Rotational Kinetic Energy Revisited
If a point-mass is located at
and is rotating about an
axis-of-rotation
with angular velocity
, then the
distance from the rotation axis to the mass is
,
or, in terms of the vector cross product,
. The tangential velocity of the mass is
then
, so that the kinetic energy can be expressed as
(cf. Eq.
(B.23))
where

In a collection of masses
having velocities
, we of
course sum the individual kinetic energies to get the total kinetic
energy.
Finally, we may also write the rotational kinetic energy as half the inner product of the angular-velocity vector and the angular-momentum vector:B.27





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Torque
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Principal Axes of Rotation