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 = 0.450 rad/s and = 1.15×102 rad/s3.

Part A Calculate the angular velocity of the merry-go-round as a function of time. Express your answer in terms of the variables , , and t. z(t) = rad/s

Part B What is the initial value of the angular velocity? z = rad/s

Part C Calculate the instantaneous value of the angular velocity z at t= 4.60 s . z = rad/s

Part D Calculate the average angular velocity avz for the time interval t=0 to t= 4.60 s . avz = rad/s

Explanation / Answer

(A) theta = gamma t + beta t^3

w = d(theta)/dt = gamma + 3 beta t^2

(b) at t = 0

w = gamma = 0.450 rad/s

(C) w = (0.450) + (1.15 x 10^-2 x 4.60) = 1.18 rad/s

(d) theta(0) = 0

theta(4.60) = 3.189 rad

average velocity = displacement / time

= 3.189 / 4.60

= 0.693 rad /s

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