Question

What is moment of inertia exactly in rotational dynamics?

Answer 1

The moment of inertia describes a body, and it always involves a specified axis of rotation! I mean, all the points of an object will rotate around this axis and will each trace a circular path relative to the axis. I mean, really simple. Like, put a stick through an object (like an apple) and spin the stick. That sort of axis of rotation.

So, the moment of inertia can't describe an object, but it can describe an object given an axis of rotation.

\(\huge\rm\color{orange}{What}\) does it describe, you might ask.
Well, You know about inertia from Newton's first law, probably. And you know about Newton's second law, \(F=ma\). So, that's for linear motion. But we can notice a similar thing in rotation.
Spin a bike wheel, and you can see that the wheel will keep its rotational motion unless acted on by an outside force (given that the wheel stays in one piece, you know..).
And think about a motor. A greater torque on it will give it a greater angular acceleration. In fact, the torque is linearly proportional to the angular acceleration. Just like force is linearly proportional to linear acceleration.

Now, rotation has a sort of inertia! For linear motion, we have mass. For rotational motion, we have the moment of inertia.

Thus, it is used to discover the behavior of objects rotating about axes!

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mi