Work and Energy for Rigid Bodies
Work and Energy for Rigid Bodies: Kinetic Energy: Kinetic energy of rigid body is the sum of kinetic energies of all the particles comprising the rigid body.
We consider three cases of motion:
(i) Translation: The translating rigid body has a mass m and all of its particles have a common velocity V. The kinetic energy of any particle of mass mi of the body is ,
So for for the entire body,
This is true for both rectilinear and curvilinear translation.
Thus, for the entire body,
where I0 is the mass moment of inertial of the body about the fixed point O.
(iii) General Plane Motion:
Let the velocity of mass center G is and its angular velocity is .
The third term is
Since, (As G itself is the mass center.)
The kinetic energy of the body is then,