DAVID G. SIMPSON
Nanopedia
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ROUTH'S RULE
Routh's rule is a mnemonic formula for finding the moment of inertia of a symmetrical solid. The rule works for a circular or elliptical cylinder rotated about the cylinder axis, or for a circular or elliptical disk about any of the axes of symmetry.
Routh's rule states that the moment of inertia I of a body of mass M about an axis is
given by [1]
where the denominator is 3 for a rectangular body, 4 for a elliptical body,
or 5 for an ellipsoidal body.
Example
For example, consider the moment of inertia of a solid uniform right circular cylinder of radius R rotated about the axis of the cylinder. Then the numerator in Routh's rule is R2 + R2 = 2R2, while the denominator is 4 (a circle is a special case of ellipse), so
See Also
References
[1] H.J. Gray and A. Isaacs (eds.). A New Dictionary of Physics. Longman, London, 1975.
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