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+ βt^{3}, where γ = 0.406 rad/s and β = 1.30×10^{−2} rad/s^{3}.

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 ω_{z} at t = 5.05 s .

d) Calculate the average angular velocity ω_{av - z} for the time interval t = 0 to t = 5.05 s .

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 ω

d) Calculate the average angular velocity ω

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