Lecture 11a - MMOI

# Lecture 11a - MMOI - Mass Moment of Inertia 2 I = r dm y dm...

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ES 11 ENGINEERING STATICS x y z O x z r dm + = + = + = = dm y x I dm z x I dm z y I dm r I z y x ) ( ) ( ) ( 2 2 2 2 2 2 2 Mass Moment of Inertia

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ES 11 ENGINEERING STATICS z z z y y y x x x + = + = + = ' ' ' x’ z x y O r dm G y’ z’ Parallel Axis Theorem
ES 11 ENGINEERING STATICS z x’ x y O r O’ y’ z’ y z x ' z ' y ' x Parallel Axis Theorem

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ES 11 ENGINEERING STATICS ) ( ) ( ' 2 ' 2 ) ' ' ( ] ) ' ( ) ' [( ) ( 2 2 2 2 2 2 2 2 2 2 ' z y m I dm z y dm z z dm y y dm z y dm z z y y dm z y I x x + + = + + + + + = + + + = + =
ES 11 ENGINEERING STATICS ) ( ) ( ) ( 2 2 2 2 2 2 ' ' ' y x m I I z x m I I z y m I I z z y y x x + + = + + = + + = 2 md I I + = REMEMBER:

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ES 11 ENGINEERING STATICS
ES 11 ENGINEERING STATICS

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ES 11 ENGINEERING STATICS
ES 11 ENGINEERING STATICS REMEMBER: I thin plate,mass = ρtI area

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ES 11 ENGINEERING STATICS t A’ A B’ B C’ C ) ( 12 1 12 1 ) 12 1 ( 12 1 ) 12 1 ( 2 2 ' ' ' 2 3 '. '. 2 3 '. '. b a m I I I mb ab t tI I ma b a t tI I BB AA CC Area BB mass BB Area AA mass AA + = + = = = = = = = ρ ρ ρ ρ
ES 11 ENGINEERING STATICS A’ A B B’ C C’ r 2 ' ' ' 2 4 '. '.

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