### 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