Define moment of inertia in terms of kinetic energy of rotation.

Asked by Topperlearning User | 11th Aug, 2014, 02:44: PM

Expert Answer:

Let us find out an expression for the kinetic energy of a rotating body-

Consider a rigid body rotating in XY plane about Z-axis, with uniform angular velocity ω.

Let the body consist of particles of masses m1,m2,m3,..... mn at perpendicular distances r1,r2,r3,.......rn from the axis of rotation.As the body is rigid , all particles complete one revolution in same time. i.e ω is the same for all particles.

 
 
The K.E. of the ith particle due to rotation=
                                                                
The K.E. of the body =
or (K.E.)rot =
or (K.E.)rot =
If we put =1, in equation (1), then
 
  
Hence moment of inertia of a body is equal to twice the K.E. of rotation of body rotating with unit angular speed.

Answered by  | 11th Aug, 2014, 04:44: PM