Stretch rule

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In classical mechanics, the stretch rule (sometimes referred to as Routh's rule) states that the moment of inertia of a rigid object is unchanged when the object is stretched parallel to an axis of rotation that is a principal axis, provided that the distribution of mass remains unchanged except in the direction parallel to the axis.^[1] This operation leaves cylinders oriented parallel to the axis unchanged in radius.

This rule can be applied with the parallel axis theorem and the perpendicular axis theorem to find moments of inertia for a variety of shapes.