FM5002-HW5-2.22.12

# 0042 18 compute d x2 d x3 sec y z x x2 yz yz the

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Unformatted text preview: cribes the rate of turn in g of the wheel, followin g this n ew e rron eous design . let C be the circle of radius 10 about the fixed pin, with the parametrization that completes on e revolution aroun d C at a constan t speed of 20 Π. Compute Ω. C We follow the notation from the class slides. FM5002−HW5−2.22.12.nb x1 , where r yr R x, y x2 r y2 , so that Cos 10 y Cos Π 4 Sin Π 4 Then V x, y Sin Π 4 Cos Π 4 Cos Sin x1 yr Sin Cos Cos2 1 an d Sin Cos Sin 2 x 0. Cos 2 Sin 2 y Cos x Cos yCos 2 2r x Cos r y Cos Sin 2 x 9 Cos 2 Sin , 2r 2 2 r y Cos so that Ω x Cos y Cos dx x Cos 2r dy. 2r Since the speed is con stan t, we n ormalize it to 1 rotation in 2 Π time. Then C (t) = (10 Cos[t], 10 Sin[t]), so that x (t) = 10 Cos[t], y (t) = 10 Sin [t], dx = −10 Sin[t] dt, an d dy = 10 Cos[t] dt. Ω, we obtain Substitutin g this in formation in to C x y Cos Ω C C 2r 1 10 dx x y Cos xy dy C 2r r 10 x y dx 2r r 10 xy dy C 2r 10 2 2Π 10 Cos t 2 0 Sin t 10 Sin t 10 Cos t Sin t 10 Cos t dt 10 2 Π. dx x y 10 2 dy...
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## This note was uploaded on 01/19/2014 for the course MATH 5002 taught by Professor Adams during the Spring '08 term at Minnesota.

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