**Subject :**Elements of Mechanical Engineering

## 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 *m _{i}* 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 *I _{0}* 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,