## DAVID G. SIMPSON Nanopedia

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### LEES' RULE

Lees' rule is a formula for computing the moment of inertia of a symmetrical solid. It is really a kind of mnemonic device for helping to recall several moment of inertia formulae. Lees' rule states that the moment of inertia I of a body of mass M about an axis is given by where a and b are the lengths of the semi-axes perpendicular to the rotation axis, and n and n' are the "numbers of principal curvature" that terminate semi-axes a and b, respectively (n, n' = 0 for a flat surface, 1 for a cylindrical surface, or 2 for a spherical surface).

#### Example

For example, suppose we want to find the the moment of inertia of a rectangular plate of dimensions ℓ × w, about an axis through the center of the plate and perpendicular to the plane of the plate. Then a = ℓ/2, b = w/2, and n = n' = 0 because the surfaces are flat. Then Lees' rule gives #### References

 H.J. Gray and A. Isaacs (eds.). A New Dictionary of Physics. Longman, London, 1975.

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