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# 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: $$\frac{a}{2}$$