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ECS221L27

# ECS221L27 - y I 2 2 x 29 m z y I I 2 2 x x ′ = 29 29 m y...

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Mass Moments of Inertia The inertia characterized by the mass (m) tends to resist linear motion. The moment of inertia characterized by the mass moment of inertia (I) tends to resist rotational motion.

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Mass Rotating About Axis The applied moment is proportional to the angular acceleration M = I α. For this problem, I = mr 2 and resistance to rotation depends on m as well as r (distribution). m r
The Continuous Body For a distributed mass, The radius of gyration k follows from the equivalence I = k 2 m dm r I 2 = m k

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General Forms I x , I y , I z x y z m r ( 29 ( 29 ( 29 dm y x I dm z x I dm z y I 2 2 z 2 2 y 2 2 x + = + = + =
Parallel Axis Theorem ( ) locates CG and is known x x y z O x’ y’ z’ C y z m z , y , x z z z y y y x x x + = + = + = ( 29 + = dm z y I 2 2

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Unformatted text preview: y I 2 2 x ( 29 m z y I I 2 2 x x + + ′ = ( 29 ( 29 m y x I I and m z x I I similiarly 2 2 z z 2 2 y y + + ′ = + + ′ = … more Recall Note is square of distance between x and x’ axes. Let d be this distance. Then Parallel Axis Theorem ( 29 m z y I I 2 2 x x + + ′ = x x y z O x’ y’ z’ C y z ∆ m ( 29 2 2 z y + m d I I 2 + = Thin Uniform Plate ∆ m = ρ t ∆ A, ρ ,t const. I A is second moment of area. Similarly, J 0 is polar moment of inertia A 2 2 I t dA r t dm r I ρ ρ = ∫ = ∫ = 2 2 J t dA r t dm r I ρ ρ = ∫ = ∫ = x y z ∆ m r...
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ECS221L27 - y I 2 2 x 29 m z y I I 2 2 x x ′ = 29 29 m y...

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