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# 2.21: Tetrahedra

Exercise $$\PageIndex{1}$$

Show that the moment of inertia about an axis through the centre of mass of a uniform solid regular tetrahedron of mass $$m$$ and edge length $$a$$ is $$\frac{1}{20} ma^2$$

Exercise $$\PageIndex{2}$$

Show that the moment of inertia of a methane molecule about an axis through the carbon atom is $$\frac{8}{3} ml^2$$ , where $$l$$ is the bond length and $$m$$ is the mass of a hydrogen atom.

And, in case you are wondering that I haven’t specified the orientation of the axis in either case, the solid regular tetrahedron and the methane molecule are both spherical tops, and the moment of inertia is the same about any axis through the centre of mass.