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Hwk12 prob A solution

Hwk12 prob A solution - Part 1 Define point C where the...

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Part 1 - Define point C where the spool contacts the floor. There, the spool has zero velocity and zero acceleration in the horizontal direction. Write the acceleration of point C relative to point A as: a C = a A + a C/A = a A – ω 2 r C/A + α x r C/A But r C/A = -5 j in, ω =6 rad/s and α = - 15 k rad/s 2 so a C = a A + (-75 i + 180 j ) in/s 2 . The i component of a C is zero due to rolling without slipping; and, by inspection of the figure, a A must be entirely in the i direction, so a A = 75 i in/s 2 which leaves a C = 180 j in/s 2 . Next, calculate a D relative to a A as follows: a D = a A + a D/A = a A – ω 2 r D/A + α x r D/A . Plugging in known values of a A, ω, and α , and noting that r D/A = -2 j in one can easily calculate a D = (45 i + 72 j ) in/s 2 . Likewise calculate a B relative to a A : a B = a A + a B/A = a A – ω 2 r B/A + α x r B/A . Plugging in known values of a A, ω, and α , and noting that r B/A = +5 j in one can easily compute a B = (150 i -180 j ) in/s 2 . Finally, a 0 of the rope is solved by inspection of the figure, no calculation required. It’s just the i
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