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 = 0.422 rad/s and = 1.45×102rad/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.

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Part B

What is the initial value of the angular velocity?

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Part C

Calculate the instantaneous value of the angular velocity z at t= 4.60 s .

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Part D

Calculate the average angular velocity avz for the time interval t=0 to t= 4.60 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 = 0.422 rad/s and = 1.45×102rad/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  

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Part B

What is the initial value of the angular velocity?

z =   rad/s  

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Part C

Calculate the instantaneous value of the angular velocity z at t= 4.60 s .

z =   rad/s  

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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) w(t) = gamma + (3 beta t2) rad/s

b)  w(t) = gamma + (3 beta t2)

gamma = 0.422 rad/s, beta = 0.0145 and t=0

w(t) = 0.422 + 0 = 0.422 rad/s

c) w(t) = 0.422 + (3 * 0.0145 * 4.62)

= 1.34 rad/s

d)  t = 0 to t = 4.60 s

( 0.422(4.6) + (0.0145*(4.63)) - 0) / (4.6 - 0)

= 0.73 rad/s

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