The moment of inertia is a measure of an object's resistance to changes in rotational motion. It is the rotational analog of mass in linear motion.
The moment of inertia is calculated by integrating the product of the mass and the square of the distance from the axis of rotation. This integral is typically denoted as I = ∫ r^2 dm.
The moment of inertia is important in understanding rotational motion and the distribution of mass in objects. It is used to calculate an object's angular momentum, angular velocity, and torque.
While mass represents an object's resistance to changes in linear motion, moment of inertia represents its resistance to changes in rotational motion. Mass is a scalar quantity while moment of inertia is a tensor quantity.
The moment of inertia increases as the mass is distributed further away from the axis of rotation. This is why objects with most of their mass concentrated closer to the axis of rotation have a smaller moment of inertia than objects with the same mass but distributed further away.