**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).

**Solution:**

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

_{}