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Analytical Mech Homework Solutions 61

Analytical Mech Homework Solutions 61 - Collecting terms...

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Collecting terms and neglecting terms in 2 ω : cos sin 0 g g x x t y y t l l ω ω + + + ±± ±± = sin cos 0 g g x x t y y t l l ω ω + + ±± ±± = 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 ω = D G A unit vector in the vertical direction is: ˆ ˆ ˆ sin cos V t V t n i j b b = + D D At the instant a point on the rim of the wheel reaches its highest point: ˆ ˆ ˆ sin cos V t V t r bn b i j b b = = + D D G Since the coordinate system is moving with the wheel, every point on the rim is
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