144_Problem CHAPTER 9 - PROBLEM 9.119 A thin plate of mass...

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PROBLEM 9.119 A thin plate of mass m has the trapezoidal shape shown. Determine the mass moment of inertia of the plate with respect to ( a ) the x axis, ( b ) the y axis. SOLUTION First note mass m V tA ρ ρ = = = ( )( ) ( )( ) 1 2 2 2 t a a a a ρ = + 2 3 ta ρ = Also mass area I tI ρ = area 2 3 m I a = ( a ) Now ( ) ( ) , area 1, area 2, area x x x I I I = + ( )( ) ( )( ) 3 3 1 1 2 2 3 12 a a a a = + 4 5 6 a = Then 4 , mass 2 5 6 3 x m I a a = × 2
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