Answer to Question #187676 in Mechanical Engineering for prathna

Question #187676

The angular acceleration of an rotating body is define by the relation 𝔞 = - kθ. Determine a) the value of k if angular velocity is 8 rad/sec at angular displacement of 0 radian and angular velocity is 0 rad/sec at angular displacement of 4 radian. B) find the angular velocity at angular displacement of 3 radian.


1
Expert's answer
2021-05-05T07:45:07-0400

a) "\\alpha =-k\\theta"


"w\u00b2 = w_0\u00b2 +2\\alpha s"


"w_0\u00b2 = 8\\ rad\/s"

"0\u00b2 = 8\u00b2 +2\\alpha(4)\\\\\n\\alpha = -8 rad\/s\u00b2"


"-8= -k(0) \\quad --(i)\\\\\n-8 = -k(4) \\quad --(ii)\\\\"


"\\therefore k = 2\\ s^{-2}"



b) "w\u00b2 = w_0\u00b2 +2\\alpha s"


"w\u00b2=8\u00b2+2(-8)(3)\\\\\nw\u00b2 = 64 - 48\\\\\nw\u00b2 = 16\\\\\nw= 4\\ rads^{-1}"

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