The mass moment of inertia
(or simply moment of
inertia), plays the role of mass in rotational dynamics, as
we saw in
Eq.(B.7) above.
The mass moment of inertia of a rigid body, relative to a given axis of rotation, is given by a weighted sum over its mass, with each mass-point weighted by the square of its distance from the rotation axis. Compare this with the center of mass (§B.4.1) in which each mass-point is weighted by its vector location in space (and divided by the total mass).
Equation (B.8) above gives the moment of inertia for a single point-mass
rotating a distance
from the axis to be
. Therefore,
for a rigid collection of point-masses
,
,B.14 the
moment of inertia about a given axis of rotation is obtained by adding
the component moments of inertia:
For a continuous mass distribution, the moment of inertia is given by integrating the contribution of each differential mass element:
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(B.10) |
where