One of the children on the merry-go-round is not holding on tight enough. If the radius of the merry-go-round is 1.3m, and the child falls off the edge at the maximum velocity of 11 rad/s, what is his new linear (tangential) velocity?
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To convert from angular to tangential velocity just multiply by the radius.
11*1.3 = 14.3m/s
11*1.3 = 14.3m/s
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His linear velocity after he lets go will equal his tangential velocity before he lets go:
v = ωr = (11 s^-1)(1.3 m) = 14.3 m/s
v = ωr = (11 s^-1)(1.3 m) = 14.3 m/s