ProblemSet 2: Problem 5.Problem:A lighthouse keeper’s son enjoys sliding down the spiral staircase railing from the light tothe ground floor. His path is a spiral of constant radius,R. The cylindrical coordinates of his positionas measured from the top of the staircase arer=R,θ=Ωtandz=−wt, wheretis time,Ωis hisangular rotation rate andwis his vertical speed. BothΩandware constant. Determine his velocityand acceleration components. If his speed along the railing is54w, what is his angular-rotation rate?Solution:Because the stairway has cylindrical symmetry and motion occurs at constant radiusr=R, wecompute the velocity-vector components by differentiating as follows.
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