Rotational Kinetic Energy
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The rotational kinetic energy of a rigid assembly of masses (or
mass distribution) is the sum of the rotational kinetic energies of
the component masses. Therefore, consider a point-mass
rotatingB.13 in a circular orbit
of radius
and angular velocity
(radians per second), as
shown in Fig.B.4. To make it a closed system, we can
imagine an effectively infinite mass at the origin
. Then the
speed of the mass along the circle is
, and its kinetic
energy is
. Since this is what we want
for the rotational kinetic energy of the system, it is
convenient to define it in terms of angular velocity
in
radians per second. Thus, we write
where
is called the mass moment of inertia.
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Mass Moment of Inertia
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Translational Kinetic Energy