MOMENT OF INERTIA OF A RECTANGLE 229 



If the principal moments of inertia are equal, then P = Q, and 



quently p ^ q. The momental ellipse becomes a circle of 



nidi us p, and therefore the moment of inertia about any axis 



drawn through the centroid in the plane of the figure is constant. 



124. The Rectangle. Let OX and OY be two axes drawn 

 parallel to the sides and passing through the centroid. These 

 are axes of symmetry, and are consequently principal axes of 

 inertia. 



Consider an elementary strip of breadth $y drawn parallel to 

 the axis OX and at a distance y from it. 



FIG. 60. 



The moment of inertia of this strip about OX = ay z $y where 

 a is the breadth of the rectangle. 



Moment of inertia of rectangle about OX = 

 Then I ox = a F b if dy 



J-2 



_ 

 8 4 



12 



By dividing the rectangle into strips of breadth &r, drawn parallel 



ba 3 

 to the axis OY, it can be shown in a similar manner that I OY = 



M,m 



