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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

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}

**Next Section:**

Torque

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Principal Axes of Rotation