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Dynamics_Part17 - Problem Set 2 Problem 5 Problem A...

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Problem Set 2: Problem 5. Problem: A lighthouse keeper’s son enjoys sliding down the spiral staircase railing from the light to the ground floor. His path is a spiral of constant radius, R . The cylindrical coordinates of his position as measured from the top of the staircase are r = R , θ = t and z = wt , where t is time, is his angular rotation rate and w is his vertical speed. Both and w are constant. Determine his velocity and acceleration components. If his speed along the railing is 5 4 w , what is his angular-rotation rate? Solution: Because the stairway has cylindrical symmetry and motion occurs at constant radius r = R , we compute the velocity-vector components by differentiating as follows.
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