Mass Moment of Inertia

 

 

Example:   Calculate the mass moment of inertia, IAz,K , of the rectangular plate with

dimensions ( b  by  h)   about point  A  shown in the figure below .  Let the mass

density,  ρ  =  1  slugs/area.  Point  A  has the coordinates  (a, a).

 

 

                   

                                    

 

 

Procedure:

                        

 

1.

 

Calculate the element of mass,  dm.     dm  =  ρ dx dy  =  dx dy

Note:  The element of mass is at an arbitrary location  (x,y).

 

 

2.

 

Calculate  r2  dm .  Here  r2  =   [ (x ˗ a)2  +  (y ˗ a)2 ] dx dy

 

 

3.

 

Set up integral.     IAz,K   =    ∫    ∫     [ (x ˗ a)2  +  (y ˗ a)2 ] dx dy

 

 

4.

 

Determine limits of integration. 

In this case:   a  ≤  x  (a + b)   and  a  ≤  y ≤  (a + h)

 

 

 

 

5. 

 

Evaluate the integral.

                                        y = a+h    x = a + b

                          IAz,K   =     ∫              ∫      [ (x ˗ a)2  +  (y ˗ a)2 ] dx dy

                                        y=a          x=a

 

 

Click here to continue with this example.

 

 

                            



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