**EXAMPLE 2: ****MASS MOMENT OF INERTIA**

Calculate the mass
moment of inertia of the triangular plate about the *y*-axis. Assume the plate is made of a uniform material and has a
mass of *m*.

**Solution:**

The
mass moment of inertia about the *y*-axis
is given by

_{}

The
element of area in rectangular coordinate system is given by

_{}

The
domain of the triangle is defined by

_{}

_{}

The
distance from the *y*-axis is *x. *Therefore, *r=x*. The mass moment of inertia about the *y*-axis can be written as

_{}

For
a uniform plate the density can be calculated using the total mass and total
area of the plate so that

_{}

Therefore,
the moment of inertia in terms of the total mass of the cone can be written as

_{}