Define moment of inertia and hence Obtain an expression for rotational kinetic energy.

Explanation

Moment of inertia may be defined as the product of mass of the whole body and the square of the radius of gyration.

(i) The moment of inertia is the algebric sum of products of the mass of particles and square of their perpendicular distances from the axis of rotation.
`I=sum_(i=1)^n=m_ir_1^2=MK^2`
Where `m_1,m_2,m_3...m_n` are mass of particles at perpendicular distances `r_1,r_2,r_3,.......r_n` respectively from the axis of rotation.
`:.` Rotational K.E of the body=Sum of linear K.E of all the particles of the rotating system.
`:.` Rotational K.E of the body `=sum_(i=1)^n1/2m_iv_i^2omega^2` where `v=romega`
`:.` Rotational K.E of the body `=(omega^2)/(i=1)sum_(i=1)^nm_ir_i^2omega^2` where `I=sum_(i=1)^nm_ir_i^2`