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EE101 HW1 - I2Noon EE 101;Homework DUE OCTOBER Thursday 1...

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EE 101; Homework 1: DUE OCTOBER 9rH Thursday I2Noon; (THERE WILL BE A COLLECTION BOX IN MARIKO WALTON'S CUBICLE ON THE 6TH FLOOR OF ENGR IV.) 1. Assume that there is a planet in space consists of only fluid enclosed by a spherical infinitesimally thin shell with radius R.. Further assume that all the mass of the planet is rotating with an angular frequency ro. Describe the linear velocity of the liquid vGp,il at anypoint (R,0,$) in the planet. {lui 2. Now assume an infinitesimal thin and small disk is floating in the planet. Because the linear velocity of the fluid at two sides of the disk will be different, the disk will rotate, as shown in the figure. Further assume that for some reason, the fluid doesn'trotate altogether anymore. Instead the linear velocity of the fluid within the planet becomes it^'''o> = g(Rsinfl'fi SinceCurl of a vector field measures the local circulation of the field, please rank the rotation extent of the disk floating at locations R ir --R 7T Ir, 4 (0, 0, 0) , Pr(+, 0,;) , and Pr (= ,:,:) '2' 3"-"" "',2 3 3' by computing
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