FM5002-HW5-2.22.12

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 01/19/2014 for the course MATH 5002 taught by Professor Adams during the Spring '08 term at Minnesota.

Ask a homework question - tutors are online