Circular logic.

Classical Mechanics Level pending

A particle is exhibiting circular motion from an initial angular velocity \( { \omega '}\) at \({ T }=0\) .

Its radius of curvature is r . It is also know that the tangential acceleration of this particle is:

\({ a }_{ T }=\ T\times \sqrt { { a }_{ N } } \times \sqrt { r } \)

Find the correct relation for the time dependence of the angular velocity ( \(\omega \) ) at the instant T(\(\neq 0\))

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