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.
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Area Moment of Inertia
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Parallel Axis Theorem
