# 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: \( \frac{a}{2}\)