a
Given : \(\theta \left( t \right) = 2{t^3} - 6{t^2}\)

\(\therefore \,\frac{{d\theta }}{{dt}} = 6{t^2} - 12t \Rightarrow \frac{{{d^2}\theta }}{{d{t^2}}} = 12t - 12\)

Angular acceleration, \(\alpha  = \frac{{{d^2}\theta }}{{d{t^2}}} = 12t - 12\)

When angular acceleration \((\alpha )\) is zero, then the torque on the wheel becomes zero \(\left( {\,\tau  = I\alpha } \right)\)

\( \Rightarrow \,12t - 12 = 0\,\,or\,t = 1\,s\)