The best way to understand Inertia is by comparing it to mass. What mass is in a linear system, Inertia plays the same role in a rotational system.
When dealing with rotational systems it is very important to move over the understanding of a linear system as it gets difficult to understand concepts of rotational motion. Moment of Inertia or Inertia is the property of a body that is dependent upon the mass of that body, its dimensions.
Unlike mass which is constant irrespective of the shape of the body (assuming differently shaped bodies have the same mass), the moment of inertia changes when you change the axis about which you’re rotating the body. Even if you keep the mass the same but change the shape of the body, moment of inertia changes.
Let’s take the example of a table fan.
Assuming all the energy generated by the rotation of the blades gets converted into kinetic energy of the wind generated by the fan. Now consider two types of blades in the fan.
Both have the same mass but different shapes. One blade is such that most of its mass is focused on the central axis and the other is such that most of the mass is focused on the outer radius. Both these blades have the same radius.
Which fan according to you would provide better air?
Use the relation, Energy = 0.5*I*ω2
Even though both blades are quite similar, the energy provided by the blade with mass towards the outer radius will be more.
Moment of inertia plays an important role in the design of the flywheel in vehicles. To put it simply, the engine does not provide constant power at all instances. Then why doesn’t your vehicle experience jerks while functioning?
This is due to the huge moment of inertia of the flywheel. After flywheel attains enough velocity. The varied power provided by the engine in a cycle affects the velocity of the flywheel insignificantly.