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Analytical Mech Homework Solutions 115

# Analytical Mech Homework Solutions 115 - 13 1212 mvcm I mgy...

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13 2 2 1 1 2 2 cm mv I mgy mgy ω + + = D cos 2 l x θ = , sin 2 l x θ θ ± ± = − , ( ) 2 cos sin 2 l x θ θ θ θ = + ± ±± ±± sin 2 l y θ = , cos 2 l y θ θ ± ± = , ( ) 2 sin cos 2 l y θ θ θ θ = + ± ±± ±± 2 2 2 2 2 2 2 sin cos 2 2 cm l l v x y 4 l θ θ θ θ θ = + = + = ± ± ± ± ± 2 12 ml I = , and ω θ = ± 2 2 2 2 1 1 sin sin 2 4 2 12 2 2 l ml l l m mg m θ g θ θ θ + + = D ± ± ( ) 2 sin sin 3 l g θ θ θ = D ± ( ) 1 2 3 sin sin g l θ θ = D ± θ ( ) ( ) 1 2 1 3 3 3 sin sin cos cos 2 2 g g l l g l θ θ θ θ θ = = − D ±± ± θ ( ) 2 3 3 cos sin sin sin cos 2 2 ml g g N mx l l θ θ θ θ = = − + D ±± θ Separation occurs when 2 0 N = : 1 sin sin sin 0 2 θ θ θ = D , 1 2 sin sin 3 θ θ =
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