### Stretch Rule

Note that the moment of inertia does not change when masses are moved along a vector parallel to the axis of rotation (see,*e.g.*, Eq.(B.9)). Thus, any rigid body may be ``stretched'' or ``squeezed'' parallel to the rotation axis without changing its moment of inertia. This is known as the

*stretch rule*, and it can be used to simplify geometry when finding the moment of inertia.

For example, we saw in §B.4.4 that the moment of inertia of a point-mass a distance from the axis of rotation is given by . By the stretch rule, the same applies to an ideal

*rod*of mass parallel to and distance from the axis of rotation. Note that mass can be also be ``stretched'' along the circle of rotation without changing the moment of inertia for the mass about that axis. Thus, the point mass can be stretched out to form a mass

*ring*at radius about the axis of rotation without changing its moment of inertia about that axis. Similarly, the ideal rod of the previous paragraph can be stretched tangentially to form a

*cylinder*of radius and mass , with its axis of symmetry coincident with the axis of rotation. In all of these examples, the moment of inertia is about the axis of rotation.

**Next Section:**

Area Moment of Inertia

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Parallel Axis Theorem