Analytical Mech Homework Solutions 61

Analytical Mech - Collecting terms and neglecting terms in 2 g g x x cos t y y sin t = 0 l l g g x x sin t y y cos t = 0 l l 24 hours sin 24 T= =

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Collecting terms and neglecting terms in 2 ω : cos sin 0 gg xx tyy t ll ωω   ′′ ++ +     ±± = sin cos 0 x xt y y t +− + = 5.21 24 sin T λ = hours 24 73.7 sin19 T == D hours 5.22 Choose a coordinate system with the origin at the center of the wheel, the x and axes pointing toward fixed points on the rim of the wheel, and the axis pointing toward the center of curvature of the track. Take the initial position of the y z x axis to be horizontal in the V D G direction, so the initial position of the y axis is vertical. The bicycle wheel is rotating with angular velocity V about its axis, so … b D ˆ l V k b = D G A unit vector in the vertical direction is: ˆˆ ˆ sin cos Vt ni j bb =+ DD At the instant a point on the rim of the wheel reaches its highest point: ˆ sin cos rb nb i j  +   G Since the coordinate system is moving with the wheel, every point on the rim is
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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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