Analytical Mech Homework Solutions 115

Analytical Mech Homework Solutions 115 - 13 1212 mvcm + Iω...

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Unformatted text preview: 13 1212 mvcm + Iω + mgy = mgy 2 2 l l x = cos θ , x = − θ sin θ , 2 2 l l y = sin θ , y = θ cos θ , 2 2 x= l2 θ cos θ + θ sin θ 2 l y = −θ 2 sin θ + θ cos θ 2 ( ) ( 2 2 22 l l lθ 2 vcm = x 2 + y 2 = − θ sin θ + θ cosθ = 4 2 2 2 ml I= , and ω = θ 12 1 l 2θ 2 1 ml 2 2 l l m + θ + mg sin θ = mg sin θ 2 4 2 12 2 2 l2 θ = g ( sin θ − sin θ ) 3 1 3g 2 θ = ( sin θ − sin θ ) l − 1 1 3g 3g 2 3g θ = ( sin θ − sin θ ) ( − cos θ )θ = − cosθ 2 l 2l l ml 3g 3g N 2 = mx = − cos θ ( sin θ − sin θ ) + sin θ − cos θ 2 l 2l Separation occurs when N 2 = 0 : 1 2 sin θ − sin θ − sin θ = 0 , θ = sin −1 sin θ 2 3 8.18 Rx = mx Ry − mg = my l l l x = sin θ , x = θ cos θ , x = −θ 2 sin θ + θ cosθ 2 2 2 l l l y = cos θ , y = − θ sin θ , y = − θ 2 cos θ + θ sin θ 2 2 2 1212 l l mvcm + Iθ + mg cos θ = mg 2 2 2 2 2 ml l I= vcm = θ , 2 12 ( ) ( 13 ) ) ...
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

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