A fan with blades takes longer time to come to rest than without the blades. Why?

We have,
Iω = constant
The moment of inertia of the fan with blade is more than the fan without blade. Since, Iω = constant, the angular velocity of the fan without blade is more than the fan with blade. As we know, time period is inversely proportional to the angular velocity, so the fan with blades has more time period than the fan without blade. Therefore, a fan with blades takes longer time to come to rest than without blades.