MOMENT OF INERTIA OF A RECTANGLE 231 



Then I oz = I ox + I OY 



12 12 



12 



Let PN be an axis drawn parallel to OZ at a distance z l from it. 



Then 



+ 



/a 2 o 2 



Putting z, = A/ + , this becomes the moment of inertia about 

 4 4 



an axis BQ which is perpendicular to the plane of the figure and 

 passes through a corner. 



If E and F are the mid points of the sides AB and AD respec- 

 tively, and ER and FS are axes drawn perpendicular to the plane 

 of the figure through these points : 



Putting Zl - -, 



a? 6 2 b^ 

 - + - + - j 



a ,fa z b z a 2 



Putting 2l = -, I FS = ab[- + - + T 



125. Example 1. Draw the momental ellipse for a rectangle 

 2" x 5" and use it to find the moments of inertia about axes 

 which pass through the centroid and make angles of 30, 45, 

 and 60 respectively, with the smaller side of the rectangle. 



Then 



and 



Q 



ix2 



20-83 

 1 



= 3-333 



