Moment of Inertia from First Principle

A. Moment of Inertia of a Rectangle

Consider an elemental strip of width dy at distance of y from a centroidal axis of a rectangle as shown in Figure 11.17.

Figure 11.17 Moment of Inertia of a Rectangle about Centroidal Axis

Moment of inertia of the strip is given by,

 

I_XX = y² dA = y²bdy

 

Now, moment of inertia of entire rectangle can be given by

B. Moment of Inertia of a Triangle

Consider an elemental strip of width dy at a distance of y from the base of a triangle as shown in Figure 11.18. Moment of inertia of the strip about its base is given by,

Figure 11.18 Moment of Inertia of a Triangle about Its Base

Now, moment of inertia of entire triangle about its base