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Analytical Mech Homework Solutions 167

Analytical Mech Homework Solutions 167 - 4 V = mg a sin b...

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4 [ ] sin cos V mg a b θ θ θ ′= + [ ] cos sin cos V mg b b a θ θ θ θ ′′= ( ) 0 V mg b a ′′ = Equilibrium … Stable Unstable a b < a b > 11.6 2 4 cos 1 ... 2! 4! θ θ θ = − + 3 5 sin ... 3! 5! θ θ θ θ = + ( ) 2 4 3 5 1 ... ... 2! 4! 3! 5! V mg a b b θ θ θ θ θ θ = + + + + 2 4 3 ... 2 24 a b a b V mg a b θ θ = + + For a = b, 4 2 ... 12 a g a θ = V m + 3 ... 3 mga V θ ′=− + terms in higher order of θ 2 ... V mga θ ′′=− + 2 ... V mga θ ′′′=− + 2 0 V mga ′′′′=− < Equilibrium is unstable 11.7 The center of mass (CM) of the hemisphere is
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