Answer:
We know that power in rotational motion, \[P=\tau
\omega \] ?.. (i)
And K.E. of rotation, \[E=\frac{1}{2}I{{\omega
}^{2}}\]
As power = time rate of doing
work in rotational motion, and work is stored in the body in the form of K.E.
\[\therefore \] \[P=\frac{d}{dt}\left( K.E.\,of\,rotaion
\right)\]
\[=\frac{d}{dt}\left( \frac{1}{2}I{{\omega }^{2}}
\right)=\frac{1}{2}I\times 2\omega \left( \frac{d\omega }{dt} \right)\]
\[P=I\omega \alpha \]
Using (i), \[P=\tau \omega
=\,I\omega \,\alpha \] or \[\tau =\,I\,\alpha \], which is the required relation.
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