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 ?= 0.350 rad/s and ?= 1.20×10?2 rad/s3. 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. B) What is the initial value of the angular velocity? C) Calculate the instantaneous value of the angular velocity ?z at t= 5.20 s . D) Calculate the average angular velocity ?av?z for the time interval t=0 to t= 5.20 s .

Explanation / Answer

part a )

w = dtheta/dt = y + 3*Bt^2

part b )

initially t = 0

w = y = 0.350 rad/s

part c )

instantaneous velocity at t = 5.20

w = y + 3*B(5.20)^2

w = 1.32 rad/s

part d )

wavg = average angular displacement / time

wavg = (0.350 * 5.20 + 1.20 *10^-2 * (5.20)^3) / 5.20

wavg = 0.674 rad/s

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