410ahw6soln - HW#6Solutions Phys410Fall 2011

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HW#6—Solutions —Phys410—Fall 2011 Prof. Ted Jacobson Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/410a/ jacobson@umd.edu 9.2 ( artificial gravity in rotating space station ) (a) Force of floor and acceleration both radial inward. (b) No acceleration, floor force radial inward, centrifugal force radial outward. (c) ω = p g/R = 0 . 5 rad/s 2 = 4.77 rpm. (d) Δ g eff /g eff = Δ R/R = 0 . 05, i.e. 5%. 9.7 ( derivative of vector in rotating frame ) (a) The vector simply rotates along with the angular velocity of the frame. (b) The vector rotates opposite to S in order to remain constant in S 0 . 9.8 ( direction of centrifugal and Coriolis forces ) (a) Moving S near pole: centrifugal S and slightly up, Coriolis W. (b) Moving E on equator: centrifugal up, Coriolis up. (c) Moving S across equator: centrifugal up, Coriolis zero. 9.11 ( Lagrangian in rotating frame and equations of motion ) vector method : Consider just the kinetic part of the Lagrangian, L = 1 2 mv 2 0 . Given v 0 = v + Ω × r , we have v 0 · v 0 = v · v + 2 v · × r ) + ( Ω × r ) · ( Ω × r ). For the derivatives with respect to the vector components of v and r I will use a vector
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410ahw6soln - HW#6Solutions Phys410Fall 2011

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