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.
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