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# Presentation3

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### Presentation3

1. 1. Kinetic Energy of Rotation: <ul><li>Consider a rigid body rotating about a fixed vertical axis. Since a body is treated as a collection of particles, a particle of mass m at a distance r from the axis of rotation, moves in a circle of radius r with an angular speed about this axis and has a tangential linear speed . </li></ul>
2. 3. <ul><li>The kinetic energy of the particle is </li></ul><ul><li>Since is same for all particles so </li></ul><ul><li>Total kinetic energy of the rotating body can be written as </li></ul>______________(1)
3. 4. <ul><li>The quantity is called Rotational Inertia of the body with respect to the particular axis of rotation and is denoted by the symbol I. That is </li></ul>_____________(2)
4. 5. <ul><li>It follows that rotational inertia of a body depends on its mass as well as distribution of mass with respect to the axis of rotation. It has the dimension as </li></ul><ul><li>[mr 2 ] = ML 2 </li></ul><ul><li>And is expressed in Kg-m 2 . Combining eq (1) and (2) we get </li></ul>________________(3)
5. 6. <ul><li>As the kinetic energy of the rotating rigid body and is analogous to the expression </li></ul>For the translational kinetic energy of a body. We see that and (translational inertia). Angular speed must be expressed in radian measure.