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Analytical Mech Homework Solutions 169

Analytical Mech Homework Solutions 169 - 6 11.9 From...

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6 11.9 From Problem 11.5, V m ( ) 0 g b a ′′ = ( ) 0 V g b a m ω ′′ = = ( ) 0 2 2 T g b a π π ω = = 11.10 From Problem 11.7, ( )( 0 3 5 8 mg b b a ′′= + ) a V a ( )( ) 0 0 2 2 4 3 5 m a T g a b b a V π π = = + ′′ 11.11 2 2 1 1 2 2 cm T mv I ϕ = + ± a b φ θ ( ) cm v b a θ = ± 2 2 5 I ma = The relationship between the angles, and θ ϕ (see Figure), can be determined from the condition that there is no slipping as the ball rolls in the hemisphere, so the length of roll measured along the ball, ( a ) θ ϕ + , must equal the length of roll measured along the hemisphere,
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