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CALC A child is pushing a merry-go-round. The angle
Chapter 11, Problem 5E(choose chapter or problem)
CALC 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 ? = 0.400 rad/s and ? = 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 ?z at t = 5.00 s and the average angular velocity ?av-z for the time interval t = 0 to t = 5.00 s. Show that ?av-z is not equal to the average of the instantaneous angular velocities at t = 0 and t = 5.00 s, and explain.
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QUESTION:
CALC 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 ? = 0.400 rad/s and ? = 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 ?z at t = 5.00 s and the average angular velocity ?av-z for the time interval t = 0 to t = 5.00 s. Show that ?av-z is not equal to the average of the instantaneous angular velocities at t = 0 and t = 5.00 s, and explain.
ANSWER:Solution 5E Angular velocity is the rate of change of angular displacement. Therefore, angular velocity = AngularTimeplaceme…..(1) Given that, (t) =t + t , where = 0.400 rad/s and = 0.0120 rad/s 3 (a) We can calculate the angular velocity as a function of time. This is done as follows. 3 Differentiating (t) =t + t wrt time, d(t) dt = + 3t 2 (t) = + 3t …..(2) This is the required expression for angular velocity as a function of time. (b) The initial value of angular velocity is giv