From work - energy theorem

$W = \Delta k$ (change in Kinetic Energy)

In rotation, $$KE = {1 \over 2}I{\omega ^2}$$

$$484 = {1 \over 2}I(\omega _f^2 - \omega _i^2)$$

$$ \Rightarrow 484 = {1 \over 2}I\left[ {{{\left( {2\pi {{360} \over {60}}} \right)}^2} - {{\left( {2\pi \times {{60} \over {60}}} \right)}^2}} \right]$$

$$ \Rightarrow 484 = {1 \over 2}I4{\pi ^2}(36 - 1)$$

$$ \Rightarrow I \simeq 0.7$$ kg-m²