15_3_9 - 9. (0 t 2 ) v = - sin ti + cos tj + k, v = 2. If...

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9. r = cos t i + sin t j + t k , ( 0 t 2 π) v = - sin t i + cos t j + k , v = 2 . If the density is δ = z = t , then m = 2 Z 2 π 0 t dt = 2 π 2 2 M x = 0 = 2 Z 2 π 0 t cos t dt = 0 M y = 0 = 2 Z 2 π 0 t sin t dt = - 2 π 2 M z = 0 = 2 Z 2 π 0 t 2 dt = 8 π 3 2 3 . (We have omitted the details of the evaluation of these integrals.) The centre of mass is
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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