Consider a rigid body rotating about a fixed axis with angular velocity w. The body can be supposed to be made up of a large number of particles m1, m2, ..., mn at distances r1, r2, ..., rn respectively, from the axis of rotation. Each particle has a kinetic energy. The kinetic energy of the body will be the sum of the kinetic energies of all the particles. If u1, u 2, ..., un be the linear speeds of the particles, respectively, then the kinetic energy of the body can be written as
where I is the moment of inertia of the body. From this expression it is clear that moment of inertia is the rotational analogue of mass.
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