A child is pushing a merrygoround The angle through which th

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 = 0.439 rad/s and = 1.40×10² 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-What is the initial value of the angular velocity?

Part C

Calculate the instantaneous value of the angular velocity z at t= 5.35 s .

Part D

Calculate the average angular velocity avz for the time interval t=0 to t= 5.35 s .

Solution

angular velocity = w (t)

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

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w₀ occur when t = 0

w (t)  = (gamma) + (3 * beta * t²)

gamma = 0.439, beta = 0.014 and t = 0

0.439 + (0) = 0.439 rad/s

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w(5.35) = 0.439 + (3 * 0.014 * 5.35²)

= 1.64 rad/s

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t = 0 to t = 5.35 seconds

( theta(5.35) - theta(0)) / ( 5.35 - 0 )

(0.439(5.35) + 0.014*(5.35³) ) ) / (5.35 - 0)

= 0.84 rad/s