Reference book: Engineering Dynamics by j.l meriam- eigth edition
Chapter 6, Problem 114.
General Plane Motion:
The rigid body executes plane motion where, at the instant considered, the velocity of its mass centre G is v and its angular velocity is w. The velocity vi of a representative particle of mass mi may be expressed in terms of the mass-centre velocity v and the velocity pw relative to the mass centre.
With the aid of the law of cosines, we write the kinetic energy of the
body as the sum Ti of the kinetic energies of all its particles. Thus,
The kinetic energy of the body is then T =1/2mv^2+1/2Iw^2
where I is the moment of inertia of the body about its mass centre. This
expression for kinetic energy clearly shows the separate contributions
to the total kinetic energy resulting from the translational velocity v of
the mass centre and the rotational velocity w about the mass centre.
