A child is pushing a merry-go-round. The angle through which the merry-go-round

Question

A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to ?(t)=?t+?t3, where ?= 0.361 rad/s and ?= 1.45*10^-2 rad/s3 A) Calculate the angular velocity of the merry-go-round as a function of time. B) Express your answer in terms of the variables ?, ?, and t. C) What is the initial value of the angular velocity? D) Calculate the instantaneous value of the angular velocity ?z at t= 5.15s . E) Calculate the average angular velocity ?av?z for the time interval t=0 to t= 5.15s .

Explanation / Answer

given theta(t) = A*t + Bt^2

anguale velocity w = (dtheta/dt)

w = A + 2*Bt

+++++++++++++++++

(b)

w = 0.361 + 2.9*10^-2t

______

(c)

at time t = 0

w = 0.361 rad/s <<<-------answer

_______

(d)

at time t = 5.15 s

w = 0.361 + (2.9*10^-2*5.15)

w = 0.51 rad/s

(e)

at time t1 = 0

theta1 = 0

at time t2 = 5.15 s

theta2 = (0.361*5.5) + (1.45*10^-2*5.15^2) = 2.37 rad

angular velocity = (theta2-theta1)/(t2-t1) = 2.37/5.15 = 0.46 rad/s

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