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Analytical Mech Homework Solutions 118

Analytical Mech Homework Solutions 118 - 16 a a 2b 2b a b...

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16 so that ( ) ( ) 2 2 a b a b α φ = and + + ( ) ( ) 2 2 a a b b a b α β + = + After some algebra … the angular velocity of B is found to be … 2 B a b α ω β α φ = + = ± ± ± ± For , we take moments about O and for A B we take moments about its center. Call T and T the components of the reaction forces tangent to and A B A B (the “upward-going” T acts on disk A B . The “downward-going” acts on disk A) A T Thus K T A A a I α = ±± (Torque on Disk A) ( ) 2 A B B B T b T b I I a b α β α φ = − + = − ±± ±± ±± ±± (Torque on Disk B) ( ) ( ) 1 2 A B B B T T M a b M a α φ = + = ±± ±± ±± α (Force on Disk B) Eliminate T and A B T ( ) 2 2 2 2 4 4 A B B K b I M a b a b 2 I α = +
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