Hi,

The moment-of-inertia tensor has this transformation law, which explains why it is called a tensor of rank 2 rather than simply a matrix. A matrix is just a square array of numbers with no particular transformation law under coordinate transformations.

The moment of inertia of a bit of mass is the product of the mass and the square of the distance of the mass from the spin axis. The moment of inertia of a body with respect to a particular spin axis is the sum of all of all the moments of its bits of mass.

Thank You.