Obtain the expression for the moment of inertia and define it. What are the factors on which the moment of inertia depends? Write its unit and dimensional formula.

(N/A) When a body is rotating about a fixed axis,each particle $i$ of the body moves in a circle with linear velocity $v_{i} = r_{i} \omega$,where $i = 1, 2, \ldots, n$.
The kinetic energy of motion of this particle is $K_{i} = \frac{1}{2} m_{i} v_{i}^{2} = \frac{1}{2} m_{i} r_{i}^{2} \omega^{2}$.
The total kinetic energy $K$ of the rotating body is the sum of the kinetic energies of all its particles:
$K = \sum K_{i} = \sum \frac{1}{2} m_{i} r_{i}^{2} \omega^{2} = \frac{1}{2} \omega^{2} \sum m_{i} r_{i}^{2}$.
Comparing this with the expression for translational kinetic energy $K = \frac{1}{2} M v^{2}$,we define the moment of inertia $I$ as $I = \sum_{i=1}^{n} m_{i} r_{i}^{2}$.
Definition: The moment of inertia of a rigid body about a given axis is defined as the sum of the products of the masses of the individual particles and the square of their respective perpendicular distances from the axis of rotation.
Factors affecting moment of inertia: It depends on the mass of the body,the shape and size of the body,the distribution of mass about the axis of rotation,and the position and orientation of the axis of rotation.
Unit: The $SI$ unit of moment of inertia is $\text{kg} \cdot \text{m}^{2}$.
Dimensional formula: The dimensional formula is $[M^{1} L^{2} T^{0}]$.