Mass Moment of Inertia

Example: Calculate the mass moment of inertia, I^A_z,_K , of the rectangular plate with

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

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

Procedure:

Calculate the element of mass, dm. dm = ρ dx dy = (x/a) dx dy

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

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

Set up integral. I^A_z,_K = ∫ ∫ (x/a) [ (x ˗ a)² + (y ˗ a)² ] dx dy

Determine limits of integration.

In this case: a ≤ x ≤ 2a and a ≤ y ≤ (a + h)

Evaluate the integral.

y = a+h x = 2a

I^A_z,_K = ∫ ∫ (x/a) [ (x ˗ a)² + (y ˗ a)² ] dx dy

y=a x=a

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