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Inertia Tensor of a Rigid Body

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A rigid body consists of six particles, each of mass m, fixed tot he ends of three light rods of length 2a, 2b, and 2c, respectively, the rods being held mutually perpendicular to one another at their midpoints.

a) Show that a set of coordinate axes defined by the rods are principal axes, and write down the inertia tensor for the system at these axes.

b) Use matrix algebra to find the angular momentum and kinetic energy of the system when it is rotating with angular velocity ¦Ø about an axis passing through the origin and the point (a,b,c).

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Solution Summary

The solution examines the inertia tensor of a rigid body. Matrix algebra is used to find the angular momentum and kinetic energy.

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