we shall consider rotation about a fixed axis only. Let us try to get an expression for the kinetic energy of a rotating body . We know that for a body rotating about a fixed axis, each particle of the body moves in a circle with linear velocity given by Eq. ( .
For a particle at a distance from the axis, the linear velocity is i r υ . The kinetic energy of motion of this particle is i i m r υ where m i is the mass of the particle. The total kinetic energy K of the body is then given by the sum of the kinetic energies of individual particles, i i K m r ω Here n is the number of particles in the body. Note ω is the same for all particles.
Hence, taking ω out of the sum, i i K m r We define a new parameter characterising the rigid body, called the moment of inertia I , given by i i m r