question_answer

The rotational K.E. of a body is given by \[\frac{1}{2}I{{\omega }^{2}}\]. Use this equation to obtain the dimensions of I.

Answer:

                K.E. of rotation = \[\frac{1}{2}I{{\omega }^{2}}\]                               \[\therefore \] \[I=\frac{2\times K.E.\,of\,rotation}{{{\omega }^{2}}}=\frac{\left[ M{{L}^{2}}{{T}^{-2}} \right]}{\left[ {{T}^{-2}} \right]}=\left[ {{M}^{1}}{{L}^{2}}{{T}^{0}} \right]\]