Rotational Kinetic Energy

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
rotating^{B.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

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