Question

Q3 At a given instant, the merry-go-round is rotating with an angular velocity w = 20 rpm while the child is moving radially outward at a constant rate of 0.7 m/s. Assuming that the angular velocity of the merry-go- round remains constant, i.e.. = 0, determine the magnitudes of the speed and of the acceleration of the child when he is 0.8 m away from the spin axis. 04. Determine the magnitude of the ag and ag at the instant t=2s, if a particle moves along a horizontal path defined by the equations r = 2 cos and 0 = t sint, where tis in seconds.

Answer 1

Given = 20 em v =0.7 m/s & = 0. 8m 20 8pm o to.7m/s 0.8m - there acts For boy moving tangential radially out velociby = sw. W= 20 epm - 21 (20) ead's. W = 2.09 ead's . V = 0.8 (2.09): 1672 m/s - Vees = √ (1.672) ² (0.77² - 1.81 m/s Similarly for components acceleration, we have two tangential & normal

ų = lx-o as x=0 an = {w² = 10.8) (9.09) ? = 3.49 m/s²

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