EXAMPLE 1: MASS MOMENT OF INERTIA
Calculate the mass moment of inertia of the cone about the z-axis. Assume the cone is made of a uniform material of density (mass per unit volume).
The mass moment of inertia about the z-axis is given by
The element of volume in a cylindrical coordinate system is given by
Therefore, the mass moment of inertia about the z-axis can be written as
For a uniform cone the density can be calculated using the total mass and total volume of the cone so that
Therefore, the moment of inertia in terms of the total mass of the cone can be written as