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# Solution: A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to θ(t)= γt+ βt3, where γ = 0.406 rad/s and β = 1.30×10−2 rad/s3.a) Calculate the angular velocity of the merry-go-round as a function of time.b) What is the initial value of the angular velocity?c) Calculate the instantaneous value of the angular velocity ωz at t = 5.05 s .d) Calculate the average angular velocity ωav - z for the time interval t = 0 to t = 5.05 s .

###### Problem
A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to θ(t)= γt+ βt3, where γ = 0.406 rad/s and β = 1.30×10−2 rad/s3.
a) Calculate the angular velocity of the merry-go-round as a function of time.
b) What is the initial value of the angular velocity?
c) Calculate the instantaneous value of the angular velocity ωz at t = 5.05 s .
d) Calculate the average angular velocity ωav - z for the time interval t = 0 to t = 5.05 s .