What is the significance of the moment of inertia in the context of rotational motion and how are its derivations calculated?

The moment of inertia is important in rotational motion because it measures an object's resistance to changes in its rotation. It is calculated by summing the mass of each particle in the object multiplied by the square of its distance from the axis of rotation. The moment of inertia helps determine how fast an object will rotate when a torque is applied to it.