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 = 0.433 rad/s and =1.50×102 rad/s3.

1-

Calculate the angular velocity of the merry-go-round as a function of time.

Express your answer in terms of the variables , , and t.

2- Calculate the instantaneous value of the angular velocity z at t= 5.45 s .

3- Calculate the average angular velocity avz for the time interval t=0 to t= 5.45 s .

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 = 0.433 rad/s and =1.50×102 rad/s3.

1-

Calculate the angular velocity of the merry-go-round as a function of time.

Express your answer in terms of the variables , , and t.

2- Calculate the instantaneous value of the angular velocity z at t= 5.45 s .

3- Calculate the average angular velocity avz for the time interval t=0 to t= 5.45 s .

Explanation / Answer

1) angular velocity, w = d theta / dt

                       = +3t2   =0.433+0.045t2

2) w = 0.433+3*0.015*5.452 =1.77 rad/s

3) divide the value of theta by time interval

average angular velocity = delta theta / delt t

                            = t+t3 / t

                          = +t2

   =0.433 +0.015*5.452

= 0.879 rad/s

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