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: aC = aA+ aC/A= aA– ω2rC/A+ αx rC/ABut rC/A= -5jin, ω =6 rad/s and α= -15krad/s2so aC= aA+ (-75i+ 180j) in/s2.The icomponent of aCis zero due to rolling without slipping; and, by inspection of the figure, aA must be entirely in the idirection, so aA= 75iin/s2which leaves aC= 180jin/s2.Next, calculate aDrelative to aAas follows: aD= aA+ aD/A= aA– ω2rD/A+ αx rD/A. Plugging in known values of aA, ω, and α, and noting that rD/A= -2jin one can easily calculate aD= (45i+ 72j) in/s2.Likewise calculate aBrelative to aA: aB= aA+ aB/A= aA– ω2rB/A+ αx rB/A. Plugging in known values of aA, ω, and α, and noting that rB/A= +5jin one can easily compute aB= (150i-180j) in/s2.Finally, a0of the rope is solved by inspection of the figure, no calculation required. It’s just the i
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