMMARY

Triangular lamina: 2/3 of way from vertex to midpoint of opposite side

Solid Tetrahedron, Pyramid, Cone: 3/4 of way from vertex to centroid of opposite face.

Hollow cone: 2/3 of way from vertex to midpoint of base.

Semicircular lamina: \(\frac{4a}{3\pi}\)

Lamina in form of a sector of a circle, angle \(2\alpha\) : \( \frac{(2a \sin\alpha)}{(3\alpha)}\) 

Semicircular wire: \( \frac{2a}{\pi}\) 

Wire in form of an arc of a circle, angle \( 2\alpha\) : \( \frac{(a \sin \alpha)}{\alpha}\) 

Solid hemisphere: \( \frac{3a}{8}\)

Hollow hemisphere: \( \frac{a}{2}\)

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