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 = 0.389 rad/s and = 1.20×102 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

Part B

What is the initial value of the angular velocity?

Part C

Calculate the instantaneous value of the angular velocity z at t= 5.10 s .

Part D

Calculate the average angular velocity avz for the time interval t=0 to t= 5.10 s .

Explanation / Answer

angular velocity=time derivative of angular displacement

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

=0.389+3*1.2*0.01*t^2

=0.389+0.036*t^2

part B:
initial value of angular veloicty =angular velocity at t=0

=0.389 rad/sec

part C:

at t=5.1 seconds,

angular velocity=0.389+0.036*5.1^2=1.3254 rad/sec

part D:

average angular veloicty=total angular displacement/total time difference

=(angular displacement at 5.1 seconds-angular displacement at t=0)/5.1

=0.70122 rad/sec

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