### 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

*mass moment of inertia*.

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Mass Moment of Inertia

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Translational Kinetic Energy