Chapter 9, Problem 9.5E

CALC 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 = 0.400 rad/s and β = 0.0120 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 ω_z at t = 5.00 s and the average angular velocity ω_v−z for the time interval t = 0 to t = 5.00 s. Show that ω_av−z is not equal to the average of the instantaneous angular velocities at t = 0 and t = 5.00 s, and explain.