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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

*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